Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal (...) use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor-immune system to design an optimal chemotherapy strategy. For this, we first propose a mathematical (...) model of tumor-immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman equation. Here, we use an upwind finite-difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects. (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) (...) stable solutions. Inspired by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

The hybridization of two or more energy sources into a single power station is one of the widely discussed solutions to address the demand and supply havoc generated by renewable production, heating power, and cooling power) and its energy storage issues. Hybrid energy sources work based on the complementary existence of renewable sources. The combined cooling, heating, and power is one of the significant systems and shows a profit from its low environmental impact, high energy efficiency, low economic investment, (...) and sustainability in the industry. This paper presents an economic model of a microgrid system containing the CCHP system and energy storage considering the energy coupling and conversion characteristics, the effective characteristics of each microsource, and energy storage unit is proposed. The random forest regression model was optimized by the gravitational search algorithm. The test results show that the GSA-RFR model improves prediction accuracy and reduces the generalization error. The detail of the MG network and the energy storage architecture connected to the other renewable energy sources is discussed. The mathematical formulation of energy coupling and energy flow of the MG network including wind turbines, photovoltaic, CCHP system, fuel cell, and energy storage devices are presented. The testing system has been analysed under load peak cutting and valley filling of energy utilization index, energy utilization rate, the heat pump, the natural gas consumption of the microgas turbine, and the energy storage unit. The energy efficiency costs were observed as 88.2% and 86.9% with heat pump and energy storage operation comparing with GSA-RFR-based operation costs as 93.2% and 93% in summer and winter season, respectively. The simulation results extended the rationality and economy of the proposed model. (shrink)

We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...) From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle. (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a noncircular justification of the optimality of induction, or, more precisely, of meta-induction (...) (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

In the first section, five major attempts to solve the problem of induction and their failures are discussed. In the second section, an account of meta-induction is introduced. It offers a novel solution to the problem of induction, based on mathematical theorems about the predictive optimality of attractivity-weighted meta-induction. In the third section, how the a priori justification of meta-induction provides a non-circular a posteriori justification of object-induction, based on its superior track record, is explained. In the fourth section, four (...) important extensions and refinements of the method of meta-induction are presented. The final section, summarizes the major impacts of the program of meta-induction for epistemology, the philosophy of science and cognitive science. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

We prove that for any computable successor ordinal of the form α = δ + 2k there exists computable torsion-free abelian group that is relatively Δα0 -categorical and not Δα−10 -categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σαc infinitary computable formulae up to automorphism, and there is no syntactically simpler family of formulae that would capture these orbits. As far as we know, the problem of finding such optimal (...) examples of Δα0-categorical TFAGs for arbitrarily large α was first raised by Goncharov at least 10 years ago, but it has resisted solution 315–356]). As a byproduct of the proof, we introduce an effective functor that transforms a 0″-computable worthy labeled tree into a computable TFAG. We expect that this techni... (shrink)

We propose a new notion of coalitional equilibria, the strong $$\beta$$ -hybrid solution, which is a refinement of the hybrid solution introduced by Zhao. Zhao’s solution is well suited to study situations where people cooperate within coalitions but where coalitions compete with one another. This paper’s solution, as opposed to the hybrid solution, assigns to each coalition a strategy profile that is strongly Pareto optimal. Moreover, like the $$\beta$$ -core, deviations by subcoalitions of any existing coalition are deterred by (...) the threat of a unique counter-strategy available to the non-deviating players. Zhao proved the existence of existence of strong $$\beta$$ -hybrid solution for transferable utility games with compact and convex strategy spaces and concave continuous payoff functions. Here, we extend his result to non-transferable utility games. (shrink)

Hybrid renewable energy system arises regularly in real life. By optimizing the capacity and running status of the microgrid, HRES can decrease the running cost and improve the efficiency. Such an optimization problem is generally a constrained mixed-integer programming problem, which is usually solved by linear programming method. However, as more and more devices are added into MG, the mathematical model of HRES refers to nonlinear, in which the traditional method is incapable to solve. To address this issue, we first (...) proposed the mathematical model of an HRES. Then, a coevolutionary multiobjective optimization algorithm, termed CMOEA-c, is proposed to handle the nonlinear part and the constraints. By considering the constraints and the objective values simultaneously, CMOEA-c can easily jump out of the local optimal solution and obtain satisfactory results. Experimental results show that, compared to other state-of-the-art methods, the proposed algorithm is competitive in solving HRES problems. (shrink)

Presently, most studies focus on the minimization of the costs and negative social effects of the location of construction waste recycling centers; however, the influence of the location on future operation is usually ignored. Aiming at solving these problems, a location model for the maximization of service reliability was devised. Service reliability includes the recycling reliability of the construction waste and the delivery reliability of the recycled product. Through maximizing service reliability, the location deviation as a result of arrival delay (...) is expected to be reduced and the service reliability improved. Then, two important parameters in our model were solved on the basis of correlative mathematical theories. Finally, an example was implemented to verify our location optimization model. A genetic algorithm was used to obtain optimal solutions, and the solutions were analyzed. Through establishing a location optimization model, a possible better solution to location problems may be obtained to help in implementing location selection for recycling centers. (shrink)

The science of operations research is one of the modern sciences that have made a great revolution in all areas of life through the methods provided by it, suitable and appropriate to solve most of the problems that were facing researchers, scholars and those interested in the development of societies, and the most beneficiaries of this science were companies and institutions that are looking for scientific methods that help them manage their work so that they achieve the greatest profit and (...) the lowest cost, and one of the important methods that have been used in the management of companies we offer in this research two methods, Dynamic programming method. This method has been used in many practical matters and helped decision-makers in companies to achieve a maximum profit and less cost by formulating the reality of the state of the company and the data provided by decision-makers with a dynamic mathematical model that is solved using methods of solving dynamic models and we will provide in this research an example of this through the issue of choosing the optimal investment for the budget of a company so that it achieves a maximum profit, and the method of programming with integers: the method that provided these companies with solutions with integer values suitable for the nature of its work, through the use of the binary integer in the formulation of the appropriate mathematical model on the one hand, and on the other hand, the use of the binary integer variable helped to convert some nonlinear models that lead to some practical problems into linear models, and it should be noted here that in the previous two methods there is something indeterminable because we must make a decision in choosing or not choosing something, but the optimal solution that we will get remains A specific value because we are building the mathematical model for any realistic issue through the data provided by those responsible for the work and these data are calculated quantities and therefore they are uncertain values because their validity depends on the circumstances surrounding the work environment, they may be exposed to increase or decrease, and therefore the optimal solution on which the company will base its decision is suitable for specific values and any change in them can cause the company an uncalculated loss, so in this research we will use the concepts of neutrosophic science, the branch of science founded by the American scientist Florentin Smarandache in 1995 based on his belief that there is no absolute truth, a science that is interested in the study of ideas and concepts that are neither true nor false, but just in between, and we will take the data (calculated quantities) neutrosophic values that are specified or unspecified values are any set close to the calculated quantities, then the resulting mathematical model is a neutrosophic model and the optimal solution has neutrosophic values and thanks to the indefinite uncertainty that these values have, companies from the development of appropriate plans for all circumstances and thus achieve the greatest profit and the lowest cost, and we will clarify the above through two issues, the issue of optimal designation of a warehouse site, which we will formulate the mathematical model of using the neutrosophic integer programming method - and the issue of capital budget, which we will present in two different forms, we use in the first form the neutrosophic integer programming method and in the second the neutrosophic dynamic programming method. (shrink)

The question “How can humans learn efficiently to make decisions in a complex, dynamic, and uncertain environment” is still a very open question. We investigate what effects arise when feedback is given in a computer-simulated microworld that is controlled by participants. This has a direct impact on training simulators that are already in standard use in many professions, e.g., for flight simulators for pilots, and a potential impact on a better understanding of human decision making in general. Our study is (...) based on a benchmark microworld with an economic framing, the IWR Tailorshop. N=94 participants played four rounds of the microworld, each 10 months, via a web interface. We propose a new approach to quantify performance and learning, which is based on a mathematical model of the microworld and optimization. Six participant groups receive different kinds of feedback in a training phase, then results in a performance phase without feedback are analyzed. As a main result, feedback of optimal solutions in training rounds improved model knowledge, early learning, and performance, especially when this information is encoded in a graphical representation. (shrink)

Architecture often relies on mathematical models, if only to anticipate the physical behavior of structures. Accordingly, mathematical modeling serves to find an optimal form given certain constraints, constraints themselves translated into a language which must be homogeneous to that of the model in order for resolution to be possible. Traditional modeling tied to design and architecture thus appears linked to a topdown vision of creation, of the modernist, voluntarist and uniformly normative type, because usually (mono)functionalist. One available instrument of (...) calculation/representation/prescription orders this conception of architecture: indeed the search for an optimal solution through mathematical calculation of a model itself mathematical, thus homogeneous and simple, is only possible when one or two functions or functional constraints are formulated, never more, and this, on a global level, therefore starting from a unique and homogenizing viewpoint. It is essential to grasp that, even applied to material and its properties or towards a particular esthetic or functional dimension, this viewpoint is thus abstractive and generalizing: disregarding singularity of context, insertion and relationship to the environment or local, social behavior. It leaves aside functional specificity and heterogeneousness – re-contextualized each time – of functions that the object or edifice are required to fulfill and optimize under diverse constraints, in their different parts. The computational turning point today’s digital design and computational architecture embody modifies these instrumental, original prescriptions, rendering them more flexible. Perhaps in light of this turnabout we should retrospectively interpret 20th century calls for modernism, functionalism and even biomorphism as being just as many ex post rationalizations in respect to techniques of strongly prescriptive modeling since our only instrument is a monolithic language, and so being, incites a top-down conception, (naturally weakly reactive to contexts), including forms whose overall appearance resembles in fine a living form. In order to liberate oneself from this and despite everything, emerge as its initiators, one has constructed from ideology and philosophy (of object, habitat, the urban) ex post, even while it is the instrument of modeling and conception that largely determines, normalizes and dictates ex ante, the possibilities and limitations of the creation of forms and living experiments4 in a given time. (shrink)

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. (...) The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers. (shrink)

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the (...) issue under study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

Let us start by some general definitions of the concept of complexity. We take a complex system to be one composed by a large number of parts, and whose properties are not fully explained by an understanding of its components parts. Studies of complex systems recognized the importance of “wholeness”, defined as problems of organization (and of regulation), phenomena non resolvable into local events, dynamics interactions in the difference of behaviour of parts when isolated or in higher configuration, etc., in (...) short, systems of various orders (or levels) not understandable by investigation of their respective parts in isolation. In a complex system it is essential to distinguish between ‘global’ and ‘local’ properties. Theoretical physicists in the last two decades have discovered that the collective behaviour of a macro-system, i.e. a system composed of many objects, does not change qualitatively when the behaviour of single components are modified slightly. Conversely, it has been also found that the behaviour of single components does change when the overall behaviour of the system is modified. There are many universal classes which describe the collective behaviour of the system, and each class has its own characteristics; the universal classes do not change when we perturb the system. The most interesting and rewarding work consists in finding these universal classes and in spelling out their properties. This conception has been followed in studies done in the last twenty years on second order phase transitions. The objective, which has been mostly achieved, was to classify all possible types of phase transitions in different universality classes and to compute the parameters that control the behaviour of the system near the transition (or critical or bifurcation) point as a function of the universality class. This point of view is not very different from the one expressed by Thom in the introduction of Structural Stability and Morphogenesis (1975). It differs from Thom’s program because there is no a priori idea of the mathematical framework which should be used. Indeed Thom considers only a restricted class of models (ordinary differential equations in low dimensional spaces) while we do not have any prejudice regarding which models should be accepted. One of the most interesting and surprising results obtained by studying complex systems is the possibility of classifying the configurations of the system taxonomically. It is well-known that a well founded taxonomy is possible only if the objects we want to classify have some unique properties, i.e. species may be introduced in an objective way only if it is impossible to go continuously from one specie to another; in a more mathematical language, we say that objects must have the property of ultrametricity. More precisely, it was discovered that there are conditions under which a class of complex systems may only exist in configurations that have the ultrametricity property and consequently they can be classified in a hierarchical way. Indeed, it has been found that only this ultrametricity property is shared by the near-optimal solutions of many optimization problems of complex functions, i.e. corrugated landscapes in Kauffman’s language. These results are derived from the study of spin glass model, but they have wider implications. It is possible that the kind of structures that arise in these cases is present in many other apparently unrelated problems. Before to go on with our considerations, we have to pick in mind two main complementary ideas about complexity. (i) According to the prevalent and usual point of view, the essence of complex systems lies in the emergence of complex structures from the non-linear interaction of many simple elements that obey simple rules. Typically, these rules consist of 0–1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. Quite intricate patterns and structures can occur in such systems. However, what can be also said is that these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. (ii) So, this bring a new aspect that seems essential and indispensable to the emergence and functioning of complex systems, namely the coordination of individual agents or elements that themselves are complex at their own scale of operation. This coordination dramatically reduces the degree of freedom of those participating agents. Even the constituents of molecules, i.e. the atoms, are rather complicated conglomerations of subatomic particles, perhaps ultimately excitations of patterns of superstrings. Genes, the elementary biochemical coding units, are very complex macromolecular strings, as are the metabolic units, the proteins. Neurons, the basic elements of cognitive networks, themselves are cells. In those mentioned and in other complex systems, it is an important feature that the potential complexity of the behaviour of the individual agents gets dramatically simplified through the global interactions within the system. The individual degrees of freedom are drastically reduced, or, in a more formal terminology, the factual space of the system is much smaller than the product of the state space of the individual elements. That is one key aspect. The other one is that on this basis, that is utilizing the coordination between the activities of its members, the system then becomes able to develop and express a coherent structure at a higher level, that is, an emergent behaviour (and emergent properties) that transcends what each element is individually capable of. (shrink)

The primary method by which science endeavors to order the world is the analytic approach, consistent with Cartesian principles of dividing the problem in as many sections as required for an optimal solution, and progressing from the simplest to the most complex reasoning. When the interactions among the various elements of the system being studied are minimal, such a procedure indeed makes it possible to formulate laws that describe chains of causality. However, when the variables are interdependent and linked (...) by non-linear equations, the atomistic method cannot account for the phenomenon in its entirety. Spurred by this inadequacy, scientists sought to discover synthetic methods which, early in the twentieth century, led to the conceptualization of holistic theories in a number of disciplines. The most highly developed fields are the psychology of form, structural anthropology (1), and the various systems theories (2). More recently, the development of epigenetic concepts in biology has corresponded to the appearance of different theories of pattern in physics and mathematics (3, 4) and to the progressive emergence of the concept of self-organization (5, 6, 7). The objective is to explain the production of complex structures on the basis of interacting elements, none of which contains a guiding scheme that dictates these structures. In biology, the challenge is to locate the constraints that are expressed in a space of possibilities (8) in order to develop a theory of organization that is capable of predicting the finite number of forms that living creatures can assume (9). This school of thought can be described as structuralist, emergentist, self-organizational, or epigeneticist, depending on the theoretical version that is emphasized. (shrink)

Open Shop Scheduling Problem is one of the most important scheduling problems in the field of engineering and industry. This kind of problem includes m machines and n jobs, each job contains a certain number of operations, and each operation has a predetermined processing time on its corresponding machine. The order of processing of these operations affects the completion times of all jobs. Therefore, the purpose of OSSP is to achieve a proper order of processing of jobs using specified machines, (...) so that the completion time of all jobs is minimized. In this paper, the strengths and limitations of three methods are evaluated by comparing the results of solving the OSSP in large-scale and small-scale benchmarks. In this case, the minimized completion time and total tardiness are considered the objective functions of the adapted methods. To solve small-scale problems, we adapt a mathematical model called Multiobjective Mixed Linear Programming. To solve large-scale problems, two metaheuristic algorithms including Multiobjective Parallel Genetic Algorithm and Multiobjective Parallel Simulated Annealing are adapted. In experimental results, we randomly generated small-scale problems to compare MOMILP with the Genetic Algorithm and Simulate Annealing. To compare MOPSA and MOPGA with the state of the art and show their strengths and limitations, we use a standard large-scale benchmark. The simulation results of the proposed algorithms show that although the MOPSA algorithm is faster, the MOPGA algorithm is more efficient in achieving optimal solutions for large-scale problems compared with other methods. (shrink)

Due to the NP-hard nature, the permutation flowshop scheduling problem is a fundamental issue for Industry 4.0, especially under higher productivity, efficiency, and self-managing systems. This paper proposes an improved genetic-shuffled frog-leaping algorithm to solve the permutation flowshop scheduling problem. In the proposed IGSFLA, the optimal initial frog in the initialized group is generated according to the heuristic optimal-insert method with fitness constrain. The crossover mechanism is applied to both the subgroup and the global group to avoid the (...) local optimal solutions and accelerate the evolution. To evolve the frogs with the same optimal fitness more outstanding, the disturbance mechanism is applied to obtain the optimal frog of the whole group at the initialization step and the optimal frog of the subgroup at the searching step. The mathematical model of PFSSP is established with the minimum production cycle as the objective function, the fitness of frog is given, and the IGSFLA-based PFSSP is proposed. Experimental results have been given and analyzed, showing that IGSFLA not only provides the optimal scheduling performance but also converges effectively. (shrink)

This paper reconstructs the history of the introduction and use of iterative algorithms in conservation biology in the 1980s and early 1990s in order to prioritize areas for protection as nature reserves. The importance of these algorithms was that they led to greater economy in spatial extent (“efficiency”) in the selection of areas to represent biological features adequately (that is, to a specified level) compared to older methods of scoring and ranking areas using criteria such as biotic “richness” (the number (...) of features of interest). The development of these algorithms was critical to producing a research program for conservation biology that was distinct from ecology and eventually led to what came to be called systematic conservation planning. Very similar algorithmic approaches were introduced independently in the 1980–1990 period in Australia, South Africa, and (arguably) the United Kingdom. The key rules in these algorithms were the use of rarity and what came to be called complementarity (the number of new or under-represented features in an area relative to those that had already been selected). Because these algorithms were heuristic, they were not guaranteed to produce optimal (most “efficient”) solutions. However, complementarity came to be seen as a principle rather than a rule in an algorithm and its use was also advocated for the former reason. Optimal solutions could be produced by reformulating the reserve selection problem in a mathematical programming formalism and using exact algorithms developed in that context. A dispute over the relevance of full optimality arose and was never resolved. Moreover, exact algorithms could not easily incorporate criteria determining the spatial configuration of networks of selected areas, in contrast to heuristic algorithms. Meanwhile metaheuristic algorithms emerged in the 1990s and came to be seen as a credible more effective alternative to the heuristic algorithms. Ultimately what was important about these developments was that the reserve selection problem came to be viewed a complex optimal decision problem under uncertainty, resource, and other constraints. It was a type of problem that had no antecedent in traditional ecology. (shrink)

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the (...) practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities. (shrink)

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an (...) endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. (shrink)

The travelling salesman problem is one of the most popular problems in combinatorial optimization. It has been frequently used as a benchmark of the performance of evolutionary algorithms. For this reason, nowadays practitioners request new and more difficult instances of this problem. This leads to investigate how to evaluate the intrinsic difficulty of the instances and how to separate ease and difficult instances. By developing methodologies for separating easy- from difficult-to-solve instances, researchers can fairly test the performance of their combinatorial (...) optimizers. In this work, a methodology for evaluating the difficulty of instances of the travelling salesman problem near the optimal solution is proposed. The question is if the fitness landscape near the optimal solution encodes enough information to separate instances in function of their intrinsic difficulty. This methodology is based on the use of a random walk to explore the closeness of the optimal solution. The optimal solution is modified by altering one connection between two cities at each step, at the same time that the fitness of the altered solution is evaluated. This permits evaluating the slope of the fitness landscape. Later, and using the previous information, the difficulty of the instance is evaluated with random forests and artificial neural networks. In this work, this methodology is confronted with a wide set of instances. As a consequence, a methodology to separate the instances of the travelling salesman problem by their degree of difficulty is proposed and evaluated. (shrink)

Frost has given us good reason to question the universality of existing computational models of reading. Yet, he has not provided arguments showing that all languages share fundamental and invariant reading universals. His goal of outlining the blueprint principles for a universal model of reading is premature. Further, it is questionable whether natural evolution can provide the optimal solutions that Frost invokes.

We study the performance of heuristics relative to the performance of optimal solutions in the rich domain of sequential search, where the decision to stop the search depends only on the applicant’s relative rank. Considering multiple variants of the secretary problem, that vary from one another in their formulation and method of solution, we find that descriptive heuristics perform well only when the optimal solution prescribes a single threshold value. We show that a computational heuristic originally proposed (...) as an approximate solution to a single variant of the secretary problem performs equally well in many other variants where the optimal solution prescribes multiple threshold values that gradually relax the criterion for stopping the search. Finally, we propose a new heuristic with near optimal performance in a competitive or strategic variant of the secretary problem with multiple employers competing with one another to hire job applicants. Both heuristics share a simple computational component: the ratio of the number of interviewed applicants to the number of those remaining to be searched. We present the subgame-perfect Nash equilibrium for this competitive variant and an algorithm for its computation. (shrink)

In this book, we present a study of linear models and algorithms to find the optimal solution for them using the concepts of neuroscientific science. We know that the linear programming method is one of the important methods of operations research, the science that was the product of the great scientific development that our contemporary world is witnessing. The name operations research is given to the group of scientific methods used. In analyzing problems and searching for optimal (...) class='Hi'>solutions, it is a science whose applications have achieved widespread success in various fields of life. What is meant by neutrosophic models are models in which the data are neutrosophic values, that is, variables such as in the objective function, which expresses profit if the model is a maximization model, and expresses a cost if the model is a minimization model, which in turn is affected by environmental conditions. (shrink)

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the (...) optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming. (shrink)

The linear programming method is one of the important methods of operations research that has been used to address many practical issues and provided optimal solutions for many institutions and companies, which helped decision makers make ideal decisions through which companies and institutions achieved maximum profit, but these solutions remain ideal and appropriate in If the conditions surrounding the work environment are stable, because any change in the data provided will affect the optimal solution and to (...) avoid losses and achieve maximum profit, we have, in previous research, reformulated the linear models using the concepts of neutrosophic science, the science that takes into account the instability of conditions and fluctuations in the work environment and leaves nothing to chance. While taking data, neutrosophic values carry some indeterminacy, giving a margin of freedom to decision makers. In another research, we reformulated one of the most important methods used to solve linear models, which is the simplex method, using the concepts of this science, and as a continuation of what we did in the previous two researches, we will reformulate in this research. The graphical method for solving linear models using the concepts of neutrosophics. We will also shed light on a case that is rarely mentioned in most operations research references, which is that when the difference between the number of unknowns and the number of constraints is equal to one, two, or three, we can also find the optimal solution graphically for some linear models. This is done by taking advantage of the conditions of non-negativity that linear models have, and we will explain this through an example in which the difference is equal to two. Also, through examples, we will explain the difference between using classical values and neutrosophic values and the extent of this’s impact on the optimal solution. (shrink)

We present a mathematically rigorous extension to quantum mechanics that accounts for consciousness while resolving longstanding paradoxes in physics. Through formal set-theoretic, group-theoretic, and category-theoretic arguments, we first demonstrate the logical impossibility of emergentism—the view that consciousness arises from complex physical processes. We then introduce a minimal dual-phase space framework in which physical states exist in a Hilbert space HΨ and phenomenal states in an orthogonal Hilbert space HΦ , connected by the awareness operator A and volition operator V. (...) These spaces maintain a precise π/2 phase relationship, with the resultant complex energy eigenvalues manifesting gravitationally as dark matter and dark energy. Our framework elegantly resolves the quantum measurement problem through the Born Rule Locus Correspondence (BRLC), which establishes that phenomenal probabilities exactly match physical probabilities when properly referenced to the observer's spacetime locus. We derive several tensor product norm identities that explain both the causal efficacy of consciousness and its imperviousness to physical detection. Finally, we demonstrate how our framework necessitates the persistence of consciousness beyond biological death through phase decoherence and recoherence processes that follow directly from the mathematical structure. Throughout, we identify specific empirical predictions that distinguish our framework from competing theories. The A|Ω⟩ formalism thus unifies quantum mechanics, consciousness, and cosmology within a single mathematical structure that preserves logical coherence while remaining empirically testable. (shrink)

In this paper I present a game-theoretical approach to the problem of induction. I investigate the comparative success of prediction methods by mathematical analysis and computer programming. Hume's problem lies in the fact that although the success of object-inductive prediction strategies is quite robust, they cannot be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. I show that there exist meta-inductive prediction strategies whose success is universally optimal, modulo short-run losses which are (...) upper-bounded. I then turn to the implications of my approach for the evolution of cognition. In the final section I suggest a revision of the paradigm of bounded rationality by introducing the distinction between local, general and universal prediction strategies. (shrink)

Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show how (...) this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation. (shrink)

The justification of induction is of central significance for cross-cultural social epistemology. Different ‘epistemological cultures’ do not only differ in their beliefs, but also in their belief-forming methods and evaluation standards. For an objective comparison of different methods and standards, one needs (meta-)induction over past successes. A notorious obstacle to the problem of justifying induction lies in the fact that the success of object-inductive prediction methods (i.e., methods applied at the level of events) can neither be shown to be universally (...) reliable (Hume's insight) nor to be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. The meta-inductivist applies the principle of induction to all competing prediction methods that are accessible to her. By means of mathematical analysis and computer simulations of prediction games I show that there exist meta-inductive prediction strategies whose success is universally optimal among all accessible prediction strategies, modulo a small short-run loss. The proposed justification of meta-induction is mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. In the final section I draw conclusions about the significance of meta-induction for the social spread of knowledge and the cultural evolution of cognition, and I relate my results to other simulation results which utilize meta-inductive learning mechanisms. (shrink)

Nature-inspired optimization techniques are useful tools in electrical engineering problems to minimize or maximize an objective function. In this paper, we use the firefly algorithm to improve the optimal solution for the problem of directional overcurrent relays (DOCRs). It is a complex and highly nonlinear constrained optimization problem. In this problem, we have two types of design variables, which are variables for plug settings (PSs) and the time dial settings (TDSs) for each relay in the circuit. The objective function (...) is to minimize the total operating time of all the basic relays to avoid unnecessary delays. We have considered four models in this paper which are IEEE (3-bus, 4-bus, 6-bus, and 8-bus) models. From the numerical results, it is obvious that the firefly algorithm with certain parameter settings performs better than the other state-of-the-art algorithms. (shrink)

Bayesian cognitive science is a research programme that relies on modelling resources from Bayesian statistics for studying and understanding mind, brain, and behaviour. Conceiving of mental capacities as computing solutions to inductive problems, Bayesian cognitive scientists develop probabilistic models of mental capacities and evaluate their adequacy based on behavioural and neural data generated by humans (or other cognitive agents) performing a pertinent task. The overarching goal is to identify the mathematical principles, algorithmic procedures, and causal mechanisms that enable cognitive (...) agents to take uncertainty into account and weigh it appropriately in producing adaptive behaviour. -/- The appeal of Bayesian cognitive science derives from its transparency, normativity, and unifying power. Resources from Bayesian statistics allow cognitive scientists to characterise transparently, in terms of random variables and probabilistic dependencies between them, the inductive problems that many mental capacities are presumed to solve. Given this characterisation, researchers can define an upper bound on one’s performance on that problem and use it as a benchmark for interpreting experimental results, formulating hypotheses about why and when deviations from optimal performance should be expected, and seeking explanations of mental capacities within one encompassing theoretical framework. -/- Although critics question the testability, explanatory power, and plausibility of Bayesian models of mental capacities, Bayesian cognitive science has proved itself to be an incredibly fruitful research programme. Fuelled by empirical and theoretical results from psychology, neuroscience, philosophy, computer science, artificial intelligence, and evolution, Bayesian cognitive science has: advanced our understanding of why cognitive systems should keep track of uncertainty and use it to facilitate adaptive behaviour; clarified how the brain might encode information about the uncertainty of its stimuli and perform computations with probability distributions; and crystallised the insight that cognitive agents’ management of uncertainty might be grounded in predictive processes aimed at avoiding surprising exchanges with the environment. (shrink)

The account of meta-induction (G. Schurz, Hume’s problem solved: the optimality of meta-induction, MIT Press, Cambridge, 2019) proposes a two-step solution to the problem of induction. Step 1 consists in a mathematical a priori justification of the predictive optimality of meta-induction, upon which step 2 builds a meta-inductive a posteriori justification of object-induction based on its superior track record (Sect. 1). Sterkenburg (Br J Philos Sci, forthcoming. 10.1086/717068/) challenged this account by arguing that meta-induction can only provide a (non-circular) justification (...) of inductive predictions for now and for the next future, but not a justification of inductive generalizations (Sect. 2). This paper develops a meta-inductive method that does provide an a posteriori justification of inductive generalizations, in the form of exchangeability conditions (Sect. 3). In Sect. 4, a limitation of the proposed method is worked out: while the method can justify weakly lawlike generalizations, the justification of strongly lawlike generalizations (claimed to hold for all eternity) requires epistemic principles going beyond meta-induction based on predictive success. (shrink)

Packing optimization problems have a wide spectrum of real-word applications. One of the applications of the problems is problem of placement of containers with spent nuclear fuel on the storage platform. The solution of the problem can be reduced to the solution of the problem of finding the optimal placement of a given set of congruent circles into a multiconnected domain taking into account technological restrictions. A mathematical model of the prob-lem is constructed and its peculiarities are considered. Our (...) approach is based on the mathematical modelling of rela-tions between geometric objects by means of phi-function technique. That allowed us to reduce the problem solving to nonlinear programming. Today, an important scientific problem is the problem of creating conditions for safe storage of spent nuclear fuel. In the process of creating any dry spent nuclear fuel storage, the following main stages can be identified: site selection, storage design, construction, operation and decommissioning. A full check for compliance of the repository and its elements with these standards usually begins at the design stage. At the stage of site selection, the inspection for compliance with safety standards is carried out only in terms of the impact of the repository as a whole on the environment. This approach cannot be considered fully appropriate, because, taking into account, for example, all the climatic features of the future storage site, it is possible to adjust the thermal storage regimes of spent nuclear fuel. Similarly, it can be considered necessary to analyze and select the shape of the storage site in order to accommo-date the maximum possible number of spent fuel containers. Such a choice, obviously, should be made taking into ac-count the norms of nuclear, radiation and thermal safety, as well as in compliance with technological limitations. The problem of finding the optimal placement of containers taking into account the given technological limitations can be formulated in the form of the problem of optimization of geometric design. Therefore, the purpose of the study is to build a mathematical model of the problem and study its characteristics to develop effective methods of solution. The proposed approach is based on mathematical modeling of relations between geometric objects using the method of phi-functions. This allowed to reduce the solution of the problem to the problem of nonlinear programming. (shrink)

The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production.Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he has been (...) a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary.General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field. (shrink)

On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the (...) principles that would optimize the structure and content of the teaching module. Given the ethical aspects of the exposure of mathematical facts behind games of chance, and starting from the slots case – where the parametric design is missing, we have to draw a line between ethical and optional information with respect to the mathematical content provided by a scholastic intervention. Arguing for the role of mathematics in problem-gambling prevention and treatment, interdisciplinary research directions are drawn toward implementing an optimal mathematical module in cognitive therapies. (shrink)

The role of mathematics in scientific practice is too readily relegated to that of formulating equations that model or describe what is being investigated, and then finding solutions to those equations. I survey the role of mathematics in: 1. Exact solutions of differential equations, especially conformal mapping; and 2. Simulations of solutions to differential equations via numerical methods and via agent-based models; and 3. The use of experimental models to solve equations (a) via physical analogies based on (...) similarity of the form of the equations, such as Prandtl’s soap-film method, and (b) the method of physically similar systems. Two major themes emerge: First, the role of mathematics in science is not well described by deduction from axioms, although it generally involves deductive reasoning. Creative leaps, the integration of experimental or observational evidence, synthesis of ideas from different areas of mathematics, and insight regarding analogous forms are required to find solutions to equations. Second, methods that involve mappings or transformations are in use in disparate contexts, from the purely mathematical context of conformal mapping where it is mathematical objects that are mapped, to the use of concrete physical experimental models, where one concrete thing is shown to correspond to another. (shrink)

How should we combine disagreeing expert judgments on the likelihood of an event? A common solution is simple averaging, which allows independent individual errors to cancel out. However, judgments can be correlated due to an overlap in their information, resulting in a miscalibration in the simple average. Optimal weights for weighted averaging are typically unknown and require past data to estimate reliably. This paper proposes an algorithm to aggregate probabilistic judgments under shared information. Experts are asked to report a (...) prediction and a meta-prediction. The latter is an estimate of the average of other individuals’ predictions. In a Bayesian setup, I show that if average prediction is a consistent estimator, the percentage of predictions and meta-predictions that exceed the average prediction should be the same. An “overshoot surprise” occurs when the two measures differ. The Surprising Overshoot algorithm uses the information revealed in an overshoot surprise to correct for miscalibration in the average prediction. Experimental evidence suggests that the algorithm performs well in moderate to large samples and in aggregation problems where individuals disagree in their predictions. (shrink)