Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming (...) provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design. (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)

One purpose of cognitive diagnostic model is designed to make inferences about unobserved latent classes based on observed item responses. A heuristic for test construction based on the CDM information index proposed by Henson and Douglas has a far-reaching impact, but there are still many shortcomings. He and other researchers had also proposed new methods to improve or overcome the inherent shortcomings of the CDI test assembly method. In this study, one test assembly method of maximizing the minimum (...) inter-class distance is proposed by using mixed-integer linear programming, which aims to overcome the shortcomings that the CDI method is limited to summarize the discriminating power of each item into a single CDI index while neglecting the discriminating power for each pair of latent classes. The simulation results show that compared with the CDI test assembly and random test assembly, the new test assembly method performs well and has the highest accuracy rate in terms of pattern and attributes correct classification rates. Although the accuracy rate of the new method is not very high under item constraints, it is still higher than the CDI test assembly with the same constraints. (shrink)

The conventional community sports facility allocation methods have high minimum costs, and a new community sports facility allocation performance optimization method is designed based on a linear programming model in order to reduce the performance capital investment. The standardized community sports facility allocation performance objective function is established, and a pairwise model is built to divide the feasible and optimal solutions, and the feasible solutions and their constraints are found out. Establish a community sports facility configuration performance (...) optimization model, delineate the boundaries of the optimal solution by bifurcation, and set the feasible domain of the performance optimization model. The performance optimization algorithm is designed to improve the speed of community sports facility allocation performance optimization. In the experiment, the method is compared with data-driven method, digital management method, and evolutionary game algorithm, which requires less capital investment in spring, autumn, and winter than digital management method and evolutionary game algorithm, and the minimum capital investment in summer is less than the other three methods. From the above experimental data, it is clear that the performance optimization method has the smallest minimum capital investment and achieves the purpose of reducing the input cost. (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)

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 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)

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)

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)

Query processing in ground definite deductive is known to correspond precisely to a linear programming problem. However, the “groundedness” requirement is a huge drawback to using linear programming techniques for logic program computations because the ground version of a logic program can be very large when compared to the original program. Furthermore, when we move from propositional logic programs to first-order logic programs, this effectively means that functions symbols may not occur in clauses. In this paper, (...) we develop a theory of “instantiate- by-need” that performs instantiations only when needed. We prove that this method is sound and complete when computing answer substitutions for non-ground logic programs including those containing function symbols. More importantly, when taken in conjunction with Colmerauer's result that unification can be viewed as linear programming, this means that resolution with unification can be completely replaced by linear programming as an operational paradigm. Additionally, our tree construction method is not rigidly tied to the linear programming paradigm-we will show that given any method M that can compute the set of atomic logical consequences of a propositional logic program, our method can use M to compute , the set of all atoms that are consequences of a first-order logic program. (shrink)

A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling and solutiontechniques. Designed to (...) be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more. (shrink)

On the basis of analyzing the complexity of railway flatcar loading optimization problem, according to the characteristics of railway flatcar loading, based on the situation of railway transport loading unit of multiple railway flatcars, this study puts forward the optimal loading optimization method of multimodel railway flatcars based on improved genetic algorithm, constructs the linear programming model of railway flatcar loading optimization problem, and combines with the improved genetic algorithm to solve the problem. The study also analyzes (...) the structural characteristics of the optimal loading materials of multimodel railway flatcars, selects the optimal materials and inputs the relevant data into the computer, and uses MATLAB to program the optimal loading algorithm of multimodel railway flatcars. Through the analysis of the calculation example, the study discusses its scope of application. The experimental results show that the average general utilization rate of the proposed method is 73%, which has higher universality, more effective application, and fully meets the research requirements. It is verified that the proposed method has a statistically significant impact on the optimal loading of multi-type railway flatcars. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method (...) for solving neutrosophic multi-objective programming problem at end of this paper. (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)

A new method of multiattribute decision making is proposed based on the max-min and min-max gray association degree. The gray association coefficients between the alternative, positive ideal solution and negative ideal solution are defined. Here, we construct a bi-objective programming model that maximizes the minimum gray association degree and minimizes the maximum gray association degree simultaneously. By using the linear weighted summation method, the bi-objective programming model is transformed into a linear programming model. (...) Thus, we can obtain the weight vector of attributes by solving the linear programming model. The ranking order of alternatives is generated according to the relative closeness. A numerical example is examined to demonstrate the applicability and implementation process of the decision method proposed in this paper. (shrink)

Many real-world problems entail multiple conflicting objectives, which makes multiobjective optimization an important subject. Much attention has been paid to Genetic Algorithm as a potent multiobjective optimization method, and the effectiveness of its hybridization with local search has recently been reported in the literature. However, there have been a relatively small number of studies on LS methods for multiobjective function optimization. Although each of the existing LS methods has some strong points, they have respective drawbacks such as high computational (...) cost and inefficiency of improving objective functions. Hence, a more effective and efficient LS method is being sought, which can be used to enhance the performance of the hybridization. Pareto descent directions are defined in this paper as descent directions to which no other descent directions are superior in improving all objective functions. Moving solutions in such directions is expected to maximally improve all objective functions simultaneously. This paper proposes a new LS method, Pareto Descent Method, which finds Pareto descent directions and moves solutions in such directions. In the case part or all of them are infeasible, it finds feasible Pareto descent directions or descent directions as necessary and moves solutions in these directions. PDM finds these directions by solving linear programming problems. Thus, it is computationally inexpensive. Experiments have shown that PDM is superior to existing methods. (shrink)

Water quality control helps in the estimation of water bodies and detects the span of pollutants and their effect on the neighboring environment. This is why the water quality of the northern part of Lake Manzala has been studied here from January to March, 2016. This study aims to model and create a program for linear and nonlinear regression of the water elements in Lake Manzala to assess and predict the water quality. Water samples have been extracted from various (...) depths, and physio-chemical properties and heavy metal concentrations have been evaluated. This study has proposed a new algorithm for predicting water quality called “Algorithm of Estimation Regression Model”. On the contrary, in renewable energy applications, statistical modeling and forecasting the solar radiation remains a significant issue with detect to reinforce power management. A new proposed method for forecasting the average Monthly Global Solar Energy in Queensland, Australia, is called, Converting Data Set into Markov Model. It was used to obtain Markov transition probability matrices for three and six states of the solar energy. The proposed forecasting method yielded accurate results with minimal error. (shrink)

The main concern of this paper is the design of a noetherian and confluent normalization for LK 2. The method we present is powerful: since it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD, delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of `programming-with-proofs' to classical logic ; it is painless: since we reduce strong normalization and confluence to the same properties for (...) class='Hi'>linear logic using appropriate embeddings ; it is unifying: it organizes known solutions in a simple pattern that makes apparent the how and why of their making. A comparison of our method to that of embedding LK into LJ brings to the fore the latter's defects for these `deconstructive purposes'. (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)

This paper studies the problems of tip position regulation and vibration suppression of flexible manipulators without using the model. Because of the two-timescale characteristics of flexible manipulators, applying the existing model-free control methods may lead to ill-conditioned numerical problems. In this paper, the dynamics of a flexible manipulator is decomposed into two subsystems which are linear and controllable at different timescales by singular perturbation theory and a model-free composite controller is designed to alleviate the ill-conditioned numerical problems. To do (...) this, a model-free composite control strategy is constructed which facilitates in designing the controller in slow and fast timescales. In the slow timescale, the slow subsystem controller is designed by adaptive dynamic programming based on the measurements of the slow inputs and the position, while the vibration in the slow timescale is estimated by the least square method. In the fast timescale, the vibration is reconstructed based on the measurements of vibration and its estimate in the slow timescale, by which the fast controller is designed using ADP. Stability of the closed-loop system is proved by SP theory. Finally, simulations are given to show the feasibility and effectiveness of the proposed methods. (shrink)

This paper presents a concept for pattern matching based on a parameter optimization system for approximative numerical calculation of some parameter combination under soft and hard constraints. The concept uses a non-linear parameter optimization method with an iterative variation of parameters. The paper focuses on the information modeling process to migrate problem-domain specific criteria into optimization-compatible objects suitable for a standardized parameter optimization procedure. A step-by-step transformation process is presented and implemented in object-oriented programming: classes and interfaces. (...) The method is applicable to a wide range of pattern-matching problems due to its flexibility and extensibility. (shrink)

Background: In this study, we aimed to investigate the effects of a mindfulness program including Mindfulness-Based Stress Reduction on the mental health of student teachers when offered at their educational institution in a real-life context.Methods: A parallel randomized controlled trial was conducted among self-selected student teachers at a Danish undergraduate program for teacher education in the autumns of 2019 and 2020. Participation was not recommended in case of clinical depression or a diagnosis of psychosis or schizophrenia, abuse of alcohol, drugs, (...) and/or medicine. Randomization was performed by a Statistician who was blinded to the identity of the students. Data was collected using self-reported questionnaires. The primary outcome was a change in perceived stress 3 months from baseline. Secondary outcome measures were symptoms of anxiety and depression, well-being, resilience, mindfulness, and thoughts and feelings during rest. The effects were analyzed according to the intention-to-treat principle using mixed-effect linear regression models. Mediating effects of mindfulness skills on the mental health outcomes were explored using structural equation modeling.Results: The study group included 67 student teachers with 34 allocated to the intervention group ; and 33 students allocated to a waiting list control group. At baseline, mean Perceived Stress Scale scores were 18.88 in the intervention group and 17.91 in the waiting list control group. A total of 56 students completed the questionnaire at a 3-month follow-up. Statistically significant effects of the intervention were found on perceived stress, symptoms of anxiety and depression, well-being, and on three of seven resting-state dimensions. No effects were found on resilience or mindfulness. Statistically significant mediated effects via resting-state dimensions were found.Conclusion The findings suggested that offering a mindfulness program at an undergraduate program for teacher education could significantly improve the mental health among self-selected students within 3 months. Results of mediation analysis supported the hypothesis that some of the effects might be explained by reduced distracting thoughts.Clinical Trial Registration: [www.ClinicalTrials.gov], identifier [NCT04558099]. (shrink)

Establishing reasonable, prior distributions remains a significant obstacle for the construction of probabilistic expert systems. Human assessment of chance is often relied upon for this purpose, but this has the drawback of being inconsistent with axioms of probability. This article advances a method for extracting a coherent distribution of probability from human judgment. The method is based on a psychological model of probabilistic reasoning, followed by a correction phase using linear programming.

Polyhedral functions provide a model for an important class of problems that includes both linear programming and applications in data analysis. General methods for minimizing such functions using the polyhedral geometry explicitly are developed. Such methods approach a minimum by moving from extreme point to extreme point along descending edges and are described generically as simplicial. The best-known member of this class is the simplex method of linear programming, but simplicial methods have found important applications (...) in discrete approximation and statistics. The general approach considered in this text, first published in 2001, has permitted the development of finite algorithms for the rank regression problem. The key ideas are those of developing a general format for specifying the polyhedral function and the application of this to derive multiplier conditions to characterize optimality. Also considered is the application of the general approach to the development of active set algorithms for polyhedral function constrained problems and associated Lagrangian forms. (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)

Let G V, E be a simple undirected complete graph with vertex and edge sets V and E, respectively. In this paper, we consider the degree-constrained k -minimum spanning tree problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2. In particular, in this paper, we consider degree values of d ∈ (...) 2,3. Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2, it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization and variable neighborhood search algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements. (shrink)

Ancient algorithms -- Sorting -- Graph algorithms -- Primality testing -- Solution of linear equations -- Newton's method -- Linear programming -- Eigenvalues and eigenvectors -- MM algorithms -- Data mining -- The fast Fourier transform -- Monte Carlo methods -- Mathematical review.

The objective of this work is to propose ten efficient scaling techniques for the Wisconsin Diagnosis Breast Cancer dataset using the support vector machine. These scaling techniques are efficient for the linear programming approach. SVM with proposed scaling techniques was applied on the WDBC dataset. The scaling techniques are, namely, arithmetic mean, de Buchet for three cases p = 1,2, and ∞, equilibration, geometric mean, IBM MPSX, and Lp-norm for three cases p = 1,2, and ∞. The experimental (...) results show that the equilibration scaling technique overcomes the benchmark normalization scaling technique used in many commercial solvers. Finally, the experimental results also show the effectiveness of the grid search technique which gets the optimal parameters for the SVM classifier. (shrink)

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer (...) class='Hi'>linear programming formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic. (shrink)

Robust techniques critically improve bearing-only target localization when the relevant measurements are being corrupted by impulsive noise. Resistance to isolated gross errors refers to the conventional least absolute residual method, and its estimate can be determined by linear programming when pseudolinear equations are set. The LAR approach, however, cannot reduce the bias attributed to the correlation between system matrices and noise vectors. In the present study, perturbations are introduced into the elements of the system matrix and the (...) data vector simultaneously, and the total optimization problem is formulated based on least absolute deviations. Subsequently, an equivalent form of total least absolute residuals is obtained, and an algorithm is developed to calculate the robust estimate by dual ascent algorithms. Moreover, the performance of the proposed method is verified through the numerical simulations by using two types of localization geometries, i.e., random and linear. As revealed from the results, the TLAR algorithm is capable of exhibiting significantly higher localization accuracy as compared with the LAR method. (shrink)

Compared to a charging scheduling and management problem characterized by predetermined trip assignment, this study takes bus and driver scheduling into account, and mealtime windows must be guaranteed as one of the major labor regulations. A discretized mixed-integer linear programming model is developed based on a single electric bus route. We aim to obtain fast and high-quality global solutions for this problem, and the model can be easily executed by bus operators by directly invoking an available optimization solver (...) such as IBM ILOG CPLEX. We test our model on a real round-trip bus route. Numerical experiments show that CPLEX takes approximately 6 sec to obtain an optimal solution. The model can not only reasonably arrange daily trips for each electric bus and driver but also effectively determine the optimal charging schedule and management for an electric bus line. Besides, we analyze the sensitivity of the key parameters in the model. With the increase in the drivers’ maximum workload, the drivers’ average idle time decreases by approximately 11.25%. The objective value decreases by approximately 38.71% and 40.04% with increases in the battery capacity and fleet size, respectively, and the objective value increases by approximately 30.06% with the decrease in the initial battery driving range. In addition, we compare the effectiveness of our time discretization modeling method in solving the same case study to that from other similar studies, and the validity of our method can be verified by the calculation time. We also compare the computational efficiency of CPLEX in solving the same case study problem with and without implementing valid inequalities, and the computational efficiency of the valid inequality method is greatly improved. Finally, through the testing of a multiline network, the potential application of the model to a large-scale traffic network is verified. (shrink)

In this paper we investigate a particular two-stage supply chain network design problem with fixed costs. In order to solve this complex optimization problem, we propose an efficient hybrid algorithm, which was obtained by incorporating a linear programming optimization problem within the framework of a genetic algorithm. In addition, we integrated within our proposed algorithm a powerful local search procedure able to perform a fine tuning of the global search. We evaluate our proposed solution approach on a set (...) of large size instances. The achieved computational results prove the efficiency of our hybrid genetic algorithm in providing high-quality solutions within reasonable running-times and its superiority against other existing methods from the literature. (shrink)

This paper describes an AFOSR-supported basic research program that focuses on developing a new framework for combining hard with soft data in order to improve space situational awareness. The goal is to provide, in an automatic and near real-time fashion, a ranking of possible threats to blue assets (assets trying to be protected) from red assets (assets with hostile intentions). The approach is based on Conceptual Spaces models, which combine features from traditional associative and symbolic cognitive models. While Conceptual Spaces (...) are revolutionary, they lack an underlying mathematical framework. Several such frameworks have attempted to represent Conceptual Spaces, but by far the most robust is the model developed by Holender. His model utilizes integer linear programming in order to obtain an overall similarity value between observations and concepts that support the formation of hypotheses. This paper will describe a method for building Conceptual Spaces models for threats that utilizes ontologies as a means to provide a clear semantic foundation for this inferencing process; in particular threat ontologies and space domain ontologies are developed and employed in this approach. A space situational awareness use-case is presented involving a kinetic kill scenario and results are shown to assess the performance of this fusion-based inferencing framework. (shrink)

ABSTRACT At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on ‘alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and (...) he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory. (shrink)

In this work we propose a labelled tableau method for ukasiewicz infinite-valued logic L . The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for L validity by reducing (...) the check of branch closure to linear programming. (shrink)

The overall goal of the approach developed in this paper is to estimate the likelihood of a given kinetic kill scenario between hostile spacebased adversaries using the mathematical framework of Complex Conceptual Spaces Single Observation. Conceptual spaces are a cognitive model that provide a method for systematically and automatically mimicking human decision making. For accurate decisions to be made, the fusion of both hard and soft data into a single decision framework is required. This presents several challenges to this (...) data fusion framework. The first is the challenge involved in handling multiple complex terminologies, which is addressed by drawing on a set of Space Domain Ontologies. Another challenge is the complex combinatorics involved when considering all possible feature combinations. This can be mitigated by using integer linear programming optimization that is outlined by the Complex Conceptual Spaces Single Observation mathematical model framework. A third challenge is the complicated physics that is involved in a spacecraft collision that must be addressed to obtain a better understanding of threat assessment. Overcoming these various challenges allows for a quantitative ranking for the potential of a kinetic kill collision across multiple spacecraft pairs. In addition to overcoming these challenges this paper will break down threat assessment into four domains and identify a ranking of threat both for each individual domain and for the four domains combined. Simulation results are shown to verify the developed concepts. (shrink)

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is (...) a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory. (shrink)

We give a sound and complete axiomatization of a probabilistic extension of intuitionistic logic. Reasoning with probability operators is also intuitionistic (in contradistinction to other works on this topic), i.e., measure functions used for modeling probability operators are partial functions. Finally, we present a decision procedure for our logic, which is a combination of linear programming and an intuitionistic tableaux method.

To address complexity information fusion problems involving fuzzy and grey uncertainty information, we develop prioritized averaging aggregation operator and Bonferroni mean aggregation operator with grey linguistic 2-tuple variables and apply them to design a new decision-making scheme. First, the grey linguistic 2-tuple prioritized averaging operator is developed to characterize the prioritization relationship among experts and employed to fuse experts’ information into an overall opinion. Second, we establish dual generalized grey linguistic 2-tuple weighted Bonferroni mean operator to capture the interrelationship among (...) any attribute subsets, which can be reduced to some conventional operators by adjusting parameter vector. On that basis, a flexible group decision-making approach with fuzzy and grey information is designed and applied to an evaluation problem, in which grey relationship analysis method and a linear programming model are combined to extract attribute weights from partially known attribute information. Furthermore, an illustrative example is employed to illustrate the practicality and flexibility of the designed method by conducting the related comparative studies. (shrink)

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is calculated as the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. The associated software package OT-Help provides a practical tool for studying large and complex linguistic systems in the HG framework and comparing the results with those of OT. We (...) describe the translation from Harmonic Grammars to systems solvable by linear programming, and we illustrate the usefulness of OT-Help with a set of studies of the predictions HG makes for phonological typology. (shrink)

In this paper, we study the introduction of modal past temporal operators in Temporal Equilibrium Logic, an hybrid formalism that mixes linear-time modalities and logic programs interpreted under stable models and their characterisation in terms of Equilibrium Logic. We show that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic. Additionally, we provide a method for removing past operators that consists in replacing past-time subformulas by fresh auxiliary (...) atoms, obtaining an equivalent formula, modulo the original alphabet. (shrink)

Given a program of a linear bounded and bijective operator T, does there exist a program for the inverse operator T−1? And if this is the case, does there exist a general algorithm to transfer a program of T into a program of T−1? This is the inversion problem for computable linear operators on Banach spaces in its non-uniform and uniform formulation, respectively. We study this problem from the point of view of computable analysis which is the Turing (...) machine based theory of computability on Euclidean space and other topological spaces. Using a computable version of Banach’s Inverse Mapping Theorem we can answer the first question positively. Hence, the non-uniform version of the inversion problem is solvable, while a topological argument shows that the uniform version is not. Thus, we are in the striking situation that any computable linear operator has a computable inverse while there exists no general algorithmic procedure to transfer a program of the operator into a program of its inverse. As a consequence, the computable version of Banach’s Inverse Mapping Theorem is a powerful tool which can be used to produce highly non-constructive existence proofs of algorithms. We apply this method to prove that a certain initial value problem admits a computable solution. As a preparation of Banach’s Inverse Mapping Theorem we also study the Open Mapping Theorem and we show that the uniform versions of both theorems are limit computable, which means that they are effectively -measurable with respect to the effective Borel hierarchy. (shrink)

Algorithmic chemistries are often based on a fixed formalism which limits the fragment of chemistry expressible in the domain of the models. This results in limited applicability of the models in contemporary mathematical chemistry and is due to the poor fit between the logic used for model construction and the system being modeled. In this paper, I propose a system-oriented methodology which selects a formalism through a mapping of chemical transformation rules to proof-theoretic structural rules. Using a formal specification framework (...) from the field of artificial chemistry, expressive adequacy is ensured by the choice of logic being based on the system properties to be modeled. To illustrate the methodology, a case study is provided that shows how the proposed approach selects linear logic for modeling resource sensitivity and the proof-theoretic interpretation facilitates translation to a programming language. Since the method results in a plurality of models, I conclude with a discussion on how the proposal contributes to multi-model paradigms in computational pharmacology. (shrink)