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Several comments on the papers by L. V. Kantorovich reproduced in this volume. Bibliography: 16 titles. [ABSTRACT FROM AUTHOR]

In the process of cement equipment manufacturing, the demand of rectangle pieces of steel structure is very large. The traditional manual nesting, which is simply cutting by hand-making according to the arrangement of the number and size, causes the low efficiency and material wasting. To solve the problem above, this paper proposes an optimizing model for nesting problem of rectangle pieces. Firstly, with the aim of the maximum utilization ratio of the sheet, the optimization mathematical model for nesting problem of rectangle pieces is established. The lowest horizontal line searching algorithm is described in detail. Secondly, the mathematical model is solved to get the optimal solution by the combination of genetic algorithm and the lowest horizontal line searching algorithm. In the solution process, this paper presents the methods of gene encoding and decoding, definition of fitness function, the design of genetic operators and the design of algorithm operating parameters. Finally, we use one sheet as an example to illustrate the proposed model and algorithm process. Experimental results have shown that the proposed approach is able to achieve rectangle pieces nesting with the maximum material utilization ratio. [ABSTRACT FROM AUTHOR]

Problems related to the extremization of functions have been studied for quite a long time not only by Russian experts but also by the world's leading experts in the field of applied mathematics. It should be noted that, nowadays, not all problems on this topic have a solution, despite the ongoing active research in mathematical modeling and mathematical programming. A serious work is underway on a deeper study of the properties of extremizable functions. This is especially topical in the context of our country's transition to a knowledge economy and, as a first step towards this, to the digital economy, when powerful supercomputers with performance of hundreds and thousands of petaflops have arisen and quantum computers begin to occur. The paper is a survey of results associated with a new class of functions that are useful in extremization problems and is based on joint work of the authors. [ABSTRACT FROM AUTHOR]

Project management is a process that schemes and controls the project life cycle via the easiest and the best way to achieve project goals. Project managers always aim to simultaneously handle conflicting goals in the organization. In this paper, a new mathematical model is proposed that simultaneously minimizes total cost and completion time and maximizes the quality in the project management decision problem. Contractual penalty cost and contractual reward cost with a new method are the other consideration in the proposed model. In the projects, the relation between time and direct cost is a nonlinear function. Hence, a linearization technique is presented with attention to variable change and piecewise linearization, in which nonlinear function is converted to the linear programming model. On the other hand, in real conditions according to uncertainty in environmental situations and incomplete information, there can be ambiguity in parameters and variables of the problem. The uncertainty of the parameters and variables is expressed with fuzzy sets theory and fuzzy mathematical programming. The other aim of this paper is to introduce a modified version of fully fuzzy multi-objective linear programming for the problem. For analyzing a fully fuzzy time–cost–quality project management model, a practical example of the literature is provided. By examining the results of the model with conflicting objectives, two scenarios are presented to explore the interactions of conflicting objectives on the project, and the results are reported. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of six multiobjective evolutionary algorithms (MOEAs) with the node-depth encoding (NDE) which have been used to solve the service restoration in distribution systems. The study has been divided into three steps: (1) the MOEAs have been evaluated taking into account the switching operations necessary to find adequate restoration plans considering multiple nonlinear constraints and objective functions; (2) the MOEAs have been employed to solve four different datasets with 3860, 7720, 15,440 and 30,880 buses, respectively; (3) comparisons have been performed using the hypervolume indicator and the results obtained with each approach are statistically compared using Kruskal-Wallis nonparametric tests and multiple comparisons. In addition, this paper provides a comprehensive evaluation of six combinations of MOEAs based on NDE and our objective is to identify the features of each approach that consistently produce best results applied to network reconfiguration for service restoration in distribution systems. Simulations results have shown that MOEA based on NDE with crowding distance and strength pareto found good configurations with low switching operations and explored the search space better than others approaches used in this paper, approximating better the pareto-optimal front. [ABSTRACT FROM AUTHOR]

Single-valued neutrosophic numbers (SVNNs) are very much useful to express uncertain environments. In real-life problems, there are many situations where players of a matrix game can not assess their payoffs by using ordinary fuzzy sets or intuitionistic fuzzy sets. In these situations, single-valued trapezoidal neutrosophic numbers (SVTNNs) play a vital role in game theory, as it includes indeterminacy in the information besides truth and falsity. The objectives of this paper are to explore matrix games with SVTNN payoffs and to investigate two different solution methodologies. To solve such games, a pair of neutrosophic mathematical programming problems have been formulated. In the first approach, the two neutrosophic mathematical programming models are converted into interval-valued multi-objective programming problems by using a new ranking order relation of SVTNNs. Finally, the reduced problems are solved using the weighted average approach and utilizing LINGO 17.0 software. It is worth mentioning that the values of the game for both the players are obtained in SVTNN forms, which is desirable. In the second approach, each neutrosophic mathematical programming model is transformed into a crisp one by using the idea of α -weighted possibility mean value for SVTNNs. A market share problem and another numerical example are illustrated to show the validity and applicability of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs. [ABSTRACT FROM AUTHOR]

The problem of optimal flow production planning at the operational scheduling stage is being studied, using the example of the out-of-furnace department of a converter-based steel-making production in the iron metallurgy industry. To solve this problem, a linear integer programming model is proposed, which fully describes the specifics of the investigated technological processes. A major advantage of this approach is its scalability for solving related optimization problems in the industry of plant logistics, as well as flexibility in adapting to changes and fine-tuning the system of constraints and objective function. The software implementation of the developed model forms the basis of the operational scheduling module of the optimal flow production planning system, which is used for a large-scale computational experiment on real-world data. [ABSTRACT FROM AUTHOR]

In this paper, a new group of optimization algorithms named Human Strategy Algorithm (HS) is proposed which is inspired by human strategies to problem solving. The main idea of HS is based on human actions to find the problem’s optima by means of accessible instruments. As the environment of an unknown problem assumed to be a black box, it is supposed that the environment of our problem is a dark room occupied by several men named blind men. The main mission of these men is to look for the optimum solution. Each man has at least one instrument as his assistance. Like real life, the instrument might be any tool such as stick, billy, rope, stone, yoyo, sweep. Any instrument by its unique features is suitable in some situations. In fact, this algorithm maps problem space and searches agents to dark room and people, respectively. In this paper, one sample algorithm of the group of human strategy, YOYO Blind Man Algorithm (YOYO-BMA), is introduced which uses yoyos as men’s accessible instruments. The performance of the YOYO-BMA is evaluated on a set of benchmark problems provided for CEC’2010 Special Session and Competition on Large-Scale Global Optimization (Tang et al. 2010). The results show superior performance of proposed algorithm in comparison with others. Moreover, the problem of designing urban traffic network is solve to evaluate the algorithm using a real complex problem. [ABSTRACT FROM AUTHOR]

Modern computer technology allows conjoining shakedown theory, optimization and ever stricter standardized design requirements in a single mathematical problem formulation. However it raises a question of reliability: easily achieved solution should not be taken for granted but should be adequately assessed. This paper focuses on the physical validation technique for optimal shakedown design problem solution in the aspect of Melan theorem (statics) and residual deformation compatibility (kinematics). For that purpose Rosen gradient projection method is used. Optimization problem of bending circular, symmetric plate at shakedown, which is subjected by a variable repeated load, is considered for illustration of the validation technique. [ABSTRACT FROM AUTHOR]

A preface focusing on mathematical programming is presented.

In this paper, we analyze an internal goal structure based on heuristic dynamic programming, named GrHDP, to tackle the 2-D maze navigation problem. Classical reinforcement learning approaches have been introduced to solve this problem in literature, yet no intermediate reward has been assigned before reaching the final goal. In this paper, we integrated one additional network, namely goal network, into the traditional heuristic dynamic programming (HDP) design to provide the internal reward/goal representation. The architecture of our proposed approach is presented, followed by the simulation of 2-D maze navigation (10*10) problem. For fair comparison, we conduct the same simulation environment settings for the traditional HDP approach. Simulation results show that our proposed GrHDP can obtain faster convergent speed with respect to the sum of square error, and also achieve lower error eventually. [ABSTRACT FROM AUTHOR]

This paper addresses a problem that is typical of multi-period capacity expansion equilibrium models: plants or sectors have different risk exposures that may warrant different costs of capital. The paper examines modifications of a capacity expansion model interpreted in equilibrium terms to account for asset-specific costs of capital. [ABSTRACT FROM AUTHOR]

This paper studies a telecommunication network design problem. In this network, users must be connected to capacitated hubs. Then, hubs that concentrate users must be connected to each other and possibly to other hubs with no users. The connections in the network must lead to a tree topology. Hence, connection between hubs can be considered as looking for forming a Steiner tree. This problem is modeled as a bi-objective mathematical programming problem. One objective function minimizes user's latency with respect to the information packages flowing through the capacitated hubs, and the other objective function aims the minimization of the total network's connection cost. To approximate the Pareto front of this bi-objective problem, a co-evolutionary algorithm is developed. In the proposed algorithm, two populations are considered. Each population is associated with one objective function. The co-evolutionary operator consists of an information exchange between both populations that occurs after the genetic operators have been applied. As a result of this co-evolutionary operator, the non-dominated solutions are identified. Computational experimentation shows that the approximated Pareto fronts are representative despite their non-convexity, and they contain a sufficient number of non-dominated solutions over the tested instances. Also, the kth distance among non-dominated solutions is relatively small, which indicates that the approximated Pareto fronts are dense. Furthermore, the required computational time is very small for a problem with the characteristics herein considered. [ABSTRACT FROM AUTHOR]

Image feature detection can be obtained from many methods including the feature point detection. This paper adopts the image feature point detection method based on second-order characteristics of point and the image feature detection algorithm based on the Hessian matrix to detect more feature points. By combining the gray-scale-based image-matching technology with the feature-based image feature detection technology, we propose a Hessian algorithm to obtain more matching points, which can search for matching more quickly. The proposed algorithm overcomes the traditional matching methods that have Ergodic properties of the search strategy. Experiments demonstrate the speed and accuracy of the proposed algorithm, and we use the correct detected feature points to realize image registration, image fusion and image stitching. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new tensor-based representation algorithm for image classification. The algorithm is realized by learning the parameter tensor for image tensors. One novelty is that the parameter tensor is learned according to the Tucker tensor decomposition as the multiplication of a core tensor with a group of matrices for each order, which endows that the algorithm preserved the spatial information of image. We further extend the proposed tensor algorithm to a semi-supervised framework, in order to utilize both labeled and unlabeled images. The objective function can be solved by using the alternative optimization method, where at each iteration, we solve the typical ridge regression problem to obtain the closed form solution of the parameter along the corresponding order. Experimental results of gray and color image datasets show that our method outperforms several classification approaches. In particular, we find that our method can implement a high-quality classification performance when only few labeled training samples are provided. [ABSTRACT FROM AUTHOR]

The fractional transportation problem (FTP) plays an important role in logistics and supply management for reducing cost and improving service. In the real world, however, the parameters in the models are seldom known exactly and have to be estimated. This paper investigates the FTP where the cost coefficients and right-hand sides are represented by fuzzy parameters. Intuitively, when the parameters in the FTP are fuzzy numbers, the derived objective value should be also a fuzzy number. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the fuzzy objective value of the FTP with fuzzy parameters. By applying the dual formulation of linear fractional programming and variable substitution techniques, the two-level mathematical programs are transformed into ordinary one-level linear programs to solve. At a specific $$\alpha $$ -cut, solving the pair of linear programs produces the bounds of the objective value of the fuzzy FTP. By collecting the bounds from different $$\alpha $$ levels, one can depict the shape of the membership function. An example illustrates how to apply the concept of this paper to solve the fuzzy FTP problem. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of parts scheduling in a cellular manufacturing system (CMS) by considering exceptional parts processed on machines located in multiple cells. To optimize the scheduling of parts as well as to minimize material handling between cells, the practice has to develop processing sequences for the parts in cells. A commonly chosen objective is to find part sequences within cells which results in a minimum tardiness. This paper proposes a nonlinear mathematical programming model of the problem by minimizing the total weighted tardiness in a CMS. To solve the mathematical model, a scatter search approach is developed, in which the common components of scatter search are redefined and redesigned so as to better fit the problem. This scatter search approach considers two different methods to generate diverse initial solutions and two improvement methods, and adopts the roulette wheel selection in the combination method to further expand the conceptual framework and implementation of the scatter search. The proposed approach is compared with the commercial solver CPLEX on a set of test problems, some of which are large dimensions. Computational results have demonstrated the effectiveness of this scatter search approach. [ABSTRACT FROM AUTHOR]

This paper proposes a novel mathematical model to solve the static and multistage transmission network expansion planning problems considering the optimal placement of series capacitive compensation (SCC) devices. This model jointly examines the construction of new transmission lines, transformers, and the optimal placement of SCC devices to minimize the total investment cost while satisfying the demand requirements in the planning horizon. The problem is formulated as a mixed-integer nonlinear programming problem, which is solved using a high-performance hybrid genetic algorithm. Simulations done in four electrical systems (IEEE 24-bus, South Brazilian 46-bus, North-Northeast Brazilian 87-bus, and Colombian 93-bus) show that inclusion of SCC devices in the planning model results in lower investment cost and a better redistribution of power flows through transmission components. [ABSTRACT FROM AUTHOR]

In the traditional fuzzy matrix game, given a pair of strategies, the payoffs of one player are usually associated with themselves, but not linked to the payoffs of the other player. Such payoffs can be called self-evaluated payoffs. However, according to the regret theory, the decision makers may care more about what they might get than what they get. Therefore, one player in a matrix game may pay more attention to the payoffs of the other player than his/her payoffs. In this paper, motivated by the pairwise comparison matrix, we allow the players to compare their payoffs and the other ones to provide their relative payoffs, which can be called the cross-evaluated payoffs. Moreover, the players' preference about the cross-evaluated payoffs is usually distributed asymmetrically according to the law of diminishing utility. Then, the cross-evaluated payoffs of players can be expressed by using the asymmetrically distributed information, i.e., the interval-valued intuitionistic multiplicative number. Comparison laws are developed to compare the cross-evaluated payoffs of different players, and aggregation operators are introduced to obtain the expected cross-evaluated payoffs of players. Based on minimax and maximin principles, several mathematical programming models are established to obtain the solution of a matrix game with cross-evaluated payoffs. It is proved that the solution of a matrix game with cross-evaluated payoffs can be obtained by solving a pair of primal–dual linear-programming models and can avoid some unreasonable results. Two examples are finally given to illustrate that the proposed method is based on the cross-evaluated payoffs of players, and can directly provide the priority degree that one player is preferred to the other player in winning the game. [ABSTRACT FROM AUTHOR]

Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations. [ABSTRACT FROM AUTHOR]

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets. [ABSTRACT FROM AUTHOR]

SML is a modeling language for the structured modeling framework, which represents the semantics as well as the mathematical structure of a model. This paper uses an SML approach to improve the object based universal relation data model. By this approach, both the relational structure of a database and the objects in relations are automatically derived by the associated SML schema. The interpretation part of an SML schema allows users to easily learn the meanings of the data before performing universal relation queries; the queries are then computed by using the automatically derived objects. With a goal of making queries simpler, this paper presents theories, table naming conventions, a confirmation approach, and a unified example illustrating many different concepts. It helps lay the foundation for the eventual development of a remarkably easy user interface for ad hoc query in computer-based modeling systems. We are hopeful that the results may in the future contribute to real applications in databases as well as in management science/operations research. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of infeasibility of systems defined by convex inequality constraints, where some or all of the variables are integer valued. In particular, we provide a polynomial time algorithm to identify a set of all constraints which may affect a feasibility status of the system after some perturbation of the right-hand sides. We establish several properties of the irreducible infeasible sets and infeasibility sets in the systems with integer variables, proving in particular that all irreducible infeasible sets and infeasibility sets are subsets of the set of constraints critical to feasibility. Furthermore, the well-known Bohnenblust-Karlin-Shapley Theorem, which requires that a system of convex inequality constraints must be defined over a compact convex set, is generalized to convex systems without the assumption on compactness of the convex region. Extension of the latter result to convex systems defined over the set of integers is also provided. [ABSTRACT FROM AUTHOR]

Statistical model checking of unbounded time properties is challenging, because it requires an algorithm to estimate the measure of paths satisfying an unbounded until property from samples of finite length paths. In this paper, we survey all proposed algorithms for this problem, and critically evaluate them. [ABSTRACT FROM AUTHOR]

Strategic staff planning in consultancies is a major problem that directly affects the firm's performance and capacity for dealing with projects appropriately. Furthermore, the decisions taken now will have long term consequences, because consultants are highly qualified workers who need very long learning periods to achieve enough expertise. In other words, the size and composition of the future workforce depends on the decisions taken today. It is important to underline that the system anticipates future capacity adjustment in response to forecasted demand requirements; therefore, it is flexible to plan the workforce in different scenarios and time horizons. This paper proposes a decision support system based on a mathematical optimization model for solving strategic staff planning, taking the company's strategies, policies and objectives into account and optimizing both the costs and the staff composition. The tool is tested by applying it in an office belonging to a multinational consulting firm. [ABSTRACT FROM AUTHOR]

In this paper, we address the non-permutation flowshop scheduling problem with minimal and maximal time lags between successive operations of each job. For this problem, the set of permutation schedules is not a dominant set but not all non-permutation schedules are feasible because they are not always able to satisfy all time lag constraints. We present a theoretical study, limited to the two-machine case, and related to the change on one machine of the order of two successive jobs of a permutation schedule. This study gives first the necessary conditions to make such move with regard to the feasibility of the schedule; secondly the necessary conditions to make such move interesting with regard to either the makespan or the number of tardy jobs. Through this analysis, we obtain new properties of dominance of permutation schedules. The results of the study are incorporated into a heuristic algorithm which starts the search with optimal permutation schedules and tries to improve them so as to obtain better non-permutation schedules. We also propose a mixed integer linear programming model. The objective function is to minimize lexicographically the number of tardy jobs as primary criterion and the makespan as secondary one. Computational experiments are performed to compare permutation with non-permutation schedules. [ABSTRACT FROM AUTHOR]

Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give an uncertainty distribution of the least cost of shipment of a commodity through a network with uncertain capacities. Uncertainty theory is used to deal with uncertain capacities, and an $$\alpha $$ -minimum cost flow problem model is proposed. After defining the $$\alpha $$ -minimum cost flow, the properties of the model are analyzed, and then an algorithm for uncertain minimum cost flow problem is developed. The algorithm can be considered as a general solution to the uncertain minimum cost flow problem. To demonstrate the efficiency of the proposed algorithm, a numerical example is illustrated. [ABSTRACT FROM AUTHOR]

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Using the Multivariate Decomposition Method (MDM), we develop an efficient algorithm for approximating the ∞-variate integral for a class of functions f that are once differentiable with respect to each variable. MDM requires efficient algorithms for d-variate versions of the problem. Such algorithms are provided by Smolyak's construction which is based on efficient algorithms for the univariate integration Detailed analysis and development of (nearly) optimal quadratures for I( f) is the main contribution of the current paper. [ABSTRACT FROM AUTHOR]

The development of mathematical and optimization models for reverse supply network design has concerned considerable interest over the past decades. However, the uncertainties that are inherent in the network design and the complex interactions among various uncertain parameters are challenging the capabilities of these developed tools. The aim of this paper is to propose a new mathematical programming model for recycling network design in the iron and steel industry. The considered recycling network is multi-echelon, multi-facility, multi-product, and multi-supplier. Moreover, another objective of this research is to introduce an interval-stochastic robust optimization methodology to deal with various uncertainties in the proposed model. Computational experiments are provided to demonstrate the applicability of the proposed model in recycling network design. [ABSTRACT FROM AUTHOR]

The last decade has seen several aspect language proposals for UML 2 sequence diagrams. Aspects allow the modeler to define crosscutting concerns of sequence diagrams and to have these woven with the sequence diagrams of a so-called base model, in order to create a woven model. In a real-world scenario, there may be multiple aspects applicable to the same base model. This raises the need to analyse the set of aspects to identify possible aspect interactions (dependencies and conflicts) between applications of aspects. We call a set of aspects terminating if they may not be applied infinitely many times for any given base model. Furthermore, we call a set of terminating aspects confluent, if they, for any given base model, always yield the same final result regardless of the order in which they are applied. Since confluence must hold for any base model, this is a much stronger result than many of the current approaches that have addressed detection of aspect interactions limited to a specific base model. Our aspects are specified using standard sequence diagrams with some extensions. In this paper, we present a confluence theory specialized for our highly expressive aspect language. For the most expressive aspects, we prove that confluence is undecidable. For another class of aspects with considerable expressiveness, we prescribe an algorithm to check confluence. This algorithm is based on what we call an extended critical pair analysis. These results are useful both for modelers and researchers working with sequence diagram aspects and for researchers wanting to establish a confluence theory for other aspect-oriented modelling or model transformation approaches. [ABSTRACT FROM AUTHOR]

This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

The alternating direction method of multipliers (ADMM) recently has found many applications in various domains whose models can be represented or reformulated as a separable convex minimization model with linear constraints and an objective function in sum of two functions without coupled variables. For more complicated applications that can only be represented by such a multi-block separable convex minimization model whose objective function is the sum of more than two functions without coupled variables, it was recently shown that the direct extension of ADMM is not necessarily convergent. On the other hand, despite the lack of convergence, the direct extension of ADMM is empirically efficient for many applications. Thus we are interested in such an algorithm that can be implemented as easily as the direct extension of ADMM, while with comparable or even better numerical performance and guaranteed convergence. In this paper, we suggest correcting the output of the direct extension of ADMM slightly by a simple correction step. The correction step is simple in the sense that it is completely free from step-size computing and its step size is bounded away from zero for any iterate. A prototype algorithm in this prediction-correction framework is proposed; and a unified and easily checkable condition to ensure the convergence of this prototype algorithm is given. Theoretically, we show the contraction property, prove the global convergence and establish the worst-case convergence rate measured by the iteration complexity for this prototype algorithm. The analysis is conducted in the variational inequality context. Then, based on this prototype algorithm, we propose a class of specific ADMM-based algorithms that can be used for three-block separable convex minimization models. Their numerical efficiency is verified by an image decomposition problem. [ABSTRACT FROM AUTHOR]

This paper proposes a relaxed mathematical model to solve the restoration problem of radial and balanced electrical distribution systems. The mathematical model is a mixed-integer linear programming formulation that can be efficiently solved by commercial solvers. After a restoration problem is solved using this model, the quality and feasibility of the corresponding solution can be verified by using a conventional radial power flow. The performance of the proposed relaxed model is evaluated through exhaustive tests and the solutions found are compared with the ones provided by an exact mathematical formulation. The results obtained demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical modelling of a scheduling problem in a heterogeneous CPU/FPGA architecture with heterogeneous communication delays in order to minimize the makespan, Cmax. This study was motivated by the quality of the available solvers for Mixed Integer Program. The proposed model includes the communication delay constraints in a heterogeneous case, depending on both tasks and computing units. These constraints are linearized without adding any extra variables and the obtained linear model is reduced to speed-up the solving with CPLEX up to 60 times. Computational results show that the proposed model is promising. For an average sized problem of up to 50 tasks and five computing units the solving time under CPLEX is a few seconds. [ABSTRACT FROM AUTHOR]

Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed qualification conditions as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible qualification conditions, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive the so-called M-stationarity conditions. The restrictiveness of assumptions and the strength of conclusions in the two forms of the MPEC is also strongly related to the qualification conditions on the “lower level”. For instance, even under the linear independence constraint qualification (LICQ) for a lower level feasible set described by C1 functions, the calmness properties of the original and the enhanced perturbation mapping are drastically different. When passing to C1,1 data, this difference still remains true under the weaker Mangasarian–Fromovitz constraint qualification, whereas under LICQ both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. After clarifying these relations, we provide a compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions. The obtained results are finally applied to MPECs with structured equilibria. [ABSTRACT FROM AUTHOR]

The forward-backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory. [ABSTRACT FROM AUTHOR]

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10 min. [ABSTRACT FROM AUTHOR]

The problem of defining suitable lines in a public transportation system (bus, railway, tram, or underground) is an important real-world problem that has also been well researched in theory. Driven by applications, it often lacks a clear description, but is rather stated in an informal way. This leads to a variety of different published line planning models. In this paper, we introduce some of the basic line planning models, identify their characteristics, and review literature on models, mathematical approaches, and algorithms for line planning. Moreover, we point out related topics as well as current and future directions of research. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dual toll pricing method to mitigate risk of hazardous materials (hazmat) transportation. We aim to simultaneously control both regular and hazmat vehicles to reduce the risk. In our model, we incorporate a new risk measure to consider duration-population-frequency of hazmat exposure. We first formulate the model as a Mathematical Program with Equilibrium Constraints (MPEC). Then we decompose the MPEC formulation into first-stage and second-stage problems. Separate methods are developed to solve each stage. A numerical example is provided and possible extensions are discussed. [ABSTRACT FROM AUTHOR]

This paper is part of an original approach of mathematical modeling for solving cyclic scheduling problems. More precisely, we consider the cyclic job shop. This kind of manufacturing systems is well fitted to medium and large production demands. Many methods have been proposed to solve the cyclic scheduling problem. Among them, we chose the exact techniques, and we focus on the mathematical programming approach. We proposed, in an earlier study, a mathematical programming model for cyclic scheduling with Work-In-Process minimization. We propose here several cutting techniques to improve the practical performances of the model resolution. Some numerical experiments are used to assess the relevance of our propositions. We made a comparison between the original mathematical model and the one endowed by the proposed cuts. This comparison is based on a set of benchmarks generated for this reason. In addition, we make another comparison based on some examples from the literature. [ABSTRACT FROM AUTHOR]

Mixed-model production is the practice of assembling different and distinct models in a line without changeovers with responding to sudden demand changes for a variety of models. In this paper, we specify sequence of models to minimize conveyer stoppages. We assume that our lines are fixed and we cannot change the balance of the lines. When the condition of lines like setup cost and demand of each model change, it is important to specify the sequence for minimizing the conveyer stoppages without balancing the line again because the main lines are fixed. We consider three objective functions simultaneously: minimizing the variation in the actual and required production capacity of the line and minimizing the objectives which increase the chance of conveyer stoppage, including: (a) minimizing the total setup time, (b) minimizing the total production variation cost, and (c) minimizing the total utility work cost. Because of conflicting objectives, we propose the fuzzy goal programming-based approach to solve the model. Finally, we present an estimator for nearness of conveyer stoppages and study about affecting of sub-lines and changing the conveyer velocity in a station for reducing stoppages. [ABSTRACT FROM AUTHOR]

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model. [ABSTRACT FROM AUTHOR]

We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modeling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particular cases for the augmenting function: the proximal Lagrangian and the sharp Lagrangian. [ABSTRACT FROM AUTHOR]

Abstract  Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data uncertainty appears in the problem is made, and it is shown how a valid inequality derived for one scenario can be made valid for other scenarios, potentially reducing solution time. Computational results amply demonstrate the effectiveness of disjunctive cuts in solving several large-scale problem instances from the literature. The results are compared to the computational results of disjunctive cuts based on the subproblem space of the formulation and it is shown that the two methods are equivalently effective on the test instances. [ABSTRACT FROM AUTHOR]

In non-cooperative models of coalition formation, players have to decide whether or not to participate in a coalition (alliance). Game theoretic analyses of the formation of alliances in games with externalities, stress the difficulties in designing self-enforcing treaties because of free-riding. The presence of a strong free-rider incentive prevents most alliances of being stable and/or effective. This paper focuses on computing stability in a game on multiple coalition formation with membership rules and different transfer schemes. A new mathematical programming notation for game theory concepts is outlined. To compute stability, the new notation is used for implementation into computer coding. Implementation and computation aspects are discussed. Numerical illustration of the algorithm shows that stability varies with the applied membership rules and transfer schemes. An application of coalition formation to International Environmental Agreements (lEAs) is provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis and comparison of semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. Our presentation is focussed on the special case of 3-SAT, but the ideas presented can in principle be extended to any instance of SAT specified by a set of boolean variables and a propositional formula in conjunctive normal form. We propose a new SDP relaxation for 3-SAT and prove some of its theoretical properties. We also show that, together with two SDP relaxations previously proposed in the literature, the new relaxation completes a trio of linearly sized relaxations with increasing rank-based guarantees for proving satisfiability. A comparison of the relative practical performances of the SDP relaxations shows that, among these three relaxations, the new relaxation provides the best tradeoff between theoretical strength and practical performance within an enumerative algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [ABSTRACT FROM AUTHOR]