The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper, we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to ob...
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The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper, we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to obtain or approximate the set of efficient solutions. In the first step, we classify and briefly describe the existing works that are essentially based on the use of metaheuristics. In the second step, we propose the adaptation of the two-phase Pareto local search (2PPLS) to the resolution of the MOMKP. With this aim, we use a very large scale neighborhood in the second phase of the method, that is the PLS. We compare our results with state-of-the-art results and show that the results we obtained were never reached before by heuristics for biobjective instances. Finally, we consider the extension to three-objective instances.
We develop a discrete-time approximation technique dealing with the time-cost trade-off problem in PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang dist...
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We develop a discrete-time approximation technique dealing with the time-cost trade-off problem in PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. It is also assumed that the amount of resource allocated to each activity is controllable. Then, we construct an optimal control problem with three conflicting objective functions. Solving this optimal control problem, optimally, is impossible. Therefore, a discrete-time approximation technique is applied to solve the original multi-objective optimal control problem, using goal attainment method. To show the advantages of the proposed technique, we also develop a Simulated Annealing (SA) algorithm to solve the problem, and compare the discrete-time approximation results against the SA and also the genetic algorithm results.
The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero compone...
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The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the 0-norm) of the solution. We propose to deal with the 0-norm by means of concave approximations depending on a smoothing parameter. We state some equivalence results between the original nonsmooth problem and the smooth approximated problem. We are thus able to define an algorithm aimed to find sparse solutions and based on the steepest descent framework for smoothmultiobjective optimization. The numerical results obtained on a classical application in portfolio selection and comparison with existing codes show the effectiveness of the proposed approach.
In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to e...
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In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn-Tucker or Fritz John points are efficient solutions. Recent papers are improved. We provide an example to show this improvement and illustrate these classes of functions and results. (C) 2009 Elsevier B.V. All rights reserved,
Rush orders are immediate customer demands that exceed the expectation of a currently effective MPS (master production schedule). Decision-makers are often hesitant in the decision of accepting such orders. This paper...
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Rush orders are immediate customer demands that exceed the expectation of a currently effective MPS (master production schedule). Decision-makers are often hesitant in the decision of accepting such orders. This paper presents a multiple criteria decision-making model for justifying the acceptance of rush orders for an assembly-to-order production system. Four criteria or production objectives are simultaneously considered and a multiple objective programming technique, the e-constraints approach, is adopted to solve the decision-making problem. This model could give the cost estimation for producing a rush order under various combinations of production objectives. The computed cost value could serve as a Valuable reference for justifying the economics of accepting the rush order, and help to determine its pricing strategy.
The paper presents a method for ranking chosen efficient solutions in a multi-objective linear programming (MOLP) problem through the use of sensitivity analysis. Reduced tolerance, which is a measure of sensitivity, ...
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The paper presents a method for ranking chosen efficient solutions in a multi-objective linear programming (MOLP) problem through the use of sensitivity analysis. Reduced tolerance, which is a measure of sensitivity, is used in the ranking method. The presented approach can be applied to a number of MOLP problems in which sensitivity analysis is important for a decision-maker. In the paper, applications of the presented methodology are shown in a transportation problem and the market model.
We introduce the class of MP-pseudoinvex multiobjective optimal control problems. We show that the concept of MP-pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every contr...
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We introduce the class of MP-pseudoinvex multiobjective optimal control problems. We show that the concept of MP-pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every control process satisfying Pontryagin's maximum principle is an optimal process are necessarily MP-pseudoinvex problems. Moreover, a sub-class of the MP-pseudoinvex problems, which we call MP-invex multiobjective optimal control problems, is defined. We prove that the set of optimal solutions of MP-invex multiobjective problems coincides with the set of optimal solutions of a related scalar problem. Copyright (C) 2008 John Wiley & Sons, Ltd.
Interactive multiobjective optimization methods operate iteratively so that a decision maker directs the solution process by providing preference information, and only solutions of interest are generated. These method...
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Interactive multiobjective optimization methods operate iteratively so that a decision maker directs the solution process by providing preference information, and only solutions of interest are generated. These methods limit the amount of information considered in each iteration and support the decision maker in learning about the trade-offs. Many interactive methods have been developed, and they differ in technical aspects and the type of preference information used. Finding the most appropriate method for a problem to be solved is challenging, and supporting the selection is crucial. Published research lacks information on the conducted experiments' specifics (e.g. questions asked), making it impossible to replicate them. We discuss the challenges of conducting experiments and offer realistic means to compare interactive methods. We propose a novel questionnaire and experimental design and, as proof of concept, apply them in comparing two methods. We also develop user interfaces for these methods and introduce a sustainability problem with multipleobjectives. The proposed experimental setup is reusable, enabling further experiments.
The steepest descent method proposed by Fliege and Svaiter has motivated the research on descent meth-ods for multiobjective optimization, which has received increasing attention in recent years. However, empirical re...
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The steepest descent method proposed by Fliege and Svaiter has motivated the research on descent meth-ods for multiobjective optimization, which has received increasing attention in recent years. However, empirical results show that the Armijo line search often results in a very small stepsize along the steepest descent direction, which decelerates the convergence seriously. This paper points out the issue is mainly due to imbalances among objective functions. To address this issue, we propose a Barzilai-Borwein de-scent method for multiobjective optimization (BBDMO), which dynamically tunes gradient magnitudes using Barzilai-Borwein's rule in direction-finding subproblem. We emphasize that the BBDMO produces a sequence of new descent directions compared to Barzilai-Borwein's method proposed by Morovati et al. With monotone and nonmonotone line search techniques, we prove that accumulation points generated by BBDMO are Pareto critical points, respectively. Furthermore, theoretical results indicate that the Armijo line search can achieve a better stepsize in BBDMO. Finally, comparative results of numerical experiments are reported to illustrate the efficiency of BBDMO and verify the theoretical results. & COPY;2023 Elsevier B.V. All rights reserved.
Data Envelopment Analysis (DEA) is one of the methods that have been proposed to determine the weights in a ranked voting system. DEA solves one model corresponding to each candidate and evaluates candidates with thei...
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Data Envelopment Analysis (DEA) is one of the methods that have been proposed to determine the weights in a ranked voting system. DEA solves one model corresponding to each candidate and evaluates candidates with their own weights. However, sometimes solving only one model, and evaluating the candidates based on a common set of weights, is preferred. In this paper, some drawbacks of existing models are explained and new approaches for determining a common set of weights are proposed. Numerical examples are utilized to illustrate the content of the paper.
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