We propose a new distributed heuristic for approximating the Pareto set of bi-objective optimization problems. Our approach is at the crossroads of parallel cooperative computation, objective space decomposition, and ...
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We propose a new distributed heuristic for approximating the Pareto set of bi-objective optimization problems. Our approach is at the crossroads of parallel cooperative computation, objective space decomposition, and adaptive search. Given a number of computing nodes, we self-coordinate them locally, in order to cooperatively search different regions of the Pareto front. This offers a trade-off between a fully independent approach, where each node would operate independently of the others, and a fully centralized approach, where a global knowledge of the entire population is required at every step. More specifically, the population of solutions is structured and mapped into computing nodes. As local information, every node uses only the positions of its neighbors in the objective space and evolves its local solution based on what we term a 'localized fitness function'. This has the effect of making the distributed search evolve, over all nodes, to a high quality approximation set, with minimum communications. We deploy our distributed algorithm using a computer cluster of hundreds of cores and study its properties and performance on rho MNK-landscapes. Through extensive large-scale experiments, our approach is shown to be very effective in terms of approximation quality, computational time and scalability. (C) 2014 Elsevier B.V. All rights reserved.
In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general form...
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In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the epsilon-constraint method, the Benson method, the hybrid method and the elastic epsilon-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between epsilon-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and epsilon-optimal solutions of the introduced scalarized problem are achieved. (C) 2013 Elsevier B.V. All rights reserved.
In this paper we study an inexact steepest descent method for multicriteria optimization whose step-size comes with Armijo's rule. We show that this method is well-defined. Moreover, by assuming the quasi-convexit...
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In this paper we study an inexact steepest descent method for multicriteria optimization whose step-size comes with Armijo's rule. We show that this method is well-defined. Moreover, by assuming the quasi-convexity of the multicriteria function, we prove full convergence of any generated sequence to a Pareto critical point. As an application, we offer a model for the Psychology's self regulation problem, using a recent variational rationality approach. (C) 2014 Elsevier B.V. All rights reserved.
In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem wi...
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In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem with truck capacity. Two objectives are considered in this research, reduction of distribution cost and balance of workloads for drivers in the routing stage. Here, we present a mathematical formulation for the bi-objective TLRP and propose a new representation for the TLRP based on priorities. This representation lets us manage the problem easily and reduces the computational effort, plus, it is suitable to be used with both local search based and evolutionary approaches. In order to demonstrate its efficiency, it was implemented in two metaheuristic solution algorithms based on the Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization (SSPMO) and on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) strategies. Computational experiments showed efficient results in solution quality and computing time. (C) 2013 Elsevier B.V. All rights reserved.
This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to a...
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This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to an efficient solution. A numerical example shows that this approach performs better than some existing algorithms. Randomly generated MOLFP problems are also solved to demonstrate the performance of new introduced algorithm. (C) 2013 Elsevier Inc. All rights reserved.
This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively,...
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This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.
One of the major issues for Markowitz mean-variance model is the errors in estimations cause "corner solutions" and low diversity in the portfolio. In this paper, we compare the mean-variance efficiency, rea...
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One of the major issues for Markowitz mean-variance model is the errors in estimations cause "corner solutions" and low diversity in the portfolio. In this paper, we compare the mean-variance efficiency, realized portfolio values, and diversity of the models incorporating different entropy measures by applying multiple criteria method. Differing from previous studies, we evaluate twenty-three portfolio over-time rebalancing strategies with considering short-sales and various transaction costs in asset diversification. Using the data of the most liquid stocks in Taiwan's market, our finding shows that the models with Yager's entropy yield higher performance because they respond to the change in market by reallocating assets more effectively than those with Shannon's entropy and with the minimax disparity model. Furthermore, including entropy in models enhances diversity of the portfolios and makes asset allocation more feasible than the models without incorporating entropy. (C) 2014 Elsevier Inc. All rights reserved.
We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design prob...
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We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent different and conflicting objectives associated with the scenarios. We utilize the interactive classification-based multiobjective optimization method NIMBUS for assessing the relative optimality of the current solution in different scenarios. This information can be utilized when considering the next step of the overall solution process. Decision making is performed by giving special attention to individual scenarios. We demonstrate our method with an example in portfolio optimization.
The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management deci...
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The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers' conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems. (C) 2013 Elsevier B.V. All rights reserved.
Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multipleobjectives in decision models. In a mathem...
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Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multipleobjectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p - 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known epsilon-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved. (C) 2013 Elsevier B.V. All rights reserved.
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