This work presents a sufficient criteria for partial efficient solutions of the cutting stock problem with two objectives. We consider two important objectives for an industry: number of processed objects (cost of raw...
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This work presents a sufficient criteria for partial efficient solutions of the cutting stock problem with two objectives. We consider two important objectives for an industry: number of processed objects (cost of raw materials) and number of different patterns (cost of setup). These optimality results are established through a new approach based on connections between discrete optimization and continuous vector optimization.
This paper is devoted to the study of unconstrained planar multiobjective location problems, where distances between points are defined by means of the Manhattan norm. We characterize the nonessential objectives and, ...
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This paper is devoted to the study of unconstrained planar multiobjective location problems, where distances between points are defined by means of the Manhattan norm. We characterize the nonessential objectives and, by eliminating them, we develop an effective algorithm for generating the whole set of efficient solutions as the union of a special family of rectangles and line segments. We prove the correctness of this algorithm, analyze its complexity, and present illustrative computational results obtained by a MATLAB-based implementation. (C) 2016 Elsevier B.V. All rights reserved.
Multi-objective optimization problems often lead to large nondominated sets, as the size of the problem or the number of objectives increases. Generating the whole nondominated set requires significant computation tim...
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Multi-objective optimization problems often lead to large nondominated sets, as the size of the problem or the number of objectives increases. Generating the whole nondominated set requires significant computation time, while most of the corresponding solutions are irrelevant to the decision maker (DM). Optimizing an aggregation function reduces the computation time and produces one or a very limited number of more focused solutions. This requires, however, the elicitation of precise preference parameters, which is often difficult and partly arbitrary, and might discard solutions of interest. An intermediate approach consists in using partial preference information with an aggregation function. In this work, we present a preference relation based on the weighted sum aggregation, where weights are not precisely defined. We give some properties of this preference relation and define the set of preferred points as the set of nondominated points with respect to this relation. We provide an efficient and generic way of generating this preferred set using any standard multi-objective optimization algorithm. This approach shows competitive performances both on computation time and quality of the generated preferred set. (C) 2017 Elsevier B.V. All rights reserved.
Recently, Luc defined a dual program for a multipleobjective linear program. The dual problem is also a multipleobjective linear problem and the weak duality and strong duality theorems for these primal and dual pro...
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Recently, Luc defined a dual program for a multipleobjective linear program. The dual problem is also a multipleobjective linear problem and the weak duality and strong duality theorems for these primal and dual problems have been established. Here, we use these results to prove some relationships between multipleobjective linear primal and dual problems. We extend the available results on single objective linear primal and dual problems to multipleobjective linear primal and dual problems. Complementary slackness conditions for efficient solutions, and conditions for the existence of weakly efficient solution sets and existence of strictly primal and dual feasible points are established. We show that primal-dual (weakly) efficient solutions satisfying strictly complementary conditions exist. Furthermore, we consider Isermann's and Kolumban's dual problems and establish conditions for the existence of strictly primal and dual feasible points. We show the existence of primal-dual feasible points satisfying strictly complementary conditions for Isermann's dual problem. Also, we give an alternative proof to establish necessary conditions for weakly efficient solutions of multipleobjective programs, assuming the Kuhn-Tucker (KT) constraint qualification. We also provide a new condition to ensure the KT constraint qualification.
Nowadays, sustainability is a major factor to consider in the decision-making process. Specifically, for companies trying to stay competitive and having some advantage in the market it is a vital issue. In this study,...
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ISBN:
(数字)9783319595139
ISBN:
(纸本)9783319595139;9783319595122
Nowadays, sustainability is a major factor to consider in the decision-making process. Specifically, for companies trying to stay competitive and having some advantage in the market it is a vital issue. In this study, we introduce a multi objective problem which aims to minimize distance and latency of a route with enough capacity to serve a set of clients. We assume that a vehicle leaves an established depot, visits all clients and returns to the depot before the end of the workday. With this bi-objective problem, we aim to improve the sustainability of the company by improving their economic and environmental contribution, through the minimization of the traveled distance of the vehicle along with the improvement of their social service by the minimization of the total waiting time of the customers. We call this problem Minimum Latency-Distance Problem (MLDP) and in this paper, we introduce a mathematical formulation which describes it.
From aeronautic equipment to aeronautic weapons,all use a large number of electronic element as it’s *** reliability of aeronautic equipment system is dependent on the reliability of aeronautic electron system to lar...
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From aeronautic equipment to aeronautic weapons,all use a large number of electronic element as it’s *** reliability of aeronautic equipment system is dependent on the reliability of aeronautic electron system to largeer *** reliability of aeronautic electron system affects the aeronautic equipment’s work and effectiveness *** this paper,a multiple objective programming model is set up from the electronic element’s redundance control and a method is given to solve this problem from the mathematical analysis.
For many practical multipleobjective network programming (MONP) problems, only integer solutions are meaningful and acceptable. Representative efficient solutions are usually generated by solving augmented weighted T...
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For many practical multipleobjective network programming (MONP) problems, only integer solutions are meaningful and acceptable. Representative efficient solutions are usually generated by solving augmented weighted Tchebycheff network programs (AWTNPs), sub-problems derived from MONP problems. However, efficient solutions generated this way are usually not integer valued. In this study, two algorithms are developed to construct integer efficient solutions starting from fractional efficient solutions. One algorithm finds a single integer efficient solution in the neighborhood of the fractional efficient solution. The other enumerates all integer efficient solutions in the same neighborhood. Theory supporting the proposed algorithms is developed. Two detailed examples are presented to demonstrate the algorithms. Computational results are reported. The best integer efficient solution is very close, if not equal, to the integer optimal solution. The CPU time taken to find integer efficient solutions is negligible, when compared with that taken to solve AWTNPs. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 362-375 2011
This paper introduces a novel and practical integration of the inventory control and vendor selection problems for a manufacturing system that provides multiple products for several stores located in different places....
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This paper introduces a novel and practical integration of the inventory control and vendor selection problems for a manufacturing system that provides multiple products for several stores located in different places. The replenishment policy of each store is the economic order quantity under a multi-sourcing strategy in which the demand rate decreases as the selling price increases. In this strategy, the ordered quantity of each store for each product can be replenished by a set of selected vendors among all. In addition, the selected vendors can deliver the required products within a certain time window based on a soft time-window mechanism. The aim is to minimize the total system cost and delivery schedule violations, simultaneously. A trade-off between the two objectives is generated using the min-max approach to obtain near fair non-dominated solutions. As the problem is known to be NP-hard, a novel meta-heuristic algorithm called binary-continuous differential evolution (BCDE) is developed to make the original differential evolution capable of solving both binary and continuous optimization problems. Moreover, an improved genetic algorithm with a multi-parent crossover operator is designed to solve the problem. While the applicability of the proposed approach and the solution methodologies are demonstrated, the solution algorithms are tuned and their performances are analyzed and compared statistically. Finally, sensitivity analyses on the size of the soft time-window and the bandwidth factor of the BCDE algorithm are conducted. (C) 2016 Elsevier Ltd. All rights reserved.
Consumers, industry, and government entities are becoming increasingly concerned about the issue of global warming. With this in mind, manufacturers have begun to develop products with consideration of low-carbon. In ...
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Consumers, industry, and government entities are becoming increasingly concerned about the issue of global warming. With this in mind, manufacturers have begun to develop products with consideration of low-carbon. In recent years, many companies are utilizing product families to satisfy various customer needs with lower costs. However, little research has been conducted on the development of a product family that considers environmental factors. In this paper, a low-carbon product family design that integrates environmental concerns is proposed. To this end, a new method of platform planning is investigated with considerations of cost and greenhouse gas (GHG) emission of a product family simultaneously. In this research, a lowcarbon product family design problem is described at first, and then a GHG emission model of product family is established. Furthermore, to support lowcarbon product family design, an optimization method is applied to make a significant trade-off between cost and GHG emission to implement a feasible platform planning. Finally, the effectiveness of the proposed method is illustrated through a case study. (C) 2016 Elsevier Ltd. All rights reserved.
As one of the most challenging combinatorial optimization problems in scheduling, the resource-constrained project scheduling problem (RCPSP) has attracted numerous scholars' interest resulting in considerable res...
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As one of the most challenging combinatorial optimization problems in scheduling, the resource-constrained project scheduling problem (RCPSP) has attracted numerous scholars' interest resulting in considerable research in the past few decades. However, most of these papers focused on the single objective RCPSP;only a few papers concentrated on the multi-objective resource-constrained project scheduling problems (MORCPSP). Inspired by a procedure called electromagnetism (EM), which can help a generic population based evolutionary search algorithm to obtain good results for single objective RCPSP, in this paper we attempt to extend EM and integrate it into three reputable state-of-the-art multi-objective evolutionary algorithms (MOEAs) i.e. non-dominated sorting based multi-objective evolutionary algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2) and multi-objective evolutionary algorithm based on decomposition (MOEA/D), for MORCPSP. We aim to optimize makespan and total tardiness. Empirical analysis based on standard benchmark datasets are conducted by comparing the versions of integrating EM to NSGA-II, SPEA2 and MOEND with the original algorithms without EM. The results demonstrate that EM can improve the performance of NSGA-II and SPEA2, especially for NSGA-II. (C) 2015 Elsevier B.V. All rights reserved.
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