A new exact algorithm for bi-objective linear integer problems is presented, based on the classic epsilon-constraint method and algebraic test sets for single-objective linear integer problems. Our method provides the...
详细信息
A new exact algorithm for bi-objective linear integer problems is presented, based on the classic epsilon-constraint method and algebraic test sets for single-objective linear integer problems. Our method provides the complete Pareto frontier N of non-dominated points and, for this purpose, it considers exactly vertical bar N vertical bar single-objective problems by using reduction with test sets instead of solving with an optimizer. Although we use Grobner bases for the computation of test sets, which may provoke a bottleneck in principle, the computational results are shown to be promising, especially for unbounded knapsack problems, for which any usual branch-and-cut strategy could be much more expensive. Nevertheless, this algorithm can be considered as a potentially faster alternative to IP-based methods when test sets are available. (C) 2019 Elsevier B.V. All rights reserved.
This paper presents a new multi-objective fuzzy mathematical model for the cellular manufacturing system (CMS) design and its solution methodology. The aim of the proposed model is to handle two important problems of ...
详细信息
This paper presents a new multi-objective fuzzy mathematical model for the cellular manufacturing system (CMS) design and its solution methodology. The aim of the proposed model is to handle two important problems of CMS design called cell formation and exceptional elements simultaneously in fuzzy environment. The objective functions of the model are minimization of the cost of exceptional element elimination, minimization of the number of outer cell operations and maximization of the utilized machine capacity. The fuzziness stems from model parameters which are part demand, machine capacity and the exceptional elements' elimination costs. To illustrate the model, an example problem with fuzzy extension is adopted from literature and computational results are obtained by using the two-phased solution procedure proposed by Arikan and Gungor [F. Arikan, Z. Gungor, A two-phased approach for multi-objectiveprogramming problems with fuzzy coefficients, Information Science 177 (2007), 5191-5202]. The approach is performed to reach simultaneous optimal solutions for all objective functions. The model solutions are investigated by using well-known performance measures and also three problem-specific performance measures are proposed. The model is capable of expressing vagueness of all the system parameters and gives the decision-maker (DM) alternative decision plans for different grades of precision. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency...
详细信息
In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical epsilon-constraint method. objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical epsilon-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided. (C) 2008 Elsevier B.V. All rights reserved.
The aim of this paper is to provide a dynamic programming formulation for the spanning tree problem (), which allows several instances of the classical to be addressed. The spanning tree structure is modelled with sta...
详细信息
The aim of this paper is to provide a dynamic programming formulation for the spanning tree problem (), which allows several instances of the classical to be addressed. The spanning tree structure is modelled with states and transition between states, defining a state-space. Several properties are shown and optimality conditions are given. Once the theoretical fundamentals of the proposed formulation are derived, the multi-objective spanning tree problem () is addressed. This problem arises in the telecommunications and transportation sectors. In these contexts, handling different criteria simultaneously plays a crucial role. The scientific literature provides several works that focus on the bi-objective version of the considered problem, in which only two criteria are taken into account. To the best of our knowledge, no works provide optimal methods to address the with an arbitrary number of objective functions. In this paper we extend the proposed dynamic programming formulation to model and solve the with criteria.
A general method to solve multi-objective de novo programming problem having both maximizing and minimizing types of objectives has been proposed. The method in one hand provides a platform to get a maximum number of ...
详细信息
A general method to solve multi-objective de novo programming problem having both maximizing and minimizing types of objectives has been proposed. The method in one hand provides a platform to get a maximum number of objectives to their targeted ideal (maximum/minimum) values and on the other hand gives the decision-maker flexibility to choose the objectives according to his/her priority towards the attainment of their ideal values. The proposed method has been illustrated with a numerical problem and a real-life example. A comparison with two other existing methods for such problems has also been provided.
Recently Georgiev, Luc, and Pardalos (2013), [Robust aspects of solutions in deterministic multipleobjective linear programming, European Journal of Operational Research, 229(1), 29-36] introduced the notion of robus...
详细信息
Recently Georgiev, Luc, and Pardalos (2013), [Robust aspects of solutions in deterministic multipleobjective linear programming, European Journal of Operational Research, 229(1), 29-36] introduced the notion of robust efficient solutions for linear multi-objective optimization problems. In this paper, we extend this notion to nonlinear case. It is shown that, under the compactness of the feasible set or convexity, each robust efficient solution is a proper efficient solution. Some necessary and sufficient conditions for robustness, with respect to the tangent cone and the non-ascent directions, are proved. An optimization problem for calculating a robustness radius followed by a comparison between the newly-defined robustness notion and two existing ones is presented. Moreover, some alterations of objective functions preserving weak/proper/robust efficiency are studied. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programm...
详细信息
In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM. (C) 2007 Elsevier Inc. All rights reserved.
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-objective Integer programming (MOIP) problem. We significantly improve the earlier recursiv...
详细信息
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-objective Integer programming (MOIP) problem. We significantly improve the earlier recursive algorithm of A-zlen and Azizoglu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.
This paper presents a fuzzy goal programming (FGP) procedure for multi objective quadratic programming problem. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functio...
详细信息
This paper presents a fuzzy goal programming (FGP) procedure for multi objective quadratic programming problem. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them and suitable membership function is defined for each objectives. Then achievement of the highest membership value of each of fuzzy goals is formulated by minimizing the negative deviational variables. The proposed methodology and its efficiency over traditional utility function approach are illustrated by the numerical examples.
Organizations have to allocate resources, time, and workforce in many projects at the same time. Selection and scheduling of the projects have a significant impact on effective project management. However, most of the...
详细信息
Organizations have to allocate resources, time, and workforce in many projects at the same time. Selection and scheduling of the projects have a significant impact on effective project management. However, most of the studies in the literature do not solve the selection and scheduling problems simultaneously. This study aims to design an interactive process to integrate selection and scheduling processes in the project management. For this purpose, a new multi objectiveprogramming model is proposed. The project scores are presented as belief de-grees (i.e., distributions to linguistic term levels) that are gathered as a result of the weighted cumulative belief degree approach. By the use of the belief degrees, projects could be selected and scheduled based on the satis-faction level of the problem owner. The proposed model considers conditions and restrictions in management of business development projects such as the progress percentage of the projects in a period, the complementary and mutual exclusive relations between projects, etc. An interactive solution procedure is developed in order to solve the proposed model. The proposed model and the solution procedure are applied in an information technology company for their business development projects
暂无评论