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A flexible job shop cell scheduling with sequence-dependent family setup times and intercellular transportation times using conic scalarization method

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2019年第6期26卷 2410-2431页

作者： Deliktas, Derya Torkul, Orhan Ustun, Ozden Sakarya Univ Dept Ind Engn Sakarya Turkey Dumlupinar Univ Dept Ind Engn Kutahya Turkey

In this paper, we propose novel mathematical models involving both single- and biobjective functions that deal with a flexible job shop scheduling problem in cellular manufacturing environment by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence-dependent family setup times, and recirculation. The problem has been known as NP-hard. The proposed models have been tested and solved using Lingo 11.0 with minimization of makespan for the problems involving about 4 cells, 4 part families, 15 parts, and 12 machines. The most suitable model among the proposed single-objective models is determined using the test results. Then, another objective function as total tardiness is added to this model. The obtained biobjective model is solved using the scalarization methods, the weighted sum method, e-constraint method, and conic scalarization method (CSM), in order to convert the mathematical model's objectives into a single-objective function. By utilizing these scalarization methods, the Pareto effective solutions are generated for a specific test problem. The advantages of the CSM are demonstrated by considering the Pareto effective solutions.

关键词： cell scheduling intercell move sequence-dependent family setup time mixed nonlinear integer programming multiobjective optimization conic scalarization method

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conic scalarization method in Multiobjective Optimization and Relations with Other scalarization methods 3rd

Conic Scalarization Method in Multiobjective Optimization an...

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3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO)

作者： Kasimbeyli, Refail Ozturk, Zehra Kamisli Kasimbeyli, Nergiz Yalcin, Gulcin Dinc Icmen, Banu Aandolu Univ Dept Ind Engn Fac Engn Iki Eylul Campus TR-26555 Eskisehir Turkey

ISBN: (纸本)9783319181615;9783319181608

The paper presents main features of the conic scalarization method in multiobjective optimization. The conic scalarization method guarantees to generate all proper efficient solutions and does not require any kind of convexity or boundedness conditions. In addition the preference and reference point information of the decision maker is taken into consideration by this method. In this paper, relations with other scalarization methods are investigated and it is shown that some efficient solutions computed by the Pascoletti-Serafini and the Benson's scalarization methods, can be obtained by the conic scalarization method.

关键词： conic scalarization method Weighted sum method Epsilon constraint method Benson's method Weighted Chebyshev method Pascoletti-Serafinimethod Multiobjective optimization proper efficiency

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A conic scalarization method in multi-objective optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第2期56卷 279-297页

作者： Kasimbeyli, Refail Izmir Univ Econ Dept Ind Syst Engn Fac Engn & Comp Sci TR-35330 Izmir Turkey

This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution.

关键词： Separable cone Cone separation theorem Augmented dual cones Sublinear scalarizing functions conic scalarization method Multi-objective optimization Proper efficiency

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Comparison of Some scalarization methods in Multiobjective Optimization: Comparison of scalarization methods

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2019年第5期42卷 1875-1905页

作者： Kasimbeyli, Refail Ozturk, Zehra Kamisli Kasimbeyli, Nergiz Yalcin, Gulcin Dinc Erdem, Banu Icmen Anadolu Univ Fac Engn Dept Ind Engn Iki Eylul Campus TR-26555 Eskisehir Turkey

The paper presents an analysis, characterizations and comparison of six commonly used scalarization methods in multiobjective optimization. The properties of these methods are investigated with respect to the basic characteristics such as ordering cone, convexity and boundedness, the ability of generating proper efficient solutions, the ability to consider reference points which is a choice of decision maker as a solution and weighting preferences of decision maker, the number of additional constraints and decision variables. The paper also presents new characteristics for these methods and relations between them. The main characteristics of these scalarization methods are illustrated on the same example.

关键词： conic scalarization method Weighted sum method epsilon-Constraint method Benson's method Weighted Chebyshev method Pascoletti-Serafini method Multiobjective optimization Proper efficiency

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Existence and characterization theorems in nonconvex vector optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第1期62卷 155-165页

作者： Kasimbeyli, Nergiz Anadolu Univ Fac Engn Dept Ind Engn TR-26555 Eskisehir Turkey

This paper presents existence conditions and characterization theorems for minimal points of nonconvex vector optimization problems in reflexive Banach spaces. Characterization theorems use special class of monotonically increasing sublinear scalarizing functions which are defined by means of elements of augmented dual cones. It is shown that the Hartley cone-compactness is necessary and sufficient to guarantee the existence of a properly minimal point of the problem. The necessity is proven in the case of finite dimensional space.

关键词： Vector optimization Nonlinear separation theorem Augmented dual cone Sublinear scalarizing functions conic scalarization method Proper efficiency Existence theorem

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Solution to scalarized environmental economic power dispatch problem by using genetic algorithm

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2012年第1期38卷 54-62页

作者： Yasar, Celal Ozyon, Serdar Dumlupinar Univ Fac Engn Dept Elect & Elect Engn TR-43100 Kutahya Turkey

Nowadays, the widespread use of fossil based fuels in power generation units requires the consideration of the environmental pollution. Therefore, in this study, the solution of scalarized environmental economic power dispatch problem in which the environmental pollution has been taken into consideration has been analyzed by using genetic algorithm (GA). In order to turn the environmental economic power dispatch problem into the single objective optimization problem, the conic scalarization method (CSM) has been used. Also, weighted sum method (WSM) has been utilized in the scalarization of the same problem for comparison with CSM. The solution algorithm is tested for the electric power system of thermal units which has been solved by different methods in the literature. The best solution values that give minimum total fuel cost and minimum total emission values have been obtained (Pareto optimal values) for different weight values under electric constraints via CSM and WSM. The obtained Pareto optimal values for different scalarization methods have been compared with each other. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Environmental economic power dispatch conic scalarization method Genetic algorithm Pareto optimal solutions

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