A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems
The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties...
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| Veröffentlicht in: | Journal of optimization theory and applications 2018-08, Vol.178 (2), p.560-590 |
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| creator | Akbari, Fereshteh Ghaznavi, Mehrdad Khorram, Esmaile |
| description | The presented study deals with the scalarization techniques for solving multiobjective optimization problems. The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples. |
| doi_str_mv | 10.1007/s10957-018-1289-2 |
| format | Article |
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The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. Moreover, the capability of the proposed approaches is demonstrated through numerical examples.</description><identifier>ISSN: 0022-3239</identifier><identifier>EISSN: 1573-2878</identifier><identifier>DOI: 10.1007/s10957-018-1289-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Calculus of Variations and Optimal Control; Optimization ; Convexity ; Engineering ; Mathematical programming ; Mathematics ; Mathematics and Statistics ; Multiple objective analysis ; Operations Research/Decision Theory ; Optimization ; Pareto optimum ; Slack variables ; Theory of Computation</subject><ispartof>Journal of optimization theory and applications, 2018-08, Vol.178 (2), p.560-590</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Journal of Optimization Theory and Applications is a copyright of Springer, (2018). 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The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. 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The Pascoletti–Serafini scalarization technique is considered, and it is attempted to sidestep two weaknesses of this method, namely the inflexibility of the constraints and the difficulties of checking proper efficiency. To this end, two modifications for the Pascoletti–Serafini scalarization technique are proposed. First, by including surplus variables in the constraints and penalizing the violations in the objective function, the inflexibility of the constraints is resolved. Moreover, by including slack variables in the constraints, easy-to-check statements on proper efficiency are obtained. Thereafter, the two proposed modifications are combined to obtain the revised Pascoletti–Serafini scalarization method. Theorems are provided on the relation of (weakly, properly) efficient solutions of the multiobjective optimization problem and optimal solutions of the proposed scalarized problems. All the provided results are established with no convexity assumption. 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| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Convexity Engineering Mathematical programming Mathematics Mathematics and Statistics Multiple objective analysis Operations Research/Decision Theory Optimization Pareto optimum Slack variables Theory of Computation |
| title | A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems |
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