Box-constrained multi-objective optimization: A gradient-like method without “a priori” scalarization

The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective func...

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Vydáno v:European journal of operational research Ročník 188; číslo 3; s. 662 - 682
Hlavní autoři: Miglierina, E., Molho, E., Recchioni, M.C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.08.2008
Elsevier
Elsevier Sequoia S.A
Edice:European Journal of Operational Research
Témata:
Algorithms
Applied sciences
Approximation
Descent directions
Exact sciences and technology
Gradient-like method
Interior point method
Mathematical programming
Multiple objective programming
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Problem solving
Pseudogradient
Studies
Vector space
Interior point method
Descent directions
Gradient-like method
Pseudogradient
Multiple objective programming
Pareto optimum
Limit point
Multiobjective programming
Scalarization
Critical point
Non linear programming
Dynamical system
Approximation algorithm
Constrained optimization
Karush Kuhn Tucker method
Objective function
Gradient method
Vector field
ISSN:0377-2217, 1872-6860
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Popis
Shrnutí:The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective function. The method does not rely on an “a priori” scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box. The key tool to define the mentioned vector field is the notion of vector pseudogradient. We prove that the limit points of the solutions of the system satisfy the Karush–Kuhn–Tucker (KKT) first order necessary condition for the box-constrained multi-objective optimization problem. These results allow us to develop an algorithm to solve box-constrained multi-objective optimization problems. Finally, we consider some test problems where we apply the proposed computational method. The numerical experience shows that the algorithm generates an approximation of the local optimal Pareto front representative of all parts of optimal front.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2007.05.015