Box-constrained multi-objective optimization: A gradient-like method without “a priori” scalarization |
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Authors: | E Miglierina E Molho MC Recchioni |
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Institution: | 1. Dipartimento di Economia, Università degli Studi dell’Insubria via Monte Generoso 71, 21100 Varese, Italy;2. Dipartimento di Ricerche Aziendali, Università degli Studi di Pavia via San Felice 5, 27100 Pavia, Italy;3. Dipartimento di Scienze Sociali “D. Serrani”, Università Politecnica delle Marche Piazza Martelli 8, 60121 Ancona, Italy |
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Abstract: | 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. |
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Keywords: | Multiple objective programming Gradient-like method Interior point method Descent directions Pseudogradient |
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