MONSS: A multi-objective nonlinear simplex search approach. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Zapotecas-Martínez, Saúl; Coello, Carlos A. Coello
• Is Part Of: Engineering optimization. Volume 48:Issue 1(2016)
• Page Start: 16
• Page End: 38
• Publication Date: 2016-01-02
• Subjects: multi-objective optimization -- multi-objective nonlinear simplex search -- multi-objective direct search methods; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2014.992889
• Languages: English
• ISSNs: 0305-215X

Abstract

Abstract : This article presents a novel methodology for dealing with continuous box-constrained multi-objective optimization problems (MOPs). The proposed algorithm adopts a nonlinear simplex search scheme in order to obtain multiple elements of the Pareto optimal set. The search is directed by a well-distributed set of weight vectors, each of which defines a scalarization problem that is solved by deforming a simplex according to the movements described by Nelder and Mead's method. Considering an MOP with n decision variables, the simplex is constructed using n +1 solutions which minimize different scalarization problems defined by n +1 neighbor weight vectors. All solutions found in the search are used to update a set of solutions considered to be the minima for each separate problem. In this way, the proposed algorithm collectively obtains multiple trade-offs among the different conflicting objectives, while maintaining a proper representation of the Pareto optimal front. In this article, it is shown that a well-designed strategy using just mathematical programming techniques can be competitive with respect to the state-of-the-art multi-objective evolutionary algorithms against which it was compared.