An extension of the non-inferior set estimation algorithm for many objectives

• Published in: European journal of operational research Vol. 284; no. 1; pp. 53 - 66
• Main Authors: Raimundo, Marcos M., Ferreira, Paulo A.V., Von Zuben, Fernando J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2020
• Subjects: Automatic estimation of a non-inferior set; Multi-objective optimization; Weighted sum method; Automatic estimation of a non-inferior set; Weighted sum method; Multi-objective optimization
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2019.11.017

•An adaptive algorithm for many objectives using the weighted sum method.•A deterministic inner and outer approximation method.•Scalability improved with combinatorial programming instead of facet enumeration.•Proved effectiveness of the proposed approach in hypervolume and computing time.•A deeper inquiry into the weighted sum method and its related adaptive algorithm. This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum method scalarization problems. The approach is called MONISE (Many-Objective NISE) because it represents an extension of the well-known non-inferior set estimation (NISE) algorithm, which was originally conceived to deal with two-dimensional objective spaces. The proposal is endowed with the following characteristics: (1) uses a mixed-integer linear programming formulation to operate in two or more dimensions, thus properly supporting many (i.e., three or more) objectives; (2) relies on an external algorithm to solve the weighted sum method scalarization problem to optimality; and (3) creates a faithful representation of the Pareto frontier in the case of convex problems, and a useful approximation of it in the non-convex case. Moreover, when dealing specifically with two objectives, some additional properties are portrayed for the estimated non-inferior set. Experimental results validate the proposal and indicate that MONISE is competitive, in convex and non-convex (combinatorial) problems, both in terms of computational cost and the overall quality of the non-inferior set, measured by the acquired hypervolume.