Pareto front approximation with adaptive weighted sum method in multiobjective simulation optimization

Abstract

This work proposes a new method for approximating the Pareto front of a multi-objective simulation optimization problem (MOP) where the explicit forms of the objective functions are not available. The method iteratively approximates each objective function using a metamodeling scheme and employs a weighted sum method to convert the MOP into a set of single objective optimization problems. The weight on each single objective function is adaptively determined by accessing newly introduced points at the current iteration and the non-dominated points so far. A trust region algorithm is applied to the single objective problems to search for the points on the Pareto front. The numerical results show that the proposed algorithm efficiently generates evenly distributed points for various types of Pareto fronts.

Multiobjective optimization using an adaptive weighting scheme

“…The general idea is to systematically move towards the Pareto front at the end of every iteration by adaptively filling the gaps between the nondominated points obtained so far. The biobjective optimization method proposed in (Deshpande et al, 2013) and (Deshpande et al, 2013a) by the authors was based on the scalarization scheme of Ryu et al (2009). However, the same adaptive weighting scheme does not work for multiobjective problems with p > 2 objectives.…”

“…However, the same adaptive weighting scheme does not work for multiobjective problems with p > 2 objectives. The algorithm presented in this paper is an alternative approach for generalizing the adaptive weighting scheme of Ryu et al (2009) to problems with more than two objectives. The algorithm employs a hybrid approach using two derivative free direct search techniques -a deterministic global search algorithm DIRECT (Jones et al, 1993) for global exploration of the design space and a local direct search method MADS (mesh adaptive direct search) (Audet and Dennis 2006) to exploit the design space by fine tuning the potentially optimal regions returned by DIRECT and to speed up the convergence.…”

Pareto- Front Generation by Classical and Meta-heuristic Methods in Flexible Job Shop Scheduling with Multiple Objectives

“…The classical and flexible methods can solve FJSSP. Some of the classical and flexible methods are based on WS method [3]. The WS method can convert multi objective optimization problem into single objective by using objective functions [4] in the multi objective decision theory.…”

A comparison of two metamodel-based methodologies for multiple criteria simulation optimization using an injection molding case study

“…Recent contributions to the area of multiobjective optimization that use metamodeling are given for stochastic simulations by Dallino and Kleijnen [4] , Ryu et al [5] , and Zakerifar et al [6] , and for deterministic simulations by Emmerich et al [7] , Keane [8] , and Svenson [2] . Among the metamodels used are response surface models, quadratic regression models, and kriging models.…”