A novel approach for solving stochastic problems with multiple objective functions

Ramzi Kasri,Fatima Bellahcene

doi:10.1051/ro/2021112

Abstract

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.

Highlights

Multiobjective stochastic linear programming (MOSLP) is an appropriate tool to model many concrete reallife problems because it is not obvious to have the complete data about the parameters
In order to obtain solutions for MOSLP problems, it is necessary to combine techniques used in stochastic programming and multiobjective programming
Ben Abdelaziz [8] and Ben Abdelaziz et al [9] qualified as multiobjective approach the perspective which transform first, the stochastic multiobjective problem into its equivalent multiobjective deterministic problem, and stochastic approach the technique that transform in first the stochastic multiobjective problem into a monobjective stochastic problem

Summary

Introduction

Multiobjective stochastic linear programming (MOSLP) is an appropriate tool to model many concrete reallife problems because it is not obvious to have the complete data about the parameters. To deal with this type of problems it is required to introduce a randomness framework. Such a class of problems includes investment and energy resources planning [2,32,35], manufacturing systems in production planning [12,14], mineral blending [18], water use planning [8, 10] and multi-product batch plant design [36]. In order to obtain solutions for MOSLP problems, it is necessary to combine techniques used in stochastic programming and multiobjective programming. Two approaches can be considered, both of them involve a double transformation, consisting on the transformation of the multiobjective problem into a monoobjective problem and the stochastic problem into its equivalent deterministic one. Ben Abdelaziz [8] and Ben Abdelaziz et al [9] qualified as multiobjective approach the perspective which transform first, the stochastic multiobjective problem into its equivalent multiobjective deterministic problem, and stochastic approach the technique that transform in first the stochastic multiobjective problem into a monobjective stochastic problem

Objectives

Results

Conclusion