Generation of Pareto optimal solutions for multi-objective optimization problems via a reduced interior-point algorithm

B El-Sobky,Y Abo-Elnaga

doi:10.1080/16583655.2018.1494422

Abstract

ABSTRACTIn this paper, a reduced interior-point (RIP) algorithm is introduced to generate a Pareto optimal front for multi-objective constrained optimization (MOCP) problem. A weighted Tchebychev metric approach is used together with achievement scalarizing function approach to convert MOCP problem to a single-objective constrained optimization (SOCO) problem. An active-set technique is used together with a Coleman–Li scaling matrix and a decrease interior-point method to solve SOCO problem. A Matlab implementation of RIP algorithm was used to solve three cases and application. The results showed that the RIP algorithm is promising when compared with well-known algorithms and the computations may be superior relevant for comprehending real-world application problems.

Highlights

A wide variety of problems in engineering, industry and many other fields involves multi-objective optimization problems (MOPs)
In multi-objective constrained optimization (MOCP) problem, there is more than one objective function and there is no single optimal solution that at the same time improves all the objective functions
Master steps of reduced interior-point (RIP) algorithm to solve single-objective constrained optimization (SOCO) problem are offered in the following algorithm

Summary

Introduction

A wide variety of problems in engineering, industry and many other fields involves multi-objective optimization problems (MOPs). We consider in this paper on the following MOCP problem: minimize [f1(x), . It is utilized to convert MOCP problem to the SOCO problem by minimizing the distance between the ideal objective vector and the feasible objective region. If the reference point utilized as a part of the objective vector inside the feasible objective region, the minimal distance to it is zero and we don’t obtain the PO solution. Many authors have used active-set algorithms to solve the general SOCO problems. The augmented Lagrangian function associated with Problem (5) without the bounded constraint α ≤ x ≤ β is defined as follows:. We offered a detailed description of the main steps to RIP algorithm to solve the system (15)

A reduced interior-point algorithm

Implementations

Test problems

Conclusion