A Novel Multiobjective Optimization Method Based on Sensitivity Analysis

Tiane Li,Zhengzheng Lu,Xiaoying Sun,Yue Wu

doi:10.1155/2016/6012805

Abstract

For multiobjective optimization problems, different optimization variables have different influences on objectives, which implies that attention should be paid to the variables according to their sensitivity. However, previous optimization studies have not considered the variables sensitivity or conducted sensitivity analysis independent of optimization. In this paper, an integrated algorithm is proposed, which combines the optimization method SPEA (Strength Pareto Evolutionary Algorithm) with the sensitivity analysis method SRCC (Spearman Rank Correlation Coefficient). In the proposed algorithm, the optimization variables are worked as samples of sensitivity analysis, and the consequent sensitivity result is used to guide the optimization process by changing the evolutionary parameters. Three cases including a mathematical problem, an airship envelope optimization, and a truss topology optimization are used to demonstrate the computational efficiency of the integrated algorithm. The results showed that this algorithm is able to simultaneously achieve parameter sensitivity and a well-distributed Pareto optimal set, without increasing the computational time greatly in comparison with the SPEA method.

Highlights

Multiobjective optimization is widely used in many practical engineering problems
Many algorithms have been proposed based on the basic concept of the Genetic algorithm [8] (GA), such as Vector Evaluated Genetic Algorithm (VEGA) [9], Multiobjective Genetic Algorithm (MOGA) [10], Nondominated Sorting Genetic Algorithm (NSGA) [11], the Niched Pareto Genetic Algorithm (NPGA) [12], Strength Pareto Evolutionary Algorithm (SPEA) [13], Nondominated Sorting Genetic Algorithm II (NSGA II) [14], Pareto Envelope-based Selection Algorithm (PESA) [15], the Pareto Archived Evolution Strategy (PAES) [16], and Micro-Genetic Algorithm (Micro-GA) [17]
The time-consumption, which relates to the computer capacity, is about 5 hours for both SPEA and Spearman Rank Correlation Coefficient (SRCC)-SPEA

Summary

Introduction

Multiobjective optimization is widely used in many practical engineering problems. Instead of a single optimal solution, multiobjective optimization problem (MOOP), with conflicting subobjectives, provides a set of compromise solutions, which is known as Pareto optimal set [1]. There are two main alternative ways to obtain the Pareto optimal set. An optimal solution corresponding to the defined weights can be obtained in a single run, so multiple optimization runs with variable objective weights are needed to obtain the solution set. This method cannot be used to find Pareto optimal solutions in problems having a nonconvex Pareto optimal front [3]. The second way enables obtaining Pareto optimal set in a single run and has been emphasized in recent years. As the basis of decision-making, the Pareto optimal set provides the decision maker with insight into the characteristics of the problem before choosing a final solution

Objectives

Methods

Results

Conclusion