### A Steady State Decomposition Based Quantum Genetic Algorithm for Many Objective Optimization

Abstract

Many objective optimization refers to the class of optimization problems involving four or more objectives. Optimal solutions of such problems lie on a hyper surface (the Pareto front) and the dimensionality of the hyper-surface is dependent on the number of objectives in conflict. Identifying well converged and well spread set of solutions spanning the hyper-surface is a non-trivial problem. In this paper we introduce a novel decomposition based steady state quantum genetic algorithm, wherein systematic sampling is used to generate the reference directions and a small population of quantum individuals (solutions with variables represented as Q-bits) is evolved using a simple variation operator. A solution represented using Q-bits has the ability to probabilistically represent a number of solutions defined through observation. We exploit the benefits of quantum representation within a steady state evolution scheme and illustrate the behavior of the algorithm using discrete formulations of the unconstrained DTLZ2 test problem involving 2, 3, 5, and 8 objectives. In order to illustrate the behavior for constrained optimization problems, we investigate the behavior of the algorithm using the water resource optimization problem involving 5 objectives. A quantum population of 5 individuals has been used to solve all the above problems. Preliminary results on the effects of the size of quantum population and the fidelity of representation are presented in this paper. Finally, a number of possible directions are suggested to further improve the performance of the algorithm.