Multiobjective Evolutionary Algorithm Based On Symmetric Latin Hypercube Designs

Coupling with the rapid development of technology and economy, people have encountered complicated Multiobjective Optimization Problems (MOPs) in various fields. The incommensurable and competing objectives which aim to be optimal synchronously are characteristic of these problems. For example, when we design the distribution of communication base stations, there are usually two objectives. One is the maximization of the communication zone covered by base stations; the other is the minimization of the quantities of base stations to save the cost. Different from the single objective optimization problems which usually have one global optimal solution, MOPs often have infinite number of Pareto optimal solutions. Therefore, it is of great urgency to design new algorithms for MOP which can generate a set of widely spread and uniformly distributed solutions on the entire Pareto front.The classical methods, such as Weighted Sums of Objectives,ε-constrained method, goal programming etc, for multiobjective optimization problems convert the multiobjective problems into scalar ones, and then solve them using the methods of Mathematical Programming. However, these algorithms often fail to produce the nondominated solutions which lie in the nonconvex region. Multiobjective evolutionary algorithms are efficient methods for global searching and can produce multiple nondominated solutions in a single round. It is insensitive to the shape and continuity of the Pareto front. Also, it has better convergence near the true Pareto optimal front compared to the classical methods.In this thesis, the basic concepts, theories and frameworks of the classical methods, multiobjective evolutionary algorithms are reviewed and analyzed systematically first. Then an improved multiobjective evolutionary algorithm called SLHD-MOEA is proposed which is based on the space-filling property of SLHD. This algorithm first creates various different sets of the weights by SLHD and then generates a scheme of multiple weighted-sum fitness function. The fitness function defined in this way can guide the search more effectively than in classical way. Moreover, a new kind of initial population and a crossover operator based on SLHD are presented. Also, the elitism strategy is introduced. By doing so, the diversity of solutions and the convergence power are increased. Simulation results demonstrate that the proposed algorithm can effectively handle nonconvex problems and has better convergence near the true Pareto optimal front compared to NSGAⅡ.