Genetic Algorithms For Multiobjective Optimization

Genetic algorithms (GAs) are stochastically search and optimization techniques which mimic the natural process of evolution. GAs have been successfully applied to locate the global optimum of complicated optimization problems. So people are paying a good deal of attention to what's going on GAs. However, as GAs are newly emerging optimization techniques, there are many research work should be substantiated. So it is very significant to seek more efficient algorithms based on GAs to solve concrete engineering problems.By following the cross fundamentals of biology GAs use crossover operators to generate new individuals. That is some portion of Alleles in two matched parents are exchanged by some means to pass down to their offsprings. Crossover, as the important characteristic, differentiates GAs from other evolutionary algorithms. Crossover plays key roles and is the main method in GAs. The design of crossover is closely related with the concrete problems and associated with encoding method. Commonly, crossover should have the ability to generate 'better' individuals by not disrupting too much good patterns of the old ones.The power of GAs arises from crossover. After we made a good investigation to some actual problems an efficient crossover, dislocation crossover (DC), is proposed in this paper. Under DC exchange is permitted between genes in the different location. DC has two attractive characteristics: (1) DC can make genes in a chromosome keep good diversity. DC overcomes the evil of traditional crossovers, which cause GAs get into prematurity. (2) DC well reduces algorithms' generations by guiding them to search in global optimal's neighborhood space. Of course DC can only be applied to such kind of optimization problems in which's chromosome every genes vary from the same range.In the next section of this paper we describe a non-generational GA for multiobjective optimization problems (MOP). In it the replacement policy is such that an offspring replaces the worst one in the current population only if it is better then it. In the same time we also use it to test the power of DC crossover. In this algorithm every element in the population a domination count is defined together with a neighborhood density measure based on a sharing function. Those two parameters are then non-linear combined in order to define the individual's fitness. Numerical experiments with three test-problems takenfrom the literatures were performed and the results suggesting that the non-generational scheme, combined with the DC crossover, can lead to a uniform group of non-dominated solutions.The multi-criteria Minimum Spanning Tree (mc-MST) problem is typical NP-hard problem and arises in many practical applications. So we also use the mc-MST problem as the test problem of the non-generational GA for MOP. In order to evaluate the algorithm's performance we made an improved algorithm, which is proved to find all true Pareto optimal solutions. In the end when we apply the non-generational GA to mc-MST problem we use the true Pareto solutions found by this algorithm to evaluate the solutions found by the non-generational GA.