Research On Genetic Algorithms For Multi-Objective Optimization Algorithms

Many real-world problems involve two types of problem difficulties: i) multiple conflicting objectives and ii) a highly complex search space. On the one hand, instead of a single optimal solution, competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. In the absence of preference information, none of the corresponding trade-offs is able to be said to be better than the others. On the other hand, the search space can be too large and complex to be solved by exacting methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties.NSGAⅡ (Fast Elitist Non-Dominated Sorting Genetic Algorithm) is one of better elitist multi-objective evolutionary algorithms. It has some merits: (1) reduce the computational complexity to (GMN~2) where G is the number of generations, M is the number of objectives and N is the population size, (2) Adopt elitist strategy, thereby assuring preservation of previously found best solutions, (3) It doesn't require specifying a sharing parameter, thereby making the algorithm independent of users.In this paper, we introduced Genetic Algorithms;the important strategies for Multi-objective Optimization Problems (MOP) were discussed. The SPEA2 and NSGAⅡ were also introduced. When we did some numerical simulations on NSGAⅡ, we found that all solutions in the population were elitists after about 20 generations. The population is not able to accept many new solutions, and the search process may terminate or prematurely converge to a local Pareto-optimal front. Lack of diversity of solutions is the most important reason. Thus, ensuring the diversity of individuals is very important. An Improved Elitist Strategy Multi-Objective Evolutionary Algorithm (IENSGAⅡ) was introduced. In this improved algorithm, we mainly improved the elitist strategy and introduced a distribution function to control the extent of elitist in each generation. The extent of elitist is able to be changed by fixing a user-defined parameter. When set an appropriate parameter, the algorithm was able to obtain the balance between diversity and convergence.In order to test the effectiveness of the improved elitist strategy, the new algorithm was compared with NSGAⅡ on six test problems. Two performance metrics were introduced to measure the two algorithms. It is clear that the improved algorithm (IENSGAⅡ) outperform NSGAⅡ. IENSGAⅡ is able to get better distribution and find better non-dominated fronts that converge near to the global Pareto-optimal front.