Study On Electromagnetism-like Algorithm For Solving Global Optimization Problems

With the continuous development of human society, more and more newoptimization problems are emerging and the limitations for the traditionaloptimization methods are increasing evident. Therefore, to carry out research for newoptimization methods has a very important practical significance. From the1980s,heuristic global optimization methods based on random search strategy have beendeveloping rapidly. The major advantage of the heuristic methods is simple structure,easy to implement on computer and combined with other optimal methods. If thecalculation accuracy required is not quiet high, the random search methods can betterdisplay its superiority in this case. Therefore, such optimizations have become one ofthe effective ways for solving the global optimization problems. In this context, theelectromagnetic-like method is proposed in recent year.First, this paper introduces the fundamentals of the electromagnetic-likealgorithm and gives the detail process. We tested EM with three different versions:(1)the process without local procedure.(2) the process added into local procedureapplied to all search points.(3) the process added into local procedure applied to thecurrent best point. The test results show that even if we only apply the local procedureto the current best point, the accuracy of the average function values is still goodenough. Therefore, to reduce the number of function evaluations and balances thenumber of evaluations and the accuracy of the results, we should add the localprocedure applied to the current best point instead of all points. Moreover, to reducethe number of evaluations, a simple optimal method is suggested for local research.The thesis researches deeply the following problems about electromagnetic-likemethod: the global convergence, the abilities for solving the optimum solutions andmulti-solutions, the choices and effects of parameters such as population size and theoriginal search locations. As a result, the following preliminary conclusions have beenreached:(1) electromagnetic-like method has very strong global search capability, andthe early convergence speed of the algorithm is very fast. However, the convergencespeed is become very slowly during the latter part of the search.(2) The EM has avery strong ability to explore unexplored area. It can find all optimum solutions byrepeatedly executed program.(3) The locations of the original search particles don’tsignificantly affect the search performance of electromagnetism-like algorithm. This is the major advantage of the algorithm.To solve the problem that the original electromagnetism-like method is easy tofall into a local minimum, an improved hybrid electromagnetism-like method wasproposed. The basic concept of algorithm is that the negative gradient direction forthe current searching particle is taken as search direction while a small search step israndomly determined in local search process. As the search direction is known and donot need to calculate the search step, the overall efficiency is very high. Experimentalresults show that the improved algorithm can solve the local minimum problem of theoriginal electromagnetism-like method.