Research On Efficient And Intelligent Algorithms For Two Classes Of Complex Optimization Problems

Various optimization problems arise in many application fields, such as science re-search, engineering etc. These optimization problems are with properties of increasingsize and complexity. Computer technology with high development provide powerful hard-ware for solving these optimization problems. Optimization methods are the necessarytechniques to use the powerful computers. However, existing optimization methods cannot meet the demands of real applications. Thus, it becomes more and more importantto study and design high-efciency optimization techniques. The main contributions ofthis thesis are as follows:1. For diferential multimodal global optimization problems, the smoothing function isoften used to eliminate the solutions worse than the best ones found so far, so thatthe influence brought by the local optimum can be reduced substantially. What’smore, smoothing function can keep the current best solution and the better solutionsunchanged, and, the diferential information of the basin lower than the current bestsolution can also be kept. However, flattened by the smoothing function, much flatarea will be produced with much diferential information lost, and this will resultin unable to use traditional search method. In order to use traditional methodsefciently, an auxiliary function called minimum-escape function is designed. Thedesigned auxiliary function can keep the advantages of the smoothing function, andcan also provide descent directions away from the current best solution for the searchmethod. Thus, this can help searching algorithms jump out from the local optimum.Using the minimum-escape function, an auxiliary function method is designed fordiferential multimodal global optimization problems. Simulation results show that,the minimum-escape function method has very stable performance in dealing withlow-dimensional global optimization problems, and also performs well in solving high-dimensional global optimization problems.2. Although existing auxiliary function methods have good performance in jumping outfrom local optimum, they can only help the algorithm find a better basin instead of theaccurate local optimal solution in the better basin. In order to overcome this disad-vantage, an improved minimum-escape function is designed. This improved function can keep the advantages of the minimum-escape function, and also can help opti-mization methods find local optimal solutions with certain precision by optimizingthe auxiliary function directly. An auxiliary function method based on the improvedminimum-escape function is designed. Experimental results indicate that the perfor-mance of the designed auxiliary function method is robust and efective.3. When solving high-dimensional global optimization problems, many existing auxil-iary function methods can not find out the global optimal solutions via each execu-tion successfully, especially for high-dimensional problems. In order to increase thesuccess rate of solving high-dimensional global optimization problems, a transformedminimum-escape function and the intelligent optimization technique are employed todesign a novel intelligent auxiliary function method. The experimental results indicatethat the proposed intelligent auxiliary function method can solve the high-dimensionalbenchmark problems with high success rate, and has stable performance.4. Experimental studies on searching strategies of circle search technique for complexglobal optimization problems are made. In the experiments, three searching strategiesare designed, and evolutionary algorithms using these three searching strategies areconstructed. Then, experimental results of each searching strategy are analyzed. Inthe first search strategy, the search circle is only to be expanded or shrunk. Exper-imental results show that the solutions found by this strategy is with low precision,and the number of function evaluations used by this strategy is large. The secondstrategy is to enlarge the searching circles first and then shrink them. This searchingstrategy can improve the precision of the solutions greatly. But this strategy needsmuch computational cost. The third strategy is to enlarge and shrink the searchingcircle alternatively. Using this strategy can find global optimal solutions with highprecision and small number of function evaluations.5. Circle search method has disadvantage over searching the edge of the search space.In order to overcome this, a new searching technique called square search method isproposed. This technique can keep the algorithm searching in the space, and can alsoexplore the edge efectively. Thus, it can improve the search efcient significantly.Through enlarging and shrinking searching squares can help optimization algorithms find high-precision solutions using much less computational cost.6. For complex nondiferential global optimization problems, a novel memetic algorithmis proposed. In the proposed memetic algorithm, the uniform crossover operator isused to search the space between two solutions. An auxiliary function is constructedaccording to the best solution in the current population, and then design a localsearch method using the designed auxiliary function, which can help the solutionalgorithm to find the local optimal solution or approximate local optimal solution;Then, the square search method is used to find out a better solution from the currentlocal optimal solution. At last, simulation results show that the proposed memeticalgorithm has stable performance.7. For constrained multiobjective optimization problems, the way to handle infeasiblesolutions often influences the search performance of a solution algorithm. Using in-feasible solutions reasonably can improve the performance of solution algorithms. Anovel clustering method is proposed based on Pareto domination, which can use infea-sible solutions efciently. A tailor-made crossover operator and square search methodare designed to explore the space efectively. Based on these strategies, a novel multi-objective evolutionary algorithm called ED-MOEA is designed. An elliptical crossoveroperator is proposed to improve the search ability of crossover operators. Then, amultiobjective genetic algorithm based on elliptical crossover operator is designed.These designed algorithms are proven to convergent to the optimal solutions withprobability1. Simulation results show that the designed algorithms have positiveperformance.