Research On Differential Evolution For Solving Complex Optimization Problems

In real-world, many optimization problems aim to find the best solutions. When satisfying certain constraints, searching a set of parameters maximize or minimize some targets of system performance. According to the properties of problems, optimization problems can be divided into different types:unimodal and multimodal problems, unconstrained and constrained optimization problems, continuous and discrete optimization problems, single object and multi-object optimization problems, low and high dimensional optimization problems. The difficulties of those problems are different. Generally, problems with less local minima, smaller number of constraints and objects, and lower dimensions are easy to solve. When problems have more local optima, algorithms are easily trapped and hard to find better solutions. When problems have more constrains, algorithms are difficult to deal with constraints and search feasible solutions. When problems have many objects, algorithms are hard to satisfy the Pareto front of objects. When increasing the dimensions of problems, the convergence speeds of algorithms are faced with a big challenge. Differential Evolution (DE) is a class of population-based global search algorithms. Compared to traditional pure mathematical methods, DE is superior to solve the above complex problems.This dissertation focuses on DE for solving several complex optimization problems, including classical optimization problems, multimodal optimization problems, constrained optimization problems and high dimensional optimization problems. According to the features of problems, we design different DE variants to solve the abovementioned problems and some real-world applications. The main contributions of this dissertation can be summarized as follows.1. For solving classical optimization problems, we present an improved DE algorithm, with employs a recently proposed DE/current-to-pbest mutation strategy. To avoid manually adjusting control parameters, we design a self-adaptive parameter tuning mechanism. Simulation studies on 20 classical benchmark optimization problems demonstrate that our approach can find promising solutions on 18 problems. When compared with some famous DE variants, our algorithm achieves better solutions on the majority of test problems.2. For solving complex multimodal optimization problems, we design a hybrid DE algorithm, which combines DE/current-to-best/2 strategy and opposition-based learning (OBL) mechanism. The former can accelerate the convergence speed, and the latter can improve the probability of finding better solutions by simultaneously evaluating current solutions and opposite solutions. Experimental studies on 11 complex multimodal problems show that our algorithm outperforms standard DE and other six improved particle swarm optimization algorithms. In order to compare multiple algorithms on the whole test suite, we conduct t-test and Friedman test. The results show that our algorithm is the best one among the eight compared algorithms.3. For solving constrained optimization problems, we propose a new DE algorithm based on multi-parent crossover, which generates offspring based on the center individual and three randomly selected individuals. The offspring created by this crossover scheme are closer to the feasible region. To deal with the solutions in the boundaries of feasible region, we apply a boundary search strategy. To handle constraints, we employ a feasible solution preferred rule (an individual with less constraint violations is better). To verify the performance of our approach, we test it on 13 well-known constrained benchmark optimization problems. Simulation results and comparisons demonstrate that our algorithm can effectively deal with constraints and achieves better feasible solutions. Additionally, we apply the algorithm to solve four real-world applications, including welded beam design optimization problem, pressure vessel design optimization problem, tension/compression spring design optimization problem and speed reducer design optimization problem. Simulation results demonstrate the effectiveness of our algorithm.4. For solving high dimensional (D=1000) optimization problems, we propose an improved DE variants, which modifies the DE mutation scheme to learn the information of global and local best individuals, and aims to balance the global and local search abilities of DE. To verify the performance of our algorithm, we test it on six common high dimensional benchmark optimization problems (D=100,500 and 1000). Simulation results show that our algorithm can find reasonable solutions on the majority of test problems. To compare multiple algorithms on the test suite, we apply Friedman test to calculate the average rankings of the involved six algorithms. The results show that our algorithm is best one among all compared algorithms. To analyze the computational running time, we use power regression model to fit the real running time. Simulation results show that the time complexity of our algorithm is below O(D2). Therefore, it is applicable to use the algorithm to solve higher dimensional problems.