Wang Yu-ping

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Abstract Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the followers functions are separable with respect to the followers variables, and the other is that the followers functions are convex if the followers variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leaders variable x , itisprovedthat the optimal solution y of the followers mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the followers programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ , a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.

A new uniform evolutionary algorithm based on decomposition and CDAS for many-objective optimization

The convergence and the diversity are two main goals of an evolutionary algorithm for many-objective optimization problems. However, achieving these two goals simultaneously is the difficult and challenging work for multi-objective evolutionary algorithms. A uniform evolutionary algorithm based on decomposition and the control of dominance area of solutions (CDAS) is proposed to achieve these two goals. Firstly, a uniform design method is utilized to generate the weight vectors whose distribution is uniform over the design space, then the initial population is classified into some sub-populations by these weight vectors. Secondly, an update strategy based on decomposition is proposed to maintain the diversity of obtained solutions. Thirdly, to improve the convergence, a crossover operator based on the uniform design method is constructed to enhance the search capacity and the CDAS is used to sort solutions of each sub-population to guide the search process to converge the Pareto optimal solutions. Moreover, the proposed algorithm compare with some efficient state-of-the-art algorithms, e.g., NSGAII-CDAS, MOEA/D, UMOEA/D and HypE, on six benchmark functions with 5–25 objectives are made, and the results indicate that the proposed algorithm is able to obtain solutions with better convergence and diversity. 2015 Elsevier B.V. All rights reserved.

Multi-objective fuzzy particle swarm optimization based on elite archiving and its convergence

Abstract A fuzzy particle swarm optimization (PSO) on the basis of elite archiving is proposed for solving multi-objective optimization problems. First, a new perturbation operator is designed, and the concepts of fuzzy global best and fuzzy personal best are given on basis of the new operator. After that, particle updating equations are revised on the basis of the two new concepts to discourage the premature convergence and enlarge the potential search space; second, the elite archiving technique is used during the process of evolution, namely, the elite particles are introduced into the swarm, whereas the inferior particles are deleted. Therefore, the quality of the swarm is ensured. Finally, the convergence of this swarm is proved. The experimental results show that the nondominated solutions found by the proposed algorithm are uniformly distributed and widely spread along the Pareto front.

An effective uniform genetic algorithm for hard optimization problems

Genetic algorithms are one of the effective algorithms for hard optimization problems. They can escape from the local minima, however, the amount of their computation is often large. To decrease the amount of the computation and enhance the algorithms, the uniform design is combined into the genetic algorithm. The new genetic operator has the local-search property similar to that in traditional optimization techniques and needs a minimal amount of computation in certain meanings. Thus the new genetic algorithm can generate a diversity of population and explore the search space effectively. Moreover, the new algorithm is globally convergent. The numerical results also show the effectiveness of the new algorithm with its less computation, and higher convergent speed for all test functions.