Convergent Analysis and Algorithmic Improvement of Differential Evolution

Abstract

To analyze the convergence of differential evolution (DE) and enhance its capability and stability, this paper first defines a differential operator (DO) as a random mapping from the solution space to the Cartesian product of solution space, and proves the asymptotic convergence of DE based on the random contraction mapping theorem in random functional analysis theory. Then, inspired by "quasi-physical personification algorithm", this paper proposes an improved differential evolution with multi-strategy cooperating evolution (MEDE) is addressed based on the fact that each evolution strategy of DE has common peculiarity but different characteristics. Its asymptotic convergence is given with the definition of multi-strategy differential operator (MDO), and the connotative peculiarity of MEDE is analyzed. Compared with the original DE, DEfirDE and DEfirSPX, the simulation results on 5 classical benchmark functions show that MEDE has obvious advantages in the convergence rate, solution-quality and adaptability. It is suitable for solving complex high-dimension numeral optimization problems.

Sufficient Conditions for Global Convergence of Differential Evolution Algorithm

“…We note that the conclusion of [30,31] is in contradiction with [29]. According to the inference process, the asymptotic convergence in [30] refers to almost sure convergence. In fact, if DE does not hold with convergence in probability, then it does not hold with almost sure convergence.…”

“…In fact, if DE does not hold with convergence in probability, then it does not hold with almost sure convergence. We also note that the value of the random mapping DO defined in [30] may be greater than 1, which is debatable. In [31], the asymptotic convergence analysis of DE/rand/1/bin, which was proved by applying Lyapunov stability theorems, should be a local convergence property.…”

“…Sun [29] developed a Markov chain modeling and proved that the classical DE does not hold with convergence in probability. He et al [30] defined the differential operator (DO) as a random mapping from the solution space to the Cartesian product of solution space and analyzed the asymptotic convergence of DE by using the random contraction mapping theorem. Ghosh et al [31] established asymptotic convergence behavior of a classical DE (DE/rand/1/bin) algorithm by applying the concepts of Lyapunov stability theorems.…”

Improved differential evolution algorithm for solving multi-person noncooperative game

“…The IDE integrates these three evolution strategies, that is, one of them is selected during each iteration. Therefore, the IDE with multiple evolution strategies not only has all the characteristics of DE, but also has the characteristics of multi-group and multi-strategy coordination evolution [11]. Moreover, in order to make the DE algorithm have better global search capability and convergence speed, an adaptive mutation operator is adopted:…”

Combinatorial Test Case Suite Generation Based on Differential Evolution Algorithm

“…As the intelligent optimization algorithm is an effective way of solving the NP-complete problem, more and more researchers have begun to use the intelligent optimization method such as the genetic algorithm, particle swarm optimization algorithm, to solve the generation problem of combinatorial test data. As the differential evolution algorithm, as an emerging intelligent optimization technique, can effectively solve the complex optimization problems [10] , this paper proposes the method of solving the generation problem of combinatorial test case with the differential evolution algorithm.…”