A fixed evolutionary mechanism is usually adopted in the multiobjective evolutionary algorithms and their operators are static during the evolutionary process, which causes the algorithm not to fully exploit the search space and is easy to trap in local optima. In this paper, a SPEA2 algorithm which is based on adaptive selection evolution operators (AOSPEA) is proposed. The proposed algorithm can adaptively select simulated binary crossover, polynomial mutation, and differential evolution operator during the evolutionary process according to their contribution to the external archive. Meanwhile, the convergence performance of the proposed algorithm is analyzed with Markov chain. Simulation results on the standard benchmark functions reveal that the performance of the proposed algorithm outperforms the other classical multiobjective evolutionary algorithms.

This paper makes an in-depth exploration into the job-shop scheduling problem (JSP). After reviewing the related literature, the local search mechanism of the particle swarm algorithm (PSA) and the largespan search principle of standard cuckoo search algorithm (CSA) were combined into an improved cuckoo search algorithm (ICSA), which is capable of both local search and global search. Later, several simulation experiments were carried out on the LA type typical library proposed by Lawrence, and the stability and accuracy of the ICSA was contrasted with those of the PSA and the genetic algorithm (GA) based on the means and variances in multiple iterations. After the comparison, a convergence analysis of the ICSA was specially designed for our model. The results demonstrate that the ICSA provides a better tool for solving the JSP than other algorithms. The research findings lay a solid theoretical basis for the JSP in the actual production process.

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Convergence of the HSAS/FFT is proved in this part. The evolutionary process of HSAS/FFT can be regarded as a series of the stochastic sequence. The stochastic sequence is used to analyse the process of HSAS/FFT. And the convergence of the HSAS/FFT is proved by the criterion in (Peng and Xie 2012). Meanwhile, two theorems are presented to prove the convergence of HSAS/FFT. Definition 1. 𝑆 = 𝐼 𝐷 is the search space, and 𝑓: 𝑆 → 𝐼 + is fitness. 𝐼 is the set of spaces divided by period that frequency corresponds to, 𝑎 * denotes the global optimal area. Then the