Abstract:

The performance of multi-objective differential evolution algorithm is significantly influenced by its parameter settings and generation strategies（crossover and mutation）. To implement real-time adaptive adjustment of control para-
meters and mutation strategies, a self-adaptive multi-objective differential evolution algorithm based on hidden Markov chain is proposed in the current study. A hidden Markov model is used to analyze the population information and then the optimal sequence is obtained. By comparing the optimal sequence with the actual state sequence, the maximum likelihood estimation values of mutation scaling factor[F]and crossover probability [CR] are obtained to automatically generate suitable parameters. Moreover, a set of strategy chains are obtained by a hidden Markov model to assist multi-objective differential evolution algorithm in selecting an appropriate mutation strategy. Compared with other nine multi-objective evolutionary algorithms on 16 test functions, the results show that the overall performance of the proposed algorithm is better than that of other compared algorithms. Finally, the algorithm is applied to solve the energy consumption optimization problem of sea-rail intermodal transportation, and the obtained results can provide different feasible schemes for decision makers.

Key words: multi-objective optimization, differential evolution algorithm, hidden Markov chain, sea-rail intermodal transportation, energy consumption optimization

摘要：

不同的控制参数设定和生成策略（交叉和变异）都会对多目标差分进化算法的性能产生显著影响。为实现其控制参数和变异策略的实时自适应调整，提出一种基于隐马尔可夫链的自适应多目标差分进化算法。该算法利用隐马尔可夫模型对种群信息进行分析并得到最优序列，通过最优序列与实际状态序列的对比得出变异缩放因子[F]与交叉概率[CR]的最大似然估计值，从而实现控制参数的自适应调整；同时，通过隐马尔可夫模型得到一组策略链来辅助多目标差分进化算法来选择合适的变异策略。通过与其他9种多目标进化算法在16个测试函数上的对比研究，结果表明所提算法的整体性能优于其他比较算法。最后，将该算法用于求解海铁联运能耗优化问题，所得结果能够为决策者提供多种可行方案。

关键词: 多目标优化, 差分进化算法, 隐马尔可夫链, 海铁联运, 能耗优化