Abstract: When solving multi-objective optimization problems, particle swarm optimization algorithms usually employ preset example selection methods and search strategies, which cannot be adjusted according to specific optimization states. In the face of different optimization problems, inappropriate search strategies cannot effectively guide the population, resulting in low search performance of the population. To solve the above problems, a multi-objective particle swarm optimization algorithm guided by extreme learning decision network (ELDN-PSO) is proposed. First of all, the multi-objective optimization problem is decomposed into several scalar subproblems, and an extreme learning decision network is constructed. The network takes the particle position as input, and selects appropriate search actions for each particle according to the optimization state. The fitness change of a particle on the subproblem is obtained as the training sample for the reinforcement learning, and the training speed is improved by extreme learning machine. In the process of optimization, the network is automatically adjusted according to the optimization states, and it selects the appropriate search strategy for the particles at different search stages. Secondly, the non-dominated solutions in the multi-objective optimization problem are difficult to compare. Thus, the leadership of each solution is quantified into a comparable value, so that the examples are more clearly selected for the particles. In addition, an external archive is used to store better particles to maintain the quality of the solutions and guide the population. Comparative experiments are carried out on the ZDT and DTLZ test functions. The results show that ELDN-PSO can effectively cope with different Pareto front shapes, improving the optimization speed as well as the convergence and diversity of the solutions.

Key words: particle swarm optimization, extreme learning machine, multi-objective optimization, objective decomposition, acceleration coefficient

摘要： 在求解多目标优化问题时，粒子群优化算法通常采用预设的榜样选择方法和搜索策略，无法根据具体的寻优状态进行调整。面对不同的优化问题，不合适的搜索策略难以有效指导种群的进化，导致种群的搜索性能降低。为了解决以上问题，提出一种极限学习决策网络指导的多目标粒子群优化算法（ELDN-PSO）。首先，将多目标优化问题分解成若干标量子问题，并构建一个极限学习决策网络。网络将粒子的位置作为输入，根据当前寻优状态为每个粒子选择合适的搜索动作。将粒子在子问题上的适应度值变化作为强化学习的样本用于训练网络，并通过极限学习机提升训练速度。在优化的过程中，网络会根据寻优状态自动调整，在不同的搜索阶段为粒子选择合适的搜索策略。其次，多目标优化问题中存在一系列难以比较的非支配解，将每个解的领导能力量化成可进行比较的数值，从而更明确地为粒子选择合适的学习榜样。此外，使用一个外部档案储存较好的粒子，用于维护解集质量并指导种群的进化。在ZDT和DTLZ测试函数上进行对比实验，结果表明ELDN-PSO能够有效应对不同形状的Pareto前沿，提升种群的寻优速度以及解集的收敛性和多样性。

关键词: 粒子群优化, 极限学习机, 多目标优化, 目标分解, 加速系数