基于改进粒子群优化算法的稳定进化策略实现

Stable Evolutionary Strategy Realization Based on Improved Particle Swarm Optimization Algorithm

摘要: 在进化博弈论中，从博弈参与者的角度研究稳定的进化策略是如何实现的至关重要。本文基于生物种群进化与粒子群算法相似的特点，对粒子群优化算法进行改进，即种群粒子群优化算法(population particle swarm optimization algorithms, PPSO)。然后，模拟生物群体中的模仿和变异行为现象，成功地找到进化稳定点的路径。经典的2 × 2博弈模型，如鹰鸽博弈，作为例子来模拟单个种群的进化过程。实验结果表明：1) PPSO不仅能清晰地显示迭代过程中各群体的位置，而且推导出的稳定进化点与期望值的偏差最小。这验证了粒子群算法在寻找进化稳定策略路径方面的有效性。2) 经过参数分析，我们发现决定进化稳定策略成功实现的前提条件不是变异的存在，而是变异的位置。

Abstract: In evolutionary game theory, it is essential to study how stable evolutionary strategies are achieved from the player’s perspective in the game. In this paper, we improve the particle swarm optimization algorithm based on the fact that biological population evolution has similar elements with the particle swarm algorithm, namely population particle swarm optimization algorithms (PPSO). Then, the phenomena of imitation and variation behaviors in biological populations are simulated to successfully find paths towards evolutionarily stable points. Classical 2 × 2 game models, such as the Hawk-Dove game, are used as examples to simulate the evolutionary process of a single population. The results of the experiment show: 1) PPSO can not only clearly show the position of each group in the iterative process, but also that the deviation of the derived stable evolution point from the expected point is minimal. This verifies the effectiveness of the PPSO in searching for paths towards evolutionarily stable strategies. 2) After parametric analysis, we find that the precondition that determines the successful realization of the evolutionarily stable strategy is not the presence of variation, but the location of the variation.