混合策略优于纯策略的初步研究
Mixed Strategy May Outperform Pure Strategy: An Initial Study
摘要：
在纯策略元搜索中，始终只应用一种搜索策略。在混合策略元分析中，每次从一个策略池中以一定概率选择一个搜索策略并应用。一个例子是经典的遗传算法，其中每次都以概率选择变异或交叉算子。本文的目的是比较混合策略和纯策略的元启发式算法的性能。首先进行了实验研究，结果表明，混合策略进化算法可以优于纯策略进化算法的0-1背包问题在高达77.8%的情况下。然后，严格证明了互补策略定理，以应用混合策略在人口水平。该定理断言，给定两个元启发式算法，其中一个使用纯策略1，另一个使用纯策略2，如果存在混合策略Meta，则纯策略2与纯策略1互补的条件是充分必要的。由这两种纯策略导出的遗传算法，其寻找最优解的期望代数不超过纯策略1，对于某些初始种群，策略1的策略比纯策略1的策略要小。
英文摘要：
In pure strategy meta-heuristics, only one search strategy is applied for all time. In mixed strategy meta-heuristics, each time one search strategy is chosen from a strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed strategy and pure strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed strategy evolutionary algorithms may outperform pure strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses pure strategy 1 and another uses pure strategy 2, the condition of pure strategy 2 being complementary to pure strategy 1 is sufficient and necessary if there exists a mixed strategy meta-heuristics derived from these two pure strategies and its expected number of generations to find an optimal solution is no more than that of using pure strategy 1 for any initial population, and less than that of using pure strategy 1 for some initial population.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
