In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem (KP). Our goal is to evolve a population of solutions that all have a profit of at least $(1-\varepsilon)\cdot OPT$, where OPT is the value of an optimal solution. Furthermore, they should differ in structure with respect to an entropy-based diversity measure. To this end we propose a simple $(\mu+1)$-EA with initial approximate solutions calculated by a well-known FPTAS for the KP. We investigate the effect of different standard mutation operators and introduce biased mutation and crossover which puts strong probability on flipping bits of low and/or high frequency within the population. An experimental study on different instances and settings shows that the proposed mutation operators in most cases perform slightly inferior in the long term, but show strong benefits if the number of function evaluations is severely limited.
翻译:在实践中,通常需要向决策者提供一整套高质量的多样化解决方案,而不是一个单一解决方案。在本文件中,我们研究对 knapsack 问题进行进化多样性优化。我们的目标是发展一套解决方案,所有解决方案的利润至少(1-\varepsilon)\cddot OTP$,而被占领土是最佳解决方案的价值。此外,它们的结构应该因基于诱导的多样化措施而有所不同。为此,我们提议一个简单的$(mu+1)美元-EA,最初的解决方案由众所周知的FPTAS为KP计算。我们调查不同标准突变操作者的影响,并引入偏差的突变和交叉,这在人口内部极有可能产生低和/或高频率的翻转点。对不同情况和背景的实验研究表明,在大多数情况下,拟议的突变操作者长期表现略低,但如果职能评估的数量非常有限,则显示出巨大的好处。