Compact optimization is an alternative paradigm in the field of metaheuristics requiring a modest use of memory to optimize a problem. As opposed to population-based algorithms, which conduct the search by employing a set of candidate solutions, compact algorithms use a probabilistic model to describe how solutions are distributed over the search space. Compared to other Estimation of Distribution Algorithms, peculiar features such as the use of simple probabilistic models, in which variables are treated independently, and the need for a minimal number of solutions to be sampled to perform the search, make these algorithms suitable for those applications plagued by memory limitations. Compact algorithms show good results on different kinds of optimization problems but often prematurely converge and perform poorly on non-separable. In this paper, we attempt to overcome these limitations by combining compact algorithms with a restart mechanism named Re-Sampled Inheritance (RI) whose purpose is to avoid premature convergence while also inheriting parts of the variables from the best solution found so far. To assess the effect of the RI mechanism, we extensively test various existing compact algorithms, with and without RI, and compare the best RI-based compact algorithm against several competing algorithms on several optimization problems at different dimensionalities. We also evaluate the effect of the RI parameters on the overall algorithmic performance. Our numerical results not only show that RI consistently enhances the performances of compact algorithms, but also shed some light on the effectiveness of different compact logics at handling problems at different dimensionalities.

紧凑优化是元启发法领域中的另一种范式，需要适度使用内存来优化问题。与基于人口的算法（通过使用一组候选解决方案进行搜索）相反，紧凑型算法使用概率模型来描述解决方案如何在搜索空间上分布。与其他分布算法估计相比，独特的功能（例如使用简单的概率模型和独立的变量处理）以及需要最少数量的解决方案样本来执行搜索的特性，使得这些算法适用于那些应用受内存限制的困扰。紧凑型算法在不同种类的优化问题上显示出了良好的结果，但是在不可分离的情况下往往会过早收敛并且表现不佳。在本文中，我们尝试通过将紧凑型算法与名为“重新采样继承”（RI）的重启机制相结合来克服这些限制，其目的是避免过早收敛，同时还从迄今为止找到的最佳解决方案中继承变量的一部分。为了评估RI机制的效果，我们广泛测试了有无RI的各种现有紧凑算法，并针对几种不同尺寸的优化问题，将基于RI的最佳紧凑算法与几种竞争算法进行了比较。我们还评估了RI参数对整体算法性能的影响。我们的数值结果不仅表明RI持续提高了紧凑算法的性能，而且还揭示了不同紧凑逻辑在处理不同维度问题上的有效性。