A Combinatorial Optimization Framework for Probability-Based Algorithms by Means of Generative Models

Abstract

Probability-based algorithms have proven to be a solid alternative for approaching optimization problems. Nevertheless, in many cases, using probabilistic models that efficiently exploit the characteristics of the problem involves large computational overheads, and therefore, lower complexity models such as those that are univariate are usually employed within approximation algorithms. With the motivation to address such an issue, in this article, we aim to introduce an iterative optimization framework that employs generative models to efficiently estimate the parameters of probability models for optimization problems. This allows the use of complex probabilistic models (or those that are appropriate for each problem) in a way that is feasible to apply them iteratively. Specifically, the framework is composed of three elements: a generative model, a probability model whose probability rule is differentiable, and a loss function. The possibility of modifying any of the three elements of the framework offers the flexibility to design algorithms that best adapt to the problem at hand. Experiments conducted on two case studies reveal that the presented approach has strong performance in terms of objective value and execution time when compared to other probability-based algorithms. Moreover, the experimental analysis demonstrates that the convergence of the algorithms is controllable by adjusting the components of the framework. For the sake of reproducibility, the source code, results, scripts, figures, and other material related to the manuscript are available at https://github.com/mikelma/nnco_lib .