A machine learning approach to algorithm selection for $\mathcal{NP}$ -hard optimization problems: a case study on the MPE problem

Abstract

Given one instance of an N P-hard optimization problem, can we tell in advance whether it is exactly solvable or not? If it is not, can we predict which approximate algorithm is the best to solve it? Since the behavior of most approximate, randomized, and heuristic search algorithms for N P-hard problems is usually very difficult to characterize analytically, researchers have turned to experimental methods in order to answer these questions. In this paper we present a machine learning-based approach to address the above questions. Models induced from algorithmic performance data can represent the knowledge of how algorithmic performance depends on some easy-to-compute problem instance characteristics. Using these models, we can estimate approximately whether an input instance is exactly solvable or not. Furthermore, when it is classified as exactly unsolvable, we can select the best approximate algorithm for it among a list of candidates. In this paper we use the MPE (most probable explanation) problem in probabilistic inference as a case study to validate the proposed methodology. Our experimental results show that the machine learning-based algorithm selection system can integrate both exact and inexact algorithms and provide the best overall performance comparing to any single candidate algorithm.

Automatic Algorithm Selection for Complex Simulation Problems

“…In [117], Guo puts forward an algorithm selection workflow consisting of seven steps and states that each one "has some important research problems to solve" [117, p. 63].…”

“…1.3), but is generally not accounted for in complexity theory. In [117], this problem is described as moving from problem complexity to problem instance complexity.…”

“…Nevertheless, algorithm selection for hard problems has almost exclusively been tackled by algorithm portfolios, except for the approaches presented in [117,145]. SATzilla [243,336] is a very successful solver for the aforementioned satisfiability (SAT) problem.…”

Algorithm Selection for the Graph Coloring Problem

“…Applications of regression include [46,31,4]. Classification techniques have been used among others in [30,41,23,40,19,18]. However, none of these approaches is specially designed for the GCP and although some also consider graph properties, there exist no specific features regarding special aspects of the graph colorability.…”

Solving optimization problems using black hole algorithm

“…Optimization approaches are divided into exact algorithms [2] and approximate algorithms [3][4][5]. Exact approaches are able to find the exact optimal answer; however, these approaches are not useful in NP-hard [2], [6][7] problems since their solving time for these NP-hard problems increases exponentially. Approximate algorithms are able to find good answers (near to optimal solutions) for NP-hard in a short time.…”