Optimization via Rejection-Free Partial Neighbor Search

TL;DR

This paper introduces Partial Neighbor Search (PNS), an enhancement of Rejection-Free Metropolis algorithms, which improves optimization efficiency by considering only parts of neighbors, demonstrated on various combinatorial problems.

Contribution

The paper proposes Rejection-Free PNS, a novel method that balances exploration and efficiency in combinatorial optimization by partial neighbor consideration.

Findings

Rejection-Free PNS outperforms traditional methods in multiple problem instances.

The approach reduces computational overhead while maintaining solution quality.

Demonstrated effectiveness on QUBO, Knapsack, XOR, and quadratic programming problems.

Abstract

Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency of rejections by considering all the neighbors at every step. As a solution to avoid the algorithm from becoming stuck in local extreme areas, we propose an enhanced version of Rejection-Free called Partial Neighbor Search (PNS), which only considers random parts of the neighbors while applying Rejection-Free. We demonstrate the superior performance of the Rejection-Free PNS algorithm by applying these methods to several examples, such as the QUBO question, the Knapsack problem, the 3R3XOR problem, and the quadratic programming.