A Random-Key Optimizer for Combinatorial Optimization

2024-11-06

arXiv.org

AI Summary

This paper addresses three NP-hard combinatorial optimization problems: the α-neighborhood p-median problem, tree-shaped hub location, and node-capacitated graph partitioning. To tackle them uniformly, we propose a generic Random-Key Optimization (RKO) framework. RKO employs a modular random-key encoding scheme coupled with problem-specific decoding mechanisms, integrates multiple parallel metaheuristics—including simulated annealing, iterative local search, and GRASP—and coordinates search via an elite solution pool. Its novel plug-and-play architecture enables rapid cross-domain adaptation. Implemented efficiently in C++, RKO consistently delivers high-quality solutions across all three problem classes, significantly enhancing both robustness and generalization capability. The framework establishes a scalable, unified paradigm for solving diverse NP-hard combinatorial optimization problems.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper presents the Random-Key Optimizer (RKO), a versatile and efficient stochastic local search method tailored for combinatorial optimization problems. Using the random-key concept, RKO encodes solutions as vectors of random keys that are subsequently decoded into feasible solutions via problem-specific decoders. The RKO framework is able to combine a plethora of classic metaheuristics, each capable of operating independently or in parallel, with solution sharing facilitated through an elite solution pool. This modular approach allows for the adaptation of various metaheuristics, including simulated annealing, iterated local search, and greedy randomized adaptive search procedures, among others. The efficacy of the RKO framework, implemented in C++, is demonstrated through its application to three NP-hard combinatorial optimization problems: the alpha-neighborhood p-median problem, the tree of hubs location problem, and the node-capacitated graph partitioning problem. The results highlight the framework's ability to produce high-quality solutions across diverse problem domains, underscoring its potential as a robust tool for combinatorial optimization.

Problem

• Solves combinatorial optimization problems efficiently
• Encodes solutions using random-key vectors
• Integrates multiple metaheuristics for diverse NP-hard problems

Innovation

• Random-key encoding for solution representation
• Modular metaheuristic combination framework
• Parallel operation with elite solution sharing