A random-key GRASP for combinatorial optimization

TL;DR

This paper introduces a problem-independent GRASP metaheuristic utilizing the random-key optimizer paradigm, applicable to various combinatorial optimization problems, demonstrated on five NP-hard problems.

Contribution

It presents a novel random-key GRASP framework combining a problem-independent component with a decoder, extending GRASP to continuous and combinatorial optimization.

Findings

Successfully applied to five NP-hard problems

Demonstrates versatility across different problem types

Provides a unified approach for combinatorial optimization

Abstract

This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a semi-greedy construction procedure followed by a local search procedure. The best solution found over all iterations is returned as the solution of the GRASP. Continuous GRASP (C-GRASP) is an extension of GRASP for continuous optimization in the unit hypercube. A random-key optimizer (RKO) uses a vector of random keys to encode a solution to a combinatorial optimization problem. It uses a decoder to evaluate a solution encoded by the vector of random keys. A random-key GRASP is a C-GRASP where points in the unit hypercube are evaluated employing a decoder. We describe random key GRASP consisting of a problem-independent component and a problem-dependent decoder. As a proof of concept, the random-key GRASP is tested on five NP-hard combinatorial optimization problems: traveling salesman problem, tree of hubs location problem, Steiner triple covering problem, node capacitated graph partitioning problem, and job sequencing and tool switching problem.