## A.A. Chaves, M.G.C. Resende, R.M.A. Silva, A random-key GRASP for combinatorial optimization

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DOI: 10.23952/jnva.8.2024.6.03

Volume 8, Issue 6, 1 December 2024, Pages 855-881

**Abstract**. This paper proposes a problem-independent GRASP metaheuristic by 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.

**How to Cite this Article**:

A.A. Chaves, M.G.C. Resende, R.M.A. Silva, A random-key GRASP for combinatorial optimization, J. Nonlinear Var. Anal. 8 (2024), 855-881.