A random-key GRASP for combinatorial optimization

TL;DR

This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm consisting of a problem-independent component and a problem-dependent decoder and is tested on five NP-hard combinatorial optimization problems.

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.

Figures (8)

• Figure 1: Illustrative example of the simplex polyhedron and the five moves of the Nelder-Mead Search. Source: based on the figure in kolda2003optimization
• Figure 2: Example of the TSP decoder with five cities.
• Figure 3: Example of the THLP decoder with ten points and three hubs.
• Figure 4: Example of the SSP decoder with five jobs and a magazine with four slots.
• Figure 5: Example of STCP input data.