A Tunable Generator of Instances of Permutation-Based Combinatorial Optimization Problems

Abstract

In this paper, we propose a tunable generator of instances of permutation-based combinatorial optimization problems. Our approach is based on a probabilistic model for permutations, called the generalized Mallows model. The generator depends on a set of parameters that permits the control of the properties of the output instances. Specifically, in order to create an instance, we solve a linear programming problem in the parameters, where the restrictions allow the instance to have a fixed number of local optima and the linear function encompasses qualitative characteristics of the instance. We exemplify the use of the generator by giving three distinct linear functions that produce three landscapes with different qualitative properties. After that, our generator is tested in two different ways. First, we test the flexibility of the model by producing instances similar to benchmark instances. Second, we account for the capacity of the generator to create different types of instances according to the difficulty for population-based algorithms. We study the influence of the input parameters in the behaviors of these algorithms, giving an example of a property that can be used to analyze their performance.