An Experimental Comparison of Biased and Unbiased Random-Key Genetic Algorithms

Abstract

Random key genetic algorithms are heuristic methods for solving combinatorial optimization problems. They represent solutions as vectors of randomly generated real numbers, the so-called random keys. A deterministic algorithm, called a decoder, takes as input a vector of random keys and associates with it a feasible solution of the combinatorial optimization problem for which an objective value or fitness can be computed. We compare three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2010); and a greedy version of Bean's algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set k-covering, and unit-cost covering by pairs. Experiments are run to construct runtime distributions for 36 heuristic/instance pairs. For all pairs of heuristics, we compute probabilities that one heuristic is faster than the other on all 12 instances. The experiments show that, in 11 of the 12 instances, the greedy version of Bean's algorithm is faster than Bean's original method and that the biased variant is faster than both variants of Bean's algorithm.

A biased random-key genetic algorithm for the capacitated minimum spanning tree problem

“…Implementation details. All the tested versions of the BRKGA were implemented in C++ using the BRKGA API of Toso and Resende (2014). Codes were compiled with g++ with flags "-c" and "-O3".…”

“…A biased random-key genetic algorithm, or BRKGA Gonçalves et al, 2014), differs from a RKGA in the way parents are selected for mating and what role each parent plays in crossover. Unlike in a RKGA, where parents are selected at random from the entire population, in a BRKGA each offspring is generated combining one individual selected at random from the elite partition of the population and another from the non-elite partition.…”

“…Furthermore, BRKGA can easily take advantage of parallel computing environments, since step 3 of the pseudo-code in Algorithm 1 can be done in parallel with each thread decoding a different vector of random keys. An object-oriented application programming interface (API) for the BRKGA framework was proposed in Toso and Resende (2014). This cross-platform library automatically handles a large portion of problem-independent modules that are part of the framework, including population management and evolutionary dynamics.…”

On the minimization of traffic congestion in road networks with tolls

“…Though the difference between RKGAs and BRKGAs is small, the resulting heuristics behave quite differently. Experimental results in Gonçalves et al (2014) show that BRKGAs are almost always faster and more effective than RKGAs.…”

A biased random key genetic algorithm applied to the electric distribution network reconfiguration problem

“…In a BRKGA, a parent is always chosen from the elite set, which introduces the elitism principle in the reproduction process. This modification is sufficient to make the biased version of the GA to outperform the unbiased version (Gonçalves et al 2014). The populations of individuals are evolved in sequence until a stopping criterion is reached.…”