6 research outputs found
Computationally Efficient Local Optima Network Construction
The codebase for this paper is available at https://github.com/fieldsend/local_optima_networksThere has been an increasing amount of research on the visualisation
of search landscapes through the use of exact and approximate
local optima networks (LONs). Although there are many papers
available describing the construction of a LON, there is a dearth
of code released to support the general practitioner constructing
a LON for their problem. Furthermore, a naive implementation of
the algorithms described in work on LONs will lead to inefficient
and costly code, due to the possibility of repeatedly reevaluating
neighbourhood members, and partially overlapping greedy paths.
Here we discuss algorithms for the efficient computation of both
exact and approximate LONs, and provide open source code online.
We also provide some empirical illustrations of the reduction in the
number of recursive greedy calls, and quality function calls that can
be obtained on NK model landscapes, and discretised versions of
the IEEE CEC 2013 niching competition tests functions, using the
developed framework compared to naive implementations. In many
instances multiple order of magnitude improvements are observed.This work was supported by the Engineering and Physical Sciences
Research Council [grant number EP/N017846/1]. The author would
like to thank Sébastien Vérel and Gabriela Ochoa for providing
inspirational invited talks on LONs at the University of Exeter
during this grant, and also Ozgur Akman, Khulood Alyahya and
Kevin Doherty
The Genetic Algorithm for Permutations
The genetic algorithm is a bright example of an
evolutionary algorithm which was developed based on the insights from
theoretical findings. This algorithm uses crossover, and it was shown to
asymptotically outperform all mutation-based evolutionary algorithms even on
simple problems like OneMax. Subsequently it was studied on a number of other
problems, but all of these were pseudo-Boolean.
We aim at improving this situation by proposing an adaptation of the
genetic algorithm to permutation-based problems. Such
an adaptation is required, because permutations are noticeably different from
bit strings in some key aspects, such as the number of possible mutations and
their mutual dependence. We also present the first runtime analysis of this
algorithm on a permutation-based problem called Ham whose properties resemble
those of OneMax. On this problem, where the simple mutation-based algorithms
have the running time of for problem size , the
genetic algorithm finds the optimum in fitness
queries. We augment this analysis with experiments, which show that this
algorithm is also fast in practice.Comment: This contribution is a slightly extended version of the paper
accepted to the GECCO 2020 workshop on permutation-based problem
Dynastic Potential Crossover Operator
An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions.
Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time.
In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.This research is partially funded by the Universidad de M\'alaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under grant number UMA18-FEDERJA-003 (PRECOG); under grant PID 2020-116727RB-I00 (HUmove) funded by MCIN/AEI/10.13039/501100011033; and TAILOR ICT-48 Network (No 952215) funded by EU Horizon 2020 research and innovation programme. The work is also partially supported in Brazil by São Paulo Research Foundation (FAPESP), under grants 2021/09720-2 and 2019/07665-4, and National Council for Scientific and Technological Development (CNPq), under grant 305755/2018-8