42 research outputs found
Standard Steady State Genetic Algorithms Can Hillclimb Faster than Mutation-only Evolutionary Algorithms
Explaining to what extent the real power of genetic algorithms lies in the ability of crossover to recombine individuals into higher quality solutions is an important problem in evolutionary computation. In this paper we show how the interplay between mutation and crossover can make genetic algorithms hillclimb faster than their mutation-only counterparts. We devise a Markov Chain framework that allows to rigorously prove an upper bound on the runtime of standard steady state genetic algorithms to hillclimb the ONEMAX function. The bound establishes that the steady-state genetic algorithms are 25% faster than all standard bit mutation-only evolutionary algorithms with static mutation rate up to lower order terms for moderate population sizes. The analysis also suggests that larger populations may be faster than populations of size 2. We present a lower bound for a greedy (2+1) GA that matches the upper bound for populations larger than 2, rigorously proving that 2 individuals cannot outperform larger population sizes under greedy selection and greedy crossover up to lower order terms. In complementary experiments the best population size is greater than 2 and the greedy genetic algorithms are faster than standard ones, further suggesting that the derived lower bound also holds for the standard steady state (2+1) GA
When move acceptance selection hyper-heuristics outperform Metropolis and elitist evolutionary algorithms and when not
Selection hyper-heuristics (HHs) are automated algorithm selection methodologies that choose between different heuristics during the optimisation process. Recently, selection HHs choosing between a collection of elitist randomised local search heuristics with different neighbourhood sizes have been shown to optimise standard unimodal benchmark functions from evolutionary computation in the optimal expected runtime achievable with the available low-level heuristics. In this paper, we extend our understanding of the performance of HHs to the domain of multimodal optimisation by considering a Move Acceptance HH (MAHH) from the literature that can switch between elitist and non-elitist heuristics during the run. In essence, MAHH is a non-elitist search heuristic that differs from other search heuristics in the source of non-elitism.
We first identify the range of parameters that allow MAHH to hillclimb efficiently and prove that it can optimise the standard hillclimbing benchmark function OneMax in the best expected asymptotic time achievable by unbiased mutation-based randomised search heuristics. Afterwards, we use standard multimodal benchmark functions to highlight function characteristics where MAHH outperforms elitist evolutionary algorithms and the well-known Metropolis non-elitist algorithm by quickly escaping local optima, and ones where it does not. Since MAHH is essentially a non-elitist random local search heuristic, the paper is of independent interest to researchers in the fields of artificial intelligence and randomised search heuristics
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
Theory and practice of population diversity in evolutionary computation
Divergence of character is a cornerstone of natural evolution. On the contrary, evolutionary optimization processes are plagued by an endemic lack of population diversity: all candidate solutions eventually crowd the very same areas in the search space. The problem is usually labeled with the oxymoron “premature convergence” and has very different consequences on the different applications, almost all deleterious. At the same time, case studies from theoretical runtime analyses irrefutably demonstrate the benefits of diversity. This tutorial will give an introduction into the area of “diversity promotion”: we will define the term “diversity” in the context of Evolutionary Computation, showing how practitioners tried, with mixed results, to promote it. Then, we will analyze the benefits brought by population diversity in specific contexts, namely global exploration and enhancing the power of crossover. To this end, we will survey recent results from rigorous runtime analysis on selected problems. The presented analyses rigorously quantify the performance of evolutionary algorithms in the light of population diversity, laying the foundation for a rigorous understanding of how search dynamics are affected by the presence or absence of diversity and the introduction of diversity mechanisms
Analysing Equilibrium States for Population Diversity
Population diversity is crucial in evolutionary algorithms as it helps with
global exploration and facilitates the use of crossover. Despite many runtime
analyses showing advantages of population diversity, we have no clear picture
of how diversity evolves over time. We study how population diversity of
algorithms, measured by the sum of pairwise Hamming distances,
evolves in a fitness-neutral environment. We give an exact formula for the
drift of population diversity and show that it is driven towards an equilibrium
state. Moreover, we bound the expected time for getting close to the
equilibrium state. We find that these dynamics, including the location of the
equilibrium, are unaffected by surprisingly many algorithmic choices. All
unbiased mutation operators with the same expected number of bit flips have the
same effect on the expected diversity. Many crossover operators have no effect
at all, including all binary unbiased, respectful operators. We review
crossover operators from the literature and identify crossovers that are
neutral towards the evolution of diversity and crossovers that are not.Comment: To appear at GECCO 202
Benchmarking a Genetic Algorithm with Configurable Crossover Probability
We investigate a family of Genetic Algorithms (GAs) which
creates offspring either from mutation or by recombining two randomly chosen
parents. By scaling the crossover probability, we can thus interpolate from a
fully mutation-only algorithm towards a fully crossover-based GA. We analyze,
by empirical means, how the performance depends on the interplay of population
size and the crossover probability.
Our comparison on 25 pseudo-Boolean optimization problems reveals an
advantage of crossover-based configurations on several easy optimization tasks,
whereas the picture for more complex optimization problems is rather mixed.
Moreover, we observe that the ``fast'' mutation scheme with its are power-law
distributed mutation strengths outperforms standard bit mutation on complex
optimization tasks when it is combined with crossover, but performs worse in
the absence of crossover.
We then take a closer look at the surprisingly good performance of the
crossover-based GAs on the well-known LeadingOnes benchmark
problem. We observe that the optimal crossover probability increases with
increasing population size . At the same time, it decreases with
increasing problem dimension, indicating that the advantages of the crossover
are not visible in the asymptotic view classically applied in runtime analysis.
We therefore argue that a mathematical investigation for fixed dimensions might
help us observe effects which are not visible when focusing exclusively on
asymptotic performance bounds