Fast Immune System-Inspired Hypermutation Operators for Combinatorial Optimization

Corus, Dogan; Oliveto, Pietro S.; Yazdani, D.

doi:10.1109/tevc.2021.3068574

Cited by 16 publications

(6 citation statements)

References 48 publications

(118 reference statements)

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“…This is the approach adopted in the Nevergrad optimization platform [26]. Due to the binomial distribution being well-concentrated for n•p 1, getting rid of it as a proxy distribution leaves most of the properties of the algorithm intact, and allowing to flip up to n bits was shown to improve the performance in certain scenarios [27]. This mutation operator also flips a positive number of bits.…”

Section: A the (1+1) Ea With Binomial And Power-law Distributionsmentioning

confidence: 99%

The $(1+(\lambda,\lambda))$ Genetic Algorithm on the Vertex Cover Problem: Crossover Helps Leaving Plateaus

Buzdalov

2022

2022 IEEE Congress on Evolutionary Computation (CEC)

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Many discrete optimization problems feature plateaus, which are hard to evolutionary algorithms due to the lack of fitness guidance. While higher mutation rates may assist in making a jump from the plateau to some better search point, an algorithm typically performs random walks on a plateau, possibly with some assistance from diversity mechanisms.The vertex cover problem is one of the important NP-hard problems. We found that the recently proposed (1 + (λ, λ)) genetic algorithm solves certain instances of this problem, including those that are hard to heuristic solvers, much faster than simpler mutation-only evolutionary algorithms.Our theoretical analysis shows that there exists an intricate interplay between the problem structure and the way crossovers are used. It results in a drift towards the points where finding the next improvement is much easier. While this condition is formally proven only on one class of instances and for a subset of search points, experiments show that it is responsible for performance improvements in a much larger range of cases.

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Section: A the (1+1) Ea With Binomial And Power-law Distributionsmentioning

confidence: 99%

The $(1+(\lambda,\lambda))$ Genetic Algorithm on the Vertex Cover Problem: Crossover Helps Leaving Plateaus

Buzdalov

2022

2022 IEEE Congress on Evolutionary Computation (CEC)

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“…It should be pointed out that the originally proposed operator flipped 𝑛 bits at every operation one by one and used a probability distribution very similar to (2) to determine whether to evaluate the solution after the 𝑀-th bit-flip and stopped the hypermutation as soon as an improvement was detected (i.e., stop at first constructive mutation). However, this is not necessary as shown in [11] and for a fairer comparison with the distribution of the Fast (1+1) AIS 𝛽 we remove this feature and only evaluate the solution once all the 𝑀 bits are flipped. If this hypermutation operator is used in the framework of Algorithm 1, we call the resulting algorithm Fast (1+1) AIS 𝑠𝛽 .…”

Section: Algorithms From the Literaturementioning

confidence: 99%

“…Both algorithms exhibit their best performance at escaping local optima via large mutations when the parameter 𝛽 is set to a value close to 1. However, with such a parameter value, the operators lose effectiveness in conjunction with the ageing operator for escaping from local optima with large basins of attraction by accepting solutions of inferior quality, because the high mutation rates lead the algorithm back to the basin of attraction of the original local optimum with high probability [11].…”

Section: Algorithms From the Literaturementioning

confidence: 99%

“…Recently, though, so called Fast AISs have been presented that are asymptotically as fast as traditional randomized local search (RLS) and EAs at hillclimbing, while still outperforming them during the exploration phases [8]. Such improved performance during the hillclimbing phases even allows for linear speed-ups of the AISs to approximate Number Partitioning [11].…”

Section: Introductionmentioning

confidence: 99%

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Automatic adaptation of hypermutation rates for multimodal optimisation

Corus

Oliveto

Yazdani

2021

Proceedings of the 16th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

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Previous work has shown that in Artificial Immune Systems (AIS) the best static mutation rates to escape local optima with the ageing operator are far from the optimal ones to do so via large hypermutations and vice-versa. In this paper we propose an AIS that automatically adapts the mutation rate during the run to make good use of both operators. We perform rigorous time complexity analyses for standard multimodal benchmark functions with significant characteristics and prove that our proposed algorithm can learn to adapt the mutation rate appropriately such that both ageing and hypermutation are effective when they are most useful for escaping local optima. In particular, the algorithm provably adapts the mutation rate such that it is efficient for the problems where either operator has been proven to be effective in the literature.

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“…Over the past decades, evolutionary algorithms have been extensively studied to solve the combinatorial optimization problems abstracted from real applications in various areas, including engineering, logistics, and economics. Although the theoretical understanding of the behavior of evolutionary algorithms (more specifically, their expected time) has achieved lots of progress, in particular, for the well-known Traveling Salesperson problem [1,2,3,4,5,6], Vertex Cover problem [7,8,9,10,11,12,13,14,15,16,17], Knapsack problem [18,19,20,21,22,23,24], Makespan Scheduling problem [25,26,27,28,29,30,31], and Minimum Spanning Tree problem [32,33,34,35,36,37], etc, its development still lags far behind its success in practical applications.…”

Section: Introductionmentioning

confidence: 99%

Time Complexity Analysis of Evolutionary Algorithms for 2-Hop (1,2)-Minimum Spanning Tree Problem

Shi¹,

Neumann²,

Wang³

2021

Preprint

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The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization performance of evolutionary algorithms. Within the paper, we consider a constrained version of the problem named 2-Hop (1,2)-Minimum Spanning Tree problem (abbr. 2H-(1,2)-MSTP) in the context of evolutionary algorithms, which has been shown to be NP-hard. Following how evolutionary algorithms are applied to solve the MSTP, we first consider the evolutionary algorithms with search points in edge-based representation adapted to the 2H-(1,2)-MSTP (including the (1+1) EA, Global Simple Evolutionary Multi-Objective Optimizer and its two variants). More specifically, we separately investigate the upper bounds on their expected time (i.e., the expected number of fitness evaluations) to obtain a 3 2 -approximate solution with respect to different fitness functions. Inspired by the special structure of 2-hop spanning trees, we also consider the (1+1) EA with search points in vertex-based representation that seems not so natural for the problem and give an upper bound on its expected time to obtain a 3 2 -approximate solution, which is better than the above mentioned ones.

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Fast Immune System-Inspired Hypermutation Operators for Combinatorial Optimization

Cited by 16 publications

References 48 publications

The $(1+(\lambda,\lambda))$ Genetic Algorithm on the Vertex Cover Problem: Crossover Helps Leaving Plateaus

The $(1+(\lambda,\lambda))$ Genetic Algorithm on the Vertex Cover Problem: Crossover Helps Leaving Plateaus

Automatic adaptation of hypermutation rates for multimodal optimisation

Time Complexity Analysis of Evolutionary Algorithms for 2-Hop (1,2)-Minimum Spanning Tree Problem

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