Mutation-based Evolutionary Algorithms Research Articles

Intelligent mutation based evolutionary optimization algorithm for genomics and precision medicine.

In this paper, genomics and precision medicine have witnessed remarkable progress with the advent of high-throughput sequencing technologies and advances in data analytics. However, because of the data's great dimensionality and complexity, the processing and interpretation of large-scale genomic data present major challenges. In order to overcome these difficulties, this research suggests a novel Intelligent Mutation-Based Evolutionary Optimization Algorithm (IMBOA) created particularly for applications in genomics and precision medicine. In the proposed IMBOA, the mutation operator is guided by genome-based information, allowing for the introduction of variants in candidate solutions that are consistent with known biological processes. The algorithm's combination of Differential Evolution with this intelligent mutation mechanism enables effective exploration and exploitation of the solution space. Applying a domain-specific fitness function, the system evaluates potential solutions for each generation based on genomic correctness and fitness. The fitness function directs the search toward ideal solutions that achieve the problem's objectives, while the genome accuracy measure assures that the solutions have physiologically relevant genomic properties. This work demonstrates extensive tests on diverse genomics datasets, including genotype-phenotype association studies and predictive modeling tasks in precision medicine, to verify the accuracy of the proposed approach. The results demonstrate that, in terms of precision, convergence rate, mean error, standard deviation, prediction, and fitness cost of physiologically important genomic biomarkers, the IMBOA consistently outperforms other cutting-edge optimization methods.

Analysis and improvements on feature selection methods based on artificial neural network weights

The alignment of protein networks between different species has become a topic of considerable interest in recent years. To perform such alignments between two protein networks, it is necessary to consider the biological functions in which proteins are involved and the structure of the networks topology. Due to the existing complexity of using both topological and biological similarity during the alignment process, many current tools sacrifice the biological similarity of their solutions in order to improve their topological score. This happens because they try to combine these two objectives that are conflicting into a single objective, which leads to the need to subjectively decide about the weight to be given to each one. To remedy this situation, we present MOMEA, a Multi-Objective Mutation-based Evolutionary Algorithm that uses intelligent mutation operators and a dominance-based approach to generate a variety of alignments. Instead of considering a single objective that relates both similarities, MOMEA analyzes the topological and biological similarities as different objectives. The generated results are high-quality and varied non-dominated alignments, i.e., located in a wide area of the solution space. Finally, to demonstrate the effectiveness of this proposal, data from live organisms have been used in order to perform comparisons with several popular biological tools and with the unique existing multi-objective approach in the scientific literature. Comparison results are good and confirm a positive performance of MOMEA compared to all the other tools.

MOMEA: Multi-Objective Mutation-based Evolutionary Algorithm for the alignment of protein networks

The alignment of protein networks between different species has become a topic of considerable interest in recent years. To perform such alignments between two protein networks, it is necessary to consider the biological functions in which proteins are involved and the structure of the networks topology. Due to the existing complexity of using both topological and biological similarity during the alignment process, many current tools sacrifice the biological similarity of their solutions in order to improve their topological score. This happens because they try to combine these two objectives that are conflicting into a single objective, which leads to the need to subjectively decide about the weight to be given to each one. To remedy this situation, we present MOMEA, a Multi-Objective Mutation-based Evolutionary Algorithm that uses intelligent mutation operators and a dominance-based approach to generate a variety of alignments. Instead of considering a single objective that relates both similarities, MOMEA analyzes the topological and biological similarities as different objectives. The generated results are high-quality and varied non-dominated alignments, i.e., located in a wide area of the solution space. Finally, to demonstrate the effectiveness of this proposal, data from live organisms have been used in order to perform comparisons with several popular biological tools and with the unique existing multi-objective approach in the scientific literature. Comparison results are good and confirm a positive performance of MOMEA compared to all the other tools.

Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift.

A decent number of lower bounds for non-elitist population-based evolutionary algorithms has been shown by now. Most of them are technically demanding due to the (hard to avoid) use of negative drift theorems-general results which translate an expected movement away from the target into a high hitting time. We propose a simple negative drift theorem for multiplicative drift scenarios and show that it can simplify existing analyses. We discuss in more detail Lehre's (2010) negative drift in populations method, one of the most general tools to prove lower bounds on the runtime of non-elitist mutation-based evolutionary algorithms for discrete search spaces. Together with other arguments, we obtain an alternative and simpler proof of this result, which also strengthens and simplifies this method. In particular, now only three of the five technical conditions of the previous result have to be verified. The lower bounds we obtain are explicit instead of only asymptotic. This allows us to compute concrete lower bounds for concrete algorithms, but also enables us to show that super-polynomial runtimes appear already when the reproduction rate is only a (1-ω(n-1/2)) factor below the threshold. For the special case of algorithms using standard bit mutation with a random mutation rate (called uniform mixing in the language of hyper-heuristics), we prove the result stated by Dang and Lehre (2016b) and extend it to mutation rates other than Θ(1/n), which includes the heavy-tailed mutation operator proposed by Doerr et al. (2017). We finally use our method and a novel domination argument to show an exponential lower bound for the runtime of the mutation-only simple genetic algorithm on OneMax for arbitrary population size.

Data Structures for Direct Spanning Tree Representations in Mutation-based Evolutionary Algorithms

Optimization methods for spanning tree problems may require efficient data structures. The node-depth-degree representation (NDDR) has achieved relevant results for direct spanning tree representation together with evolutionary algorithms (EAs). Its two mutation operators have average time $O(\sqrt {n})$ , where $n$ is the number of vertices of the graph, while similar operators implemented by predecessor arrays, a typical tree data structure, have time $O(n)$ . Dynamic trees are also relevant when investigating tree representations since they have low time complexity, but there is no proper extension of them for EAs. Using aspects of both a dynamic tree and NDDR, namely, Euler tours and structural sharing, we propose a data structure called 2LETT, whose mutation operators have time $O(\sqrt {n})$ in the worst case. Experiments with the mutation operators using 2LETT, predecessor arrays, and NDDR are carried out for graphs with up to 300 000 vertices. For a mutation operator that exchanges any two valid edges, predecessor arrays present the best performance for random trees with fewer than 10 000 vertices; while 2LETT has the best performance for trees with more than 10 000 vertices. Especially, noteworthy is the fact that 2LETT is the only structure whose running time is independent of tree diameter.

On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism.

Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis has been focused on experimental approaches that have shown that clearing is a powerful diversity-preserving mechanism. Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic distance function always succeeds in optimising all functions of unitation for small niches in polynomial time, while a genotypic distance function requires exponential time. Finally, we prove that with phenotypic and genotypic distances, clearing is able to find both optima for and several general classes of bimodal functions in polynomial expected time. We use empirical analysis to highlight some of the characteristics that makes it a useful mechanism and to support the theoretical results.

On Proportions of Fit Individuals in Population of Mutation-Based Evolutionary Algorithm with Tournament Selection.

In this article, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness above given thresholds. In the case of so-called monotone mutation, the obtained bounds imply that increasing the tournament size improves the EA performance. As corollaries, we obtain an exponentially vanishing tail bound for the Randomized Local Search on unimodal functions and polynomial upper bounds on the runtime of EAs on the 2-SAT problem and on a family of Set Cover problems proposed by E. Balas.

How Crossover Speeds up Building Block Assembly in Genetic Algorithms

We reinvestigate a fundamental question: How effective is crossover in genetic algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter, we show that using crossover makes every ([Formula: see text]+[Formula: see text])genetic algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate[Formula: see text] and[Formula: see text]. Crossover is beneficial because it can capitalize on mutations that have both beneficial and disruptive effects on building blocks: crossover is able to repair the disruptive effects of mutation in later generations. Compared to mutation-based evolutionary algorithms, this makes multibit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from [Formula: see text] to [Formula: see text]. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building block functions.

Analysis of Randomised Search Heuristics for Dynamic Optimisation.

Dynamic optimisation is an area of application where randomised search heuristics like evolutionary algorithms and artificial immune systems are often successful. The theoretical foundation of this important topic suffers from a lack of a generally accepted analytical framework as well as a lack of widely accepted example problems. This article tackles both problems by discussing necessary conditions for useful and practically relevant theoretical analysis as well as introducing a concrete family of dynamic example problems that draws inspiration from a well-known static example problem and exhibits a bi-stable dynamic. After the stage has been set this way, the framework is made concrete by presenting the results of thorough theoretical and statistical analysis for mutation-based evolutionary algorithms and artificial immune systems.

The Effects of Constant and Bit-Wise Neutrality on Problem Hardness, Fitness Distance Correlation and Phenotypic Mutation Rates

Kimura's neutral theory of evolution has inspired researchers from the evolutionary computation community to incorporate neutrality into evolutionary algorithms (EAs) in the hope that it can aid evolution. The effects of neutrality on evolutionary search have been considered in a number of studies, the results of which, however, have been highly contradictory. In this paper, we analyze the reasons for this and make an effort to shed some light on neutrality by addressing them. We consider two very simple forms of neutrality: constant neutrality-a neutral network of constant fitness, identically distributed in the whole search space-and bit-wise neutrality, where each phenotypic bit is obtained by transforming a group of genotypic bits via an encoding function. We study these forms of neutrality both theoretically and empirically (both for standard benchmark functions and a class of random MAX-SAT problems) to see how and why they influence the behavior and performance of a mutation-based EA. In particular, we analyze how the fitness distance correlation of landscapes changes under the effect of different neutral encodings and how phenotypic mutation rates vary as a function of genotypic mutation rates. Both help explain why the behavior of a mutation-based EA may change so radically as problem, form of neutrality, and mutation rate are varied.

Particle swarm optimizer with adaptive tabu and mutation

Evolutionary Algorithms (EAs) and Swarm Intelligence (SI) are widely used to tackle black-box global optimization problems when no prior knowledge is available. In order to increase search diversity and avoid stagnation in local optima, the mutation operator was introduced and has been extensively studied in EAs and SI-based algorithms. However, the performance after introducing mutation can be affected in many aspects and the parameters used to perform mutations are very hard to determine. For the purpose of developing efficient mutation operators, this article proposes a unified tabu and mutation framework with parameter adaptations in the context of the Particle Swarm Optimizer (PSO). The proposed framework is a significant extension of our preliminary work [Wang et al. 2007]. Empirical studies on 25 benchmark functions indicate that under the proposed framework: (1) excellent performance can be achieved even with a small number of mutations; (2) the derived algorithm consistently performs well on diverse types of problems and overall performance even surpasses the state-of-the-art PSO variants and representative mutation-based EAs; and (3) fast convergence rates can be preserved despite the use of a long jump mutation operator (the Cauchy mutation).

On the Choice of the Parent Population Size

Evolutionary algorithms (EAs) are population-based randomized search heuristics that often solve problems successfully. Here the focus is on the possible effects of changing the parent population size in a simple, but still realistic, mutation-based EA. It preserves diversity by avoiding duplicates in its population. On the one hand its behavior on well-known pseudo-Boolean example functions is investigated by means of a rigorous runtime analysis. A comparison with the expected runtime of the algorithm's variant that does not avoid duplicates demonstrates the strengths and weaknesses of maintaining diversity. On the other hand, newly developed functions are presented for which the optimizer considered that even a decrease of the population size by a single increment leads from efficient optimization to enormous runtime and overwhelming probability. This is proven for all feasible population sizes and thereby this result forms a hierarchy theorem. In order to obtain all these results new methods for the analysis of the EA are developed.

When to use bit-wise neutrality

Representation techniques are important issues when designing successful evolutionary algorithms. Within this field the use of neutrality plays an important role. We examine the use of bit-wise neutrality introduced by Poli and López (2007) from a theoretical point of view and show that this mechanism only enhances mutation-based evolutionary algorithms if not the same number of genotypic bits for each phenotypic bit is used. Using different numbers of genotypic bits for the bits in the phenome we point out by rigorous runtime analyses that it may reduce the optimization time significantly.

Evolution and Learning Mediated by Differences in Developmental Timing

The present paper introduces a mutation-based evolutionary algorithm that evolves genes to regulate the developmental timings of phenotypic values. For each generation, an individual in the evolutionary algorithm time-sequentially generates a given number of entire phenotypes before finishing its life. Each gene represents a cycle time of changing probability for determining its corresponding phenotypic value, which is an indicator of developmental timing. In addition, the algorithm has a learning mechanism such that, during the lifetime of an individual, genes representing a long cycle time can change the probability of adaptation more easily than genes representing a short cycle time. Therefore, if the diversity of the genes is maintained, it can be expected that the algorithm provides a different evolution speed to each phenotypic value. The present paper also discusses a new approach to depicting an evolutionary optimization process. An evolutionary optimization process involves the identification of linkage between variables, and therefore, network structures formed using the identified linkage information determine how the evolutionary algorithm solves a given optimization problem. The proposed approach regards an evolutionary optimization process as a change in the network topology that emerges in the process of linkage identification. The simulation results indicate that evolution and learning mediated by the difference in developmental timing helps to sequentially solve hard uniformly-scaled bit optimization problems with linkage between variables.

How the (1+1) ES using isotropic mutations minimizes positive definite quadratic forms

The (1+1) evolution strategy (ES), a simple, mutation-based evolutionary algorithm for continuous optimization problems, is analyzed. In particular, we consider the most common type of mutations, namely Gaussian mutations, and the 1 5 -rule for mutation adaptation, and we are interested in how the runtime/number of function evaluations to obtain a predefined reduction of the approximation error depends on the dimension of the search space. The most discussed function in the area of ES is the so-called S PHERE-function given by S PHERE : R n → R with x ↦ x ⊤ Ix (where I ∈ R n × n is the identity matrix), which also has already been the subject of a runtime analysis. This analysis is extended to arbitrary positive definite quadratic forms that induce ellipsoidal fitness landscapes which are “close to being spherically symmetric”, showing that the order of the runtime does not change compared to S PHERE. Furthermore, certain positive definite quadratic forms f : R n → R with x ↦ x ⊤ Qx , where Q ∈ R n × n , inducing ellipsoidal fitness landscapes that are “far away from being spherically symmetric” are exemplarily investigated, namely f ( x ) = ξ · x 1 2 + ⋯ + x n / 2 2 + x n / 2 + 1 2 + ⋯ + x n 2 with ξ = poly ( n ) such that 1 / ξ → 0 as n → ∞ . It is proved that the optimization very quickly stabilizes and that, subsequently, the runtime to halve the approximation error is Θ ( ξ · n ) compared to Θ ( n ) for S PHERE.