Single-objective Evolutionary Algorithms Research Articles

Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives.

Multiobjective evolutionary algorithms are successfully applied in many real-world multiobjective optimization problems. As for many other AI methods, the theoretical understanding of these algorithms is lagging far behind their success in practice. In particular, previous theory work considers mostly easy problems that are composed of unimodal objectives. As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OneJumpZeroJump problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark. We prove that the simple evolutionary multiobjective optimizer (SEMO) with probability one does not compute the full Pareto front, regardless of the runtime. In contrast, for all problem sizes n and all jump sizes k∈[4..n2-1], the global SEMO (GSEMO) covers the Pareto front in an expected number of Θ((n-2k)nk) iterations. For k=o(n), we also show the tighter bound 32enk+1±o(nk+1), which might be the first runtime bound for an MOEA that is tight apart from lower-order terms. We also combine the GSEMO with two approaches that showed advantages in single-objective multimodal problems. When using the GSEMO with a heavy-tailed mutation operator, the expected runtime improves by a factor of at least kΩ(k). When adapting the recent stagnation-detection strategy of Rajabi and Witt (2022) to the GSEMO, the expected runtime also improves by a factor of at least kΩ(k) and surpasses the heavy-tailed GSEMO by a small polynomial factor in k. Via an experimental analysis, we show that these asymptotic differences are visible already for small problem sizes: A factor-5 speed-up from heavy-tailed mutation and a factor-10 speed-up from stagnation detection can be observed already for jump size 4 and problem sizes between 10 and 50. Overall, our results show that the ideas recently developed to aid single-objective evolutionary algorithms to cope with local optima can be effectively employed also in multiobjective optimization.

An Evolutionary-Based Mutation With Functional Annotation to Identify Protein Complexes Within PPI Networks

The research deals with an evolutionary-based mutation with functional annotation to identify protein complexes within PPI networks. An important field of research in computational biology is the difficult and fundamental challenge of revealing complexes in protein interaction networks. The complex detection models that have been developed to tackle challenges are mostly dependent on topological properties and rarely use the biological properties of PPI networks. This research aims to push the evolutionary algorithm to its maximum by employing gene ontology (GO) to communicate across proteins based on biological information similarity for direct genes. The outcomes show that the suggested method can be utilized to improve the predictability of the complexes identified. The GO functional annotation of proteins as a heuristic guide is injected into the framework of single-objective evolutionary algorithms (EAs), while the complex detection community score (CS) model works as a fitness function in EAs. In the experiments, we analyzed the performance of our proposed algorithm when applied to the publicly accessible yeast protein networks. The results show a considerable improvement in the detection ability of complexes in the PPI network.

Information-Theory-based Nondominated Sorting Ant Colony Optimization for Multiobjective Feature Selection in Classification.

Feature selection (FS) has received significant attention since the use of a well-selected subset of features may achieve better classification performance than that of full features in many real-world applications. It can be considered as a multiobjective optimization consisting of two objectives: 1) minimizing the number of selected features and 2) maximizing classification performance. Ant colony optimization (ACO) has shown its effectiveness in FS due to its problem-guided search operator and flexible graph representation. However, there lacks an effective ACO-based approach for multiobjective FS to handle the problematic characteristics originated from the feature interactions and highly discontinuous Pareto fronts. This article presents an Information-theory-based Nondominated Sorting ACO (called INSA) to solve the aforementioned difficulties. First, the probabilistic function in ACO is modified based on the information theory to identify the importance of features; second, a new ACO strategy is designed to construct solutions; and third, a novel pheromone updating strategy is devised to ensure the high diversity of tradeoff solutions. INSA's performance is compared with four machine-learning-based methods, four representative single-objective evolutionary algorithms, and six state-of-the-art multiobjective ones on 13 benchmark classification datasets, which consist of both low and high-dimensional samples. The empirical results verify that INSA is able to obtain solutions with better classification performance using features whose count is similar to or less than those obtained by its peers.

Design of Cross-Coupled Nonlinear PID Controller Using Single-Objective Evolutionary Algorithms

The effectiveness of evolutionary algorithms (EAs) such as differential search algorithm (DSA), Real-Coded genetic algorithm with simulated binary crossover (RGA-SBX), particle swarm optimization (PSO), and chaotic gravitational search algorithm (CGSA) on the optimal design of cross-coupled nonlinear PID controllers is compared in this paper. A cross-coupled multivariable PID controller structure for the binary distillation column was developed with two inputs and two outputs. EA simulations are run to lower IAE using two stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax plus PID parameter and IAE tolerance. Over 20 separate trials were used to compare the performances of several EAs using statistical measures such as best, mean, standard deviation of outcomes, and average calculation time. This article presents the design of a cross-coupled nonlinear PID controller using single-objective evolutionary algorithms. Using evolutionary algorithms (EAs) with a multicrossover strategy, the results achieved by various EAs are compared to previously reported results. The results of a multivariable cross-coupled system clearly show that a single-objective nonlinear PID controller performs better. Simulations further show that all four techniques evaluated are suitable for PID controller tweaking off-line. However, only the single-objective evolutionary algorithms are acceptable for online PID tuning due to their higher consistency and shorter computation time.

An Autoselection Strategy of Multiobjective Evolutionary Algorithms Based on Performance Indicator and its Application

The use of ensemble approaches in the single-objective evolutionary algorithms is ubiquitous, but ensembles of multiobjective evolutionary algorithms (MOEAs) have achieved relatively little attention. On the other hand, manually selecting a suitable MOEA to solve an actual multiobjective optimization problem (MOP) is time-consuming and challenging. Therefore, developing a multiobjective hyperheuristic to allocate computational resources for multiple MOEAs in an intelligent approach is beneficial. In this work, an autoselection strategy of MOEAs based on the performance indicator (MOEAS-PI) is introduced to alleviate the abovementioned problem. In the MOEAS-PI, the performance of each constituent MOEA in the pool is assessed according to a real-time and comprehensive performance indicator, which contains both the current and future performances. The MOEAS-PI is able to easily choose the best performing MOEA during the evolutionary process. Also, it can enhance the robustness of MOEAs and reduce the application risk. The effectiveness of the MOEAS-PI is carefully evaluated on 23 MOPs. Simulation results demonstrate that the MOEAS-PI is an effective and efficient method to integrate the advantages of each individual algorithm. Finally, the MOEAS-PI is utilized to solve a translation control problem of an immersed tunnel element under current flow. Experimental results reveal that the MOEAS-PI is a reliable and effective optimization approach to solve actual MOPs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Multiobjective optimization problems (MOPs) have been commonly found in various fields. However, a single MOEA cannot guarantee its sufficient robustness and adaptability in solving MOPs. Therefore, this study aims to propose a multiobjective hyperheuristic algorithm to improve the robustness of MOEAs. The performance of the proposed algorithm is tested on benchmark test functions and an actual MOP. The results show that the proposed approach can select a suitable MOEA to solve a particular type of MOPs during the evolutionary process and provide a solution set for decision-makers to control the translation of an immersed tunnel element under different objectives/operator environments.

Design of Cross Coupled Non-Linear Pid Controller Using Single Objective Evolutionary Algorithms

Design of Cross Coupled Non-Linear Pid Controller Using Single Objective Evolutionary Algorithms

Pearson coefficient matrix for studying the correlation of community detection scores in multi-objective evolutionary algorithm

Assessing a community detection algorithm is a difficult task due to the absence of finding a standard definition for objective functions to accurately identify the structure of communities in complex networks. Traditional methods generally consider the detecting of community structure as a single objective issue while its optimization generally leads to restrict the solution to a specific property in the community structure. In the last decade, new community detection models have been developed. These are based on multi-objective formulation for the problem, while ensuring that more than one objective (normally two) can be simultaneously optimized to generate a set of non-dominated solutions. However the issue of which objectives should be co-optimized to enhance the efficiency of the algorithm is still an open area of research. In this paper, first we generate a candidate set of partitions by saving the last population that has been generated using single objective evolutionary algorithm (SOEA) and random partitions based on the true partition for a given complex network. We investigate the features of the structure of communities which found by fifteen existing objectives that have been used in literature for discovering communities. Then, we found the correlation between any two objectives using the pearson coefficient matrix. Extensive experiments on four real networks show that some objective functions have a strong correlation and others either neutral or weak correlations.

A lexicographic cooperative co-evolutionary approach for feature selection

This paper starts with two hypotheses. The first one is that the simultaneous optimization of the hyperparameters regulating the classifier within a wrapper method, while the best subset of features is being determined, should improve the results with respect to those obtained with a pre-parameterized classifier. The second one is that solving these two problems can be formulated as a lexicographic optimization problem, allowing the use of a simple single-objective evolutionary algorithm to solve this multi-objective problem.The fitness function is of key importance for such wrapper methods. It is responsible for guiding the search towards potentially good solutions and it also consumes most of the runtime. Having these issues in mind, this paper also proposes a new lexicographic fitness function, designed to minimize the runtime of the algorithm and also to avoid over-fitting. Furthermore, the execution time and the quality of the results obtained by the wrapper procedure also depend on some algorithmic hyperparameters: the similarity thresholds used when comparing two different solutions lexicographically and the percentage of data samples used for validation during the training process. Thus, an experimental analysis has been carried out to find adequate values for these hyperparameters. Finally, the lexicographic cooperative co-evolutionary wrapper approach, using the new fitness function proposed in this paper, has been tested with several datasets belonging to the University of California, Irvine (UCI) repository and also with some real high-dimensional datasets, obtaining quite good results, compared to other state-of-the-art wrapper methods. The comparison has also been made lexicographically, with a new methodology proposed in this paper.

A parallel multi-objective evolutionary algorithm for community detection in large-scale complex networks

Community detection in large-scale complex networks has recently received significant attention as the volume of available data is becoming larger. The use of evolutionary algorithms (EAs) for community detection in large-scale networks has gained considerable popularity because these algorithms are fairly effective in networks with a relatively small number of nodes. In this paper, we propose a parallel multi-objective EA, called PMOEA, for community detection in large-scale networks, where the communities associated with key network nodes are detected in parallel. Specifically, we develop a multi-objective and a single-objective EA. The former is used to detect the communities of a key node instead of all communities in the network. The latter obtains the communities in the entire network using the previously detected communities of each key node. The performance of the proposed method was verified on both large-scale synthetic benchmark networks and real-world networks. The results demonstrated the superiority of PMOEA over six EA-based and two non-EA-based community-detection algorithms for large-scale networks.

Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives

Previous theory work on multi-objective evolutionary algorithms considers mostly easy problems that are composed of unimodal objectives. This paper takes a first step towards a deeper understanding of how evolutionary algorithms solve multi-modal multi-objective problems. We propose the OneJumpZeroJump problem, a bi-objective problem whose single objectives are isomorphic to the classic jump functions benchmark. We prove that the simple evolutionary multi-objective optimizer (SEMO) cannot compute the full Pareto front. In contrast, for all problem sizes n and all jump sizes k in [4..n/2-1], the global SEMO (GSEMO) covers the Pareto front in Θ((n-2k)n^k) iterations in expectation. To improve the performance, we combine the GSEMO with two approaches, a heavy-tailed mutation operator and a stagnation detection strategy, that showed advantages in single-objective multi-modal problems. Runtime improvements of asymptotic order at least k^Ω(k) are shown for both strategies. Our experiments verify the substantial runtime gains already for moderate problem sizes. Overall, these results show that the ideas recently developed for single-objective evolutionary algorithms can be effectively employed also in multi-objective optimization.

Evolutionary multi-objective set cover problem for task allocation in the Internet of Things

Efficient distribution of tasks in an Internet of Things (IoT) network ensures the fulfillment for all objects to dynamically cooperate with their limited energy, processing and memory capabilities. The main contribution of this paper is threefold. Firstly, we address the task allocation in the IoT as an optimization problem with a new formulation derived from the context of set cover problem. To the best of our knowledge, no such study has been considered in the literature. Secondly, we extend the set cover problem to further express the conflict that meets with both operational period and stability. Thirdly, an evolutionary single objective and multi-objective algorithms are developed to tackle the formulated problem. Two heuristic operators are also introduced and injected within the framework of the evolutionary algorithms where the need arises to harness their strength in terms of both operational period and network stability. Performance evaluation is reported while different problem dimensions are experimented with in the simulations. The results show that the proposed multi-objective evolutionary algorithm is quite appropriate to converge to more accurate solutions than the counterpart single objective evolutionary algorithm. Further, the results give plausible evidence supporting the importance of the proposed heuristic operators to mitigate against the contradictory nature of the network lifetime in terms of operational period and stability.

Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem

One of the main components of most modern Multi-Objective Evolutionary Algorithms (MOEAs) is to maintain a proper diversity within a population in order to avoid the premature convergence problem. Due to this implicit feature that most MOEAs share, their application for Single-Objective Optimization (SO) might be helpful, and provides a promising field of research. Some common approaches to this topic are based on adding extra—and generally artificial—objectives to the problem formulation. However, when applying MOEAs to implicit Multi-Objective Optimization Problems (MOPs), it is not common to analyze how effective said approaches are in relation to optimizing each objective separately. In this paper, we present a comparative study between MOEAs and Single-Objective Evolutionary Algorithms (SOEAs) when optimizing every objective in a MOP, considering here the bi-objective case. For the study, we focus on two well-known and widely studied optimization problems: the Knapsack Problem (KNP) and the Travelling Salesman Problem (TSP). The experimental study considers three MOEAs and two SOEAs. Each SOEA is applied independently for each optimization objective, such that the optimized values obtained for each objective can be compared to the multi-objective solutions achieved by the MOEAs. MOEAs, however, allow optimizing two objectives at once, since the resulting Pareto fronts can be used to analyze the endpoints, i.e., the point optimizing objective 1 and the point optimizing objective 2. The experimental results show that, although MOEAs have to deal with several objectives simultaneously, they can compete with SOEAs, especially when dealing with strongly correlated or large instances.

A comparison of multi-objective optimization algorithms for weight setting problems in traffic engineering

Traffic engineering approaches are increasingly important in network management to allow an optimized configuration and resource allocation. In link-state routing, setting appropriate weights to the links is an important and challenging optimization task. Different approaches have been put forward towards this aim, including evolutionary algorithms (EAs). This work addresses the evaluation of a single and two multi-objective EAs, in two tasks related to weight setting optimization towards optimal intra-domain routing, knowing the network topology and aggregated traffic demands and seeking to minimize network congestion. In both tasks, the optimization considers scenarios where there is a dynamic alteration in the network, with (1) changes in the traffic demand matrices, and (2) link failures. The methods will simultaneously optimize for both conditions, the normal and the altered one, following a preventive TE approach. Since this leads to a bi-objective function, the use of multi-objective EAs, such as SPEA2 and NSGA-II, came naturally; those are compared to a single-objective EA previously proposed by the authors. The results show a remarkable performance and scalability of NSGA-II in the proposed tasks presenting itself as the most promising option for TE.

A local-to-global scheme-based multi-objective evolutionary algorithm for overlapping community detection on large-scale complex networks

Recently, multi-objective evolutionary algorithms (MOEAs) have been shown promising performance for detecting overlapping community structure in complex networks. However, it is still challenging to design MOEAs for overlapping community detection on large-scale complex networks due to the curse of dimensionality. Along this avenue, this paper proposes a local-to-global scheme-based MOEA named LG-MOEA for overlapping community detection on large-scale complex networks, which mainly consists of two stages: a local community structure detection stage and a global community structure determination stage. To be specific, in the local community structure detection stage, the key nodes that are central to community and essential to the connectedness of community are firstly identified. Then for each key node, an MOEA with the proposed community boundary control strategy is suggested to detect a set of local overlapping communities through local expansion around the key node. In the global community structure determination stage, a single objective evolutionary algorithm is adopted to search for a suitable local overlapping community for each key node and combine them as one global community partition of the whole network. The proposed LG-MOEA is compared with several competitive overlapping community detection algorithms on both real-world small-scale and large-scale networks, and the experimental results show its superiority for overlapping community detection in terms of the generalized normalized mutual information gNMI and the extended modularity $$Q_{ov}$$ , especially has competitive superiority for large-scale complex networks.

Explicit Control of Implicit Parallelism in Decomposition-Based Evolutionary Many-Objective Optimization Algorithms [Research Frontier

Over the past two decades, Evolutionary Multi-objective Optimization (EMO) algorithms have demonstrated their ability to find and maintain multiple trade-off solutions in two and three-objective problems, making EMO as one of the most emergent and exciting fields of research and application within Computational Intelligence (CI) area. The main reason for EMO's success is that the population-based EMO operators are able to establish an implicit parallel search within an evolving population to find multiple Pareto-optimal regions of the search space parallelly. For many-objective optimization problems involving a largedimensional objective space, the extent of implicit parallelism is argued here to be too generic, compared to the same in a lower-dimensional objective space. Decomposition-based EMO algorithms - a recent trend in EMO literature - which divide the overall computing task into a number of sub-tasks of focusing within a region of the search space have found to be successful in solving many-objective problems. In this paper, we study the effect of explicit control of an algorithm's implicit parallelism mechanism for achieving an enhanced performance of decomposition-based EMO algorithms. We consider three decomposition-based many-objective evolutionary algorithms (EAs) - MOEA/D, MOEA/D-M2M, and NSGA-III - for this purpose. We also investigate another explicit control strategy of suitably choosing a normalization method of objectives for improving the performance of MOEA/D and MOEA/ D-M2M methods, and report much improved performance than their original counterparts. The principles of this study are valid for any population-based search and optimization algorithms and can be extended to improve the performance other single-objective EA, EMO, and other relevant CI methods.

Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims to design a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 constrained optimization competition benchmark suite. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimization. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective evolutionary algorithms for constrained optimization, but MOEAs based on non-dominance, such as PMODE, may not.

Heuristic Modularity for Complex Identification in Protein-Protein Interaction Networks

Due to the significant role in understanding cellular processes, the decomposition of Protein-Protein Interaction (PPI) networks into essential building blocks, or complexes, has received much attention for functional bioinformatics research in recent years. One of the well-known bi-clustering descriptors for identifying communities and complexes in complex networks, such as PPI networks, is modularity function. The contribution of this paper is to introduce heuristic optimization models that can collaborate with the modularity function to improve its detection ability. The definitions of the formulated heuristics are based on nodes and different levels of their neighbor properties. The modularity function and the formulated heuristics are then injected into the mechanism of a single objective Evolutionary Algorithm (EA) tailored specifically to tackle the problem, and thus, to identify possible complexes from PPI networks. In the experiments, different overlapping scores are used to evaluate the detection accuracy in both complex and protein levels. According to the evaluation metrics, the results reveal that the introduced heuristics have the ability to harness the accuracy of the existing modularity while identifying protein complexes in the tested PPI networks.

ESOEA: Ensemble of single objective evolutionary algorithms for many-objective optimization

Inspired by the success of decomposition based evolutionary algorithms and the necessary search for a versatile many-objective optimization algorithm which is adaptive to several kinds of characteristics of the search space, the proposed work presents an adaptive framework which addresses many-objective optimization problems by using an ensemble of single objective evolutionary algorithms (ESOEA). It adopts a reference-direction based approach to decompose the population, followed by scalarization to transform the many-objective problem into several single objective sub-problems which further enhances the selection pressure. Additionally, with a feedback strategy, ESOEA explores the directions along difficult regions and thus, improving the search capabilities along those directions. For experimental validation, ESOEA is integrated with an adaptive Differential Evolution and experimented on several benchmark problems from the DTLZ, WFG, IMB and CEC 2009 competition test suites. To assess the efficacy of ESOEA, the performance is noted in terms of convergence metric, inverted generational distance, and hypervolume indicator, and is compared with numerous other multi- and/or many-objective evolutionary algorithms. For a few test cases, the resulting Pareto-fronts are also visualized which help in the further analysis of the results and in establishing the robustness of ESOEA.

Hiding sensitive itemsets with multiple objective optimization

Privacy-preserving data mining (PPDM) has become an important research topic, as it can hide sensitive information, while ensuring that information can still be extracted for decision making. While performing the sanitization progress for hiding the sensitive information, three side effects such as hiding failure, missing cost, and artificial cost happen at the same time. Several evolutionary algorithms were introduced to minimize those three side effects of PPDM using a single-objective function that generates one solution for sanitization. This paper presents a multiobjective algorithm (NSGA2DT) with two strategies for hiding sensitive information with transaction deletion based on the NSGA-II framework. To obtain better balance of side effects, the designed NSGA2DT takes database dissimilarity (Dis) as one more factor to achieve better performance in terms of four side effects. Moreover, instead of a single solution of the sanitization progress, the designed NSGA2DT provides more than one solutions than those of single-objective evolutionary algorithms, which shows flexibility to select the most appropriate transactions for deletion depending on user’s preference. A Fast SoRting strategy (FSR) and the pre-large concept are utilized, respectively, in this paper to find the optimized transactions for deletion and speed up the iterative process. Based on the developed NSGA2DT, the set of several Pareto solutions can be easily discovered, thus avoiding the problem of local optimization of single-objective approaches. Besides, the designed NSGA2DT does not require to set initial weights for evaluating the side effects, and thus, the results could not be seriously influenced by the predefined weights. Experimental results show that the proposed NSGA2DT provides satisfactory results with reduced side effects, compared to previous evolutionary approaches with single-objective function.

Evolutionary computing methodology for small wind turbine supporting structures

The paper presents a comprehensive, complex, numerical, optimization methodology (computational framework) dedicated for supporting structures of small-scale wind turbines. The small wind turbine (SWT) supporting structure is one of the key components determining the cost of such a device. Therefore, the supporting structure optimization will allow cost reduction and, hence, popularization of these devices around the world. The presented methodology is based on the following: single-objective (aggregation-approach to multi-objective problem) evolutionary algorithm driven optimization, finite-element structural analyses, estimation of wind energy capture efficiency (coupled aero-servo-elastic numerical simulations), and economic evaluation (based on real meteorological data). Then, the methodology is proposed for a guy-wired mast structure of an arbitrary chosen SWT model. The optimization of chosen design features of the structure is performed and as a result the optimal solution for given assumptions is presented and scaling factor for that case is identified (total mass of the foundations). The successful use of combined numerical methods (genetic algorithms, FE method analyses, coupled aero-servo-elastic numerical simulations, pre-/post-processing scripts, and economic evaluation models) is the main novelty of this work.