Offspring Solutions Research Articles

Hierarchicity-based (self-similar) hybrid genetic algorithm for the grey pattern quadratic assignment problem

In this paper, we present a hierarchicity-based (self-similar) hybrid genetic algorithm for the solution of the grey pattern quadratic assignment problem. This is a novel hybrid genetic search-based heuristic algorithm with the original, hierarchical architecture and it is in connection with what is known as self-similarity—this means that an object (in our case, algorithm) is exactly or approximately similar to constituent parts of itself. The two main aspects of the proposed algorithm are the following: (1) the hierarchical (self-similar) structure of the genetic algorithm itself, and (2) the hierarchical (self-similar) form of the iterated tabu search algorithm, which is integrated into the genetic algorithm as an efficient local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm.

Paired Offspring Generation for Constrained Large-Scale Multiobjective Optimization

Constrained multiobjective optimization problems (CMOPs) widely exist in real-world applications, and they are challenging for conventional evolutionary algorithms (EAs) due to the existence of multiple constraints and objectives. When the number of objectives or decision variables is scaled up in CMOPs, the performance of EAs may degenerate dramatically and may fail to obtain any feasible solutions. To address this issue, we propose a paired offspring generation-based multiobjective EA for constrained large-scale optimization. The general idea is to emphasize the role of offspring generation in reproducing some promising feasible or useful infeasible offspring solutions. We first adopt a small set of reference vectors for constructing several subpopulations with a fixed number of neighborhood solutions. Then, a pairing strategy is adopted to determine some pairwise parent solutions for offspring generation. Consequently, the pairwise parent solutions, which could be infeasible, may guide the generation of well-converged solutions to cross the infeasible region(s) effectively. The proposed algorithm is evaluated on CMOPs with up to 1000 decision variables and ten objectives. Moreover, each component in the proposed algorithm is examined in terms of its effect on the overall algorithmic performance. Experimental results on a variety of existing and our tailored test problems demonstrate the effectiveness of the proposed algorithm in constrained large-scale multiobjective optimization.

Combining Global and Local Information for Offspring Generation in Evolutionary Multiobjective Optimization

The Pareto optimal set of a continuous multiobjective optimization problem shows some kinds of structure, which is called the regularity property and it has been applied to design effective offspring reproduction operators in multiobjective optimization evolutionary algorithms (MOEAs). Usually, the probability model sampling and neighbor based mating are the main strategies to implement the regularity property in designing reproduction operators. In fact, different information is used in these methods. There is no doubt that combining the global and local information will favor the search. To use more information in the offspring reproduction, in this paper, we propose a regularity assisted MOEA, RAMEA for short, that combines Gaussian sampling and neighbor based mating for offspring reproduction. In RAMEA, the $k$ -means clustering method is used to learn the manifold structure information and partition the population into $K$ clusters. A Gaussian probability model is built with $K$ mean vectors of clusters, and $K$ trial offspring solutions are sampled from thus model. Moreover, these sampled trial solutions are added to each cluster as mating parents to generate other offspring solutions. In this way, the global and local information are combined to generate offspring solutions in RAMEA. The proposed approach has been executed in several test instances with complicated characteristics, and compared with seven classical or newly developed MOEAs. The results have demonstrated its advantages over other algorithms.

CBGA-ES+: A Cluster-Based Genetic Algorithm with Non-Dominated Elitist Selection for Supporting Multi-Objective Test Optimization

Many real-world test optimization problems (e.g., test case prioritization) are multi-objective intrinsically and can be tackled using various multi-objective search algorithms (e.g., Non-dominated Sorting Genetic Algorithm (NSGA-II)). However, existing multi-objective search algorithms have certain randomness when selecting parent solutions for producing offspring solutions. In a worse case, suboptimal parent solutions may result in offspring solutions with bad quality, and thus affect the overall quality of the solutions in the next generation. To address such a challenge, we propose CBGA-ES+, a novel cluster-based genetic algorithm with non-dominated elitist selection to reduce the randomness when selecting the parent solutions to support multi-objective test optimization. We empirically compared CBGA-ES+ with random search and greedy (as baselines), four commonly used multi-objective search algorithms (i.e., Multi-objective Cellular genetic algorithm (MOCell), NSGA-II, Pareto Archived Evolution Strategy (PAES), and Strength Pareto Evolutionary Algorithm (SPEA2)), and the predecessor of CBGA-ES+ (named CBGA-ES) using five multi-objective test optimization problems with eight subjects (two industrial, one real world, and five open source). The results showed that CBGA-ES+ managed to significantly outperform the selected search algorithms for a majority of the experiments. Moreover, for the solutions in the same search space, CBGA-ES+ managed to perform better than CBGA-ES, MOCell, NSGA-II, PAES, and SPEA2 for 2.2, 13.6, 14.5, 17.4, and 9.9 percent, respectively. Regarding the running time of the algorithm, CBGA-ES+ was faster than CBGA-ES for all the experiments.

A Bagging Based Multiobjective Differential Evolution With Multiple Subpopulations

Different from multiobjective differential evolution algorithm (MODE) based on traditional mutation operators and a single population, this paper developed a bagging based MODE with multiple subpopulations (BagMPMODE) by incorporating the idea of bagging into the evolution process of MODE. In this algorithm, multiple subpopulations with different evolution operators are adopted to maintain search diversity, as did by some previous researches on MODE. During evolution, the subpopulations will compete with each other, i.e., the size of each subpopulation will be adjusted based on its contribution to the whole search result. Based on the multiple subpopulation strategy, the idea of bagging ensemble is adopted to generate offspring solutions, which can be viewed as the cooperation of these multiple subpopulations. The proposed BagMPMODE algorithm is evaluated on a set of 22 benchmark problems, and computational experiments illustrate that the BagMPMODE algorithm is competitive or even superior to several state-of-the-art MODEs and some other multiobjective evolutionary algorithms in the literature for most problems.

Fine-Grained Ensemble of Evolutionary Operators for Objective Space Partition Based Multi-Objective Optimization

Decomposition-based multi-objective optimization algorithms have been widely accepted as a competitive technique in solving complex multi-objective optimization problems (MOPs). Motivated by the facts that evolutionary operators are sensitive to the properties of problems, and even different search stages of an evolutionary operator often pose distinct properties when solving a problem. So far, numerous ensemble approaches have been designed to adaptively choose evolutionary operators for evolving population during different optimization stages. Then, during one stage, all the subproblems/subspaces in these existing ensemble approaches use the same evolutionary operator. But, for a complex MOP, the properties of its subproblems/subspaces are different. Based on the fact that existing ensemble approaches ignore this point, this article develops a fine-grained ensemble approach, namely FGEA, to choose suitable evolutionary operators for different subspaces during one generation. To be specific, the local and global contributions for each evolutionary operator in each subproblem/subspace are first defined. Then, an adaptive strategy is designed to encourage evolutionary operators making more contributions to obtain more opportunities to generate more offspring solutions. When choosing an evolutionary operator for a subspace, the proposed adaptive strategy considers both the local and global contributions of the evolutionary operators. Finally, based on 35 complex MOPs, we evaluate the effectiveness of the proposed FGEA by comparing it with five baseline algorithms. The experimental results reveal the competitive performance of the FGEA, which achieves the lowest inverted generational distance (IGD) values and the highest hypervolume values on 20 and 19 MOPs, respectively.

Global optimization with one-class classification-assisted selection

Abstract Selection in evolutionary algorithms (EAs) selects promising solutions from a set of candidates. Most selection strategies are fitness-driven, where each solution is selected based on its fitness value. This fitness-based strategy leads to a waste of fitness evaluations, since some unpromising solutions are thrown away without providing valuable search information while still being evaluated. Our intention is to reduce the number of fitness evaluations during the selection procedure. We treat selection as a one-class classification procedure so that the offspring solutions similar to the current population, which has the best solutions up to that point, are more likely to be selected. We use the classifier to predict the categories of newly generated solutions. Only those predicted ‘promising’ solutions can be selected for evaluation purposes. The efficiency of EAs can be greatly improved, since the procedure is based on the decision variables (features) before the fitness evaluations. Based on this consideration, we propose a One-class Classification-assisted Selection (OCAS) strategy for EAs. We apply the OCAS strategy to two EAs and study them on three test suites. Our experimental results reveal that the number of fitness evaluations can be clearly decreased by OCAS.

Handling Constrained Many-Objective Optimization Problems via Problem Transformation.

Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective optimization problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained many-objective evolutionary algorithms (CMaOEAs), and they always give priority to satisfy constraints, while ignoring the maintenance of the population diversity for dealing with conflicting objectives. Consequently, the population may be pushed toward some locally feasible optimal or locally infeasible areas in the high-dimensional objective space. To alleviate this issue, this article presents a problem transformation technique, which transforms a CMaOP into a dynamic CMaOP (DCMaOP) for handling constraints and optimizing objectives simultaneously, to help the population cross the large and discrete infeasible regions. The well-known reference-point-based NSGA-III is tailored under the problem transformation model to solve CMaOPs, namely, DCNSGA-III. In this article, ε -feasible solutions play an important role in the proposed algorithm. To this end, in DCNSGA-III, a mating selection mechanism and an environmental selection operator are designed to generate and choose high-quality ε -feasible offspring solutions, respectively. The proposed algorithm is evaluated on a series of benchmark CMaOPs with three, five, eight, ten, and 15 objectives and compared against six state-of-the-art CMaOEAs. The experimental results indicate that the proposed algorithm is highly competitive for solving CMaOPs.

PCA-assisted reproduction for continuous multi-objective optimization with complicated Pareto optimal set

Abstract In terms of generating offspring solutions, simulated binary crossover (SBX) and differential evolution (DE) are two of the most representative reproduction operators in evolutionary multi-objective algorithms (EMOAs). However, they are found as less effective on multi-objective problems (MOPs) with complicated Pareto optimal set (PS). Under mild conditions, the PS of an MOP is an ( m − 1 ) -dimensional piecewise continuous manifolds where m is the number of objectives. Inspired from this regularity property, this study proposes a simple yet effective reproduction operator, namely, PCA-assisted reproduction (PCA-ar). Specifically, the PCA-ar first applies principal component analysis (PCA) method to construct a new decision space with reduced number of dimensions based on the information extracted from several well converged solutions. The PS is then estimated by a hyperplane in the new decision space. To this end, new offspring are sampled from the estimated PS, and then re-converted to the original decision space for fitness calculation. In order to systematically examine the effectiveness of the PCA-ar operator, we integrate it into NSGA-II and MOEA/D, and compare the derived algorithms, nNSGA-II and nMOEA/D, with their original versions (NSGA-II with SBX operator and MOEA/D with DE operator) as well as the regularity model based multi-objective estimated distribution algorithm (RM-MEDA) on the modified DTLZ benchmarks with up to 8 objectives. Experimental results show that nNSGA-II and nMOEA/D outperform the competitor EMOAs for most of problems, which indicate that the PCA-ar is effective. Lastly, the PCA-ar is also demonstrated to have good scalability to the number of decision variables.

A two-phase tabu search based evolutionary algorithm for the maximum diversity problem

In this paper, we study the maximum diversity problem (MDP) which is equivalent to the quadratic unconstrained binary optimization (QUBO) problem with cardinality constraint. The MDP aims to select a subset of elements with given cardinality such that the sum of pairwise distances between any two elements in the selected subset is maximized. For solving this computationally challenging problem, we propose a two-phase tabu search based evolutionary algorithm (TPTS/EA), which integrates several distinguishing features to ensure the diversity and the quality of the evolution, such as a two-phase tabu search algorithm which consists of a dynamic candidate list (DCL) strategy-based traditional tabu search in the first phase and a solution-based tabu search procedure to refine the search in the second phase, and two path-relinking based recombination operators to generate new offspring solutions. Tested on three sets of totally 140 public instances in the literature, the study demonstrates the efficacy of the proposed TPTS/EA algorithm in terms of both solution quality and computational efficiency. Specifically, our proposed TPTS/EA algorithm is able to improve the previous best known results for 2 instances, while matching the previous best-known solutions for 130 instances. We also provide experimental evidences to highlight the beneficial effect of several important components in our TPTS/EA algorithm.

A Multi-Objective Evolutionary Algorithm Based on KNN-Graph for Traffic Network Attack

The research of vulnerability in complex network plays a key role in many real-world applications. However, most of existing work focuses on some static topological indexes of vulnerability and ignores the network functions. This paper addresses the network attack problems by considering both the topological and the functional indexes. Firstly, a network attack problem is converted into a multi-objective optimization network vulnerability problem (MONVP). Secondly to deal with MONVPs, a multi-objective evolutionary algorithm is proposed. In the new approach, a k-nearest-neighbor graph method is used to extract the structure of the Pareto set. With the obtained structure, similar parent solutions are chosen to generate offspring solutions. The statistical experiments on some benchmark problems demonstrate that the new approach shows higher search efficiency than some compared algorithms. Furthermore, the experiments on a subway system also suggests that the multi-objective optimization model can help to achieve better attach plans than the model that only considers a single index.

Multi-objective evolutionary clustering with complex networks

Evolutionary clustering (EC) refers to the applications of evolutionary optimization algorithms such as genetic algorithm to data clustering. Although multi-objective evolutionary clustering algorithms were proposed to simultaneously consider different cluster properties such as compactness and separation, these techniques usually suffer from a reasonable initial population and a pre-defined number of clusters. Besides, the effectiveness of evolutionary operators is decreased in dealing with the clustering problem. On the other side, complex networks play an essential role in different fields of machine learning. In a complex network, points are considered as nodes, and the dataset is shown as a connected weighted graph. Also, complex networks tend to present a modular structure. This paper applies two concepts of complex networks including node centrality and community modularity to introduce a novel multi-objective evolutionary clustering. The proposed centrality modularity-based multi-objective evolutionary clustering (CMMOEC) takes the advantage of nodes similarity to find the best initial population of clustering solutions and provide new structural-based modularity to determine the optimal number of clusters automatically. Moreover, the proposed modularity is used to design a new recombination and mutation operator so that it generates offspring solutions that satisfy more diversity. Experiments carried out on several artificial and real-world datasets with different structures. The performance of the proposed algorithm is evaluated by the Adjusted Rand Index (ARI). Simulation results indicate that the proposed algorithm satisfies better performance in comparison to traditional methods.

Adaptive simulated binary crossover for rotated multi-objective optimization

Abstract Crossover is a crucial operation for generating promising offspring solutions in evolutionary multi-objective optimization. Among various crossover operators, the simulated binary crossover (SBX) is the most widely used in evolutionary multi-objective optimization. Despite that SBX is effective in solving problems with regular Pareto sets, its performance degenerates dramatically on problems with rotated Pareto sets.To address this issue, we propose a modified SBX, named the rotation-based simulated binary crossover (RSBX), to improve the performance of multi-objective evolutionary algorithms (MOEAs) on rotated problems whose Pareto sets are not parallel with the decision variables. The main idea is to introduce the rotation property into the SBX, and then an adaptive selection strategy is proposed to make use of both SBX and RSBX. The proposed method is embedded in three representative MOEAs, and they are compared with their original versions on some problems with rotated Pareto sets, respectively. Experimental results demonstrate that the proposed method is efficient in promoting the performance of conventional MOEAs for handling rotated multi-objective optimization problems.

Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

The minimum weight vertex independent dominating set (MWVIDS) problem is an important version of the minimum independent dominating set. The MWVIDS problem has a number of applications in many fields. However, the MWVIDS problem is known to be NP-hard and thus computationally challenging. In this work, we present the improved memetic algorithm called MSSAS for solving the MWVIDS problem. The proposed MSSAS algorithm combines probability-based dynamic optimization (PDO) (to generate good and diverse offspring solutions by assembling elements of existing good solutions) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism). The extensive results on popular DIMACS and BHOLIB benchmarks demonstrate that MSSAS competes favorably with the state-of-the-art algorithms. In addition, we analyze the benefits of the newly raised components including two above proposed ideas with our memetic framework. It is worth mentioning that the combination of both components has excellent effects for the MWVIDS problem.

Adaptive Offspring Generation for Evolutionary Large-Scale Multiobjective Optimization

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs.

Memetic search for composing medical crews with equity and efficiency

Composing medical crews with equity and efficiency is an important practical problem commonly arising from health care system management. This work presents the first hybrid memetic algorithm for this problem. The proposed approach integrates an original backbone-based crossover for generating promising offspring solutions and a tabu search based local optimization algorithm exploring both feasible and infeasible search regions. Computational experiments on two sets of benchmark instances in the literature are conducted to assess the proposed algorithm with reference to existing methods. This study advances the state-of-the-art of solving this relevant practical problem and is expected to inspire new solution methods to similar problems.

An opposition-based memetic algorithm for the maximum quasi-clique problem

Given a simple undirected graph G=(V,E) and a constant γ, the γ-quasi-clique is defined as a subset of vertices that induces a subgraph with the edge density of at least γ. The maximum γ-quasi-clique problem (MQCP) is to find a γ-quasi-clique of the maximum cardinality in G. This problem has many practical applications, especially in social network analysis. We present an opposition-based memetic algorithm (OBMA) for MQCP, which relies on a backbone-based crossover operator to generate new offspring solutions and on a constrained neighborhood tabu search for local improvement. OBMA further integrates the concept of opposition-based learning (OBL) to enhance the search ability of the classic memetic algorithm. Computational results on a large set of both dense and sparse graphs show that the proposed heuristic competes very favorably with the current state-of-the-art algorithms from the MQCP literature. In particular, it is able to find improved best-known solutions for 47 out of the 100 dense graphs, while reaching the best-known solution for all but few of the remaining instances. Several essential components of the proposed approach are investigated to understand their impacts to the algorithm’s performance.

A novel high speed multi-objective evolutionary optimisation algorithm

Multi-objective optimisation problems (MOOPs) consider multiple objectives simultaneously. Solving these problems does not render one unique solution but instead a set of equally optimal solutions, i.e., the Pareto front. The goal of solving a MOOP is to accurately and efficiently approximate the Pareto front. The use of evolutionary optimisation algorithms is widespread in this discipline. During each iteration, parent solutions are combined and mutated to create new offspring solutions. Both populations are subsequently combined and sorted. Only the N fittest solutions of the combined set are selected as the parent solutions for the subsequent iteration. The fitness of a solution is defined by its convergence to the Pareto front and its contribution to the overall solution diversity. Widely used evolutionary algorithms, like NSGA-II (Deb et al., 2002), use non-dominated sorting to assess the convergence of solutions and the concept of crowding distance to ensure a high solution diversity. Both concepts, however, require that all N solutions of the population are compared with all other (N — 1) solutions for both aspects, and this for all M objectives. This results in a computational complexity of O(MN2). In this contribution, a novel evolutionary algorithm is presented, boasting a significantly lower computational complexity of O(N log(N)). This is achieved by subdividing the feasible space into angular sections. Solutions are scored based on their distance from the current Utopia point and the overall crowdedness of their respective section. Sorting the population based on the attributed scores allows the selection of the N fittest solutions, without having to mutually compare them.

Solving the Latin Square Completion Problem by Memetic Graph Coloring

The Latin square completion (LSC) problem involves completing a partially filled Latin square of order ${n}$ by assigning numbers from 1 to ${n}$ to the empty grids such that each number occurs exactly once in each row and each column. LSC has numerous applications and is, however, NP-complete. In this paper, we investigate an approach for solving LSC by converting an LSC instance to a domain-constrained Latin square graph and then solving the associated list coloring problem. To be effective, we first employ a constraint propagation-based kernelization technique to reduce the graph model and then call for a dedicated memetic algorithm to find a legal list coloring. The population-based memetic algorithm combines a problem-specific crossover operator to generate meaningful offspring solutions, an iterated tabu search procedure to improve the offspring solutions, and a distance-quality-based pool updating strategy to maintain a healthy diversity of the population. Extensive experiments on more than 1800 LSC benchmark instances in the literature show that the proposed approach can successfully solve all the instances, surpassing the state-of-the-art methods. To our knowledge, this is the first approach achieving such a performance for the considered problem. We also report computational results for the related partial Latin square extension problem.

An evolution strategy approach to the team orienteering problem with time windows

The team orienteering problem with time windows (TOPTW) is a highly constrained NP-hard problem having many practical applications in vehicle routing and production scheduling. The TOPTW is an extended variant of the Orienteering Problem (OP), where each node has a predefined time window during which the service has to be started. The aim is to maximize the total collected score by visiting a set of nodes with a limited number of tours since the given distance budget is limited. We propose an evolution strategy (ES) together with an effective constructive heuristic for solving the TOPTW. The main feature of the ES is to generate an offspring solution through ruin and recreate (RR) heuristic, where a number of nodes are removed from the incumbent solution and then, they are reinserted into tours until a complete solution is obtained. The ES is hybridized with an efficient random local search to enhance solution quality. For survivor selection, we use a goodness of scores approach to determine and diversify the population for the next generation. Parameters of the ES are determined through the design of experiment approach to tune them. The computational results show that the constructive heuristic is slightly better than existing heuristics in the literature. Furthermore, the detailed computation results on the benchmark suite from the literature confirm the effectiveness of the evolution strategy. Ultimately, the evolution strategy obtains new best-known solutions for 7 benchmark problem instances.