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Multi-label classification is a machine learning task to construct a model for assigning an entity in the dataset to two or more class labels. In order to improve the performance of multi-label classification, a multi-objective feature selection algorithm has been proposed in this paper. Feature selection as a preprocessing task for Multi-label classification problems aims to choose a subset of relevant features. Selecting a small number of high-quality features decreases the computational cost and at the same time maximizes the classification performance. However extreme decreasing the number of features causes the failure of classification. As a result, feature selection has two conflicting objectives, namely, minimizing the classification error and minimizing the number of selected features. This paper proposes a multi-objective optimization algorithm to tackle the multi-label feature selection. The task is to find a set of solutions (a subset of features) in a sophisticated large-scale search space using a reference-based multi-objective optimization method. The proposed algorithm utilizes an opposition-based binary operator to generate more diverse solutions. Injection of extreme point of the Pareto-front is another component of the algorithm which aims to find feature subsets with less classification error. The proposed method is compared with two other existing methods on eight multi-label benchmark datasets. The experimental results show that the proposed method outperforms existing algorithms in terms of various multi-objective evaluation measures, such as Hyper-volume indicator, Pure diversity, Two-set coverage, and Pareto-front proportional contribution. The proposed method leads to get a set of well-distributed trade-off solutions which reach less classification error in comparing with competitors, even with the fewer number of features. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems often load in the multi-scenario environment, and they can be modeled as multi-scenario multi-objective optimization problems (MSMOs). So far, existing research on MSMOs mainly focuses on the specific method in engineering applications, and general methods are quite scarce. This paper develops an integrated information-based evolutionary framework to find a set of scenario-based non-dominated solutions for MSMOs. Sequentially, a scenario-based dominance principle evolutionary algorithm and a decomposition-based evolutionary algorithm are combined with the framework to construct two integration algorithms, respectively. Furthermore, the crucial components in both algorithms are developed under the multi-scenario environment, such as scenario-based constraint handling, scenario-based dominance concept, scenario-based crowded degree and multi-scenario decomposition method. Additionally, we design a novel comprehensive evaluation indicator for MSMOs. Finally, the proposed framework is tested on numerous artificial and engineering problems. Experiments demonstrate that the framework has superiority over four existing state-of-the-art peer competitors concerning the indicator. Two integration algorithms are able to find a set of good scenario-based non-dominated solutions. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) are promising methods for addressing computationally expensive problems. This paper proposes a multiple surrogates and offspring-assisted differential evolution (MSODE) algorithm for high-dimensional expensive problems. Ensemble models consisting of multiple base models are built based on bagging. The ensemble models contribute toward reducing the variations of predictions and the uncertainty of base models. The algorithm proposes a multiple-offspring evolution strategy in which it generates multiple offspring for each parent individual to enhance the search ability of the population. The appropriate number of offspring was investigated, considering the tradeoff between optimization results and efficiency. MSODE consists of a global prescreening search, local search, and uncertainty prescreening search. The global prescreening search adopts a global ensemble to prescreen promising offspring. The local search accelerates the convergence by searching for the optimum of a local ensemble. The uncertainty prescreening search requires a number of fitness evaluations that slightly deteriorate the results. A comprehensive analysis was conducted to determine the optimal parameter settings. MSODE was compared with meta -heuristic algorithms and SAEAs on a series of benchmark problems. The results show that MSODE behaves better than most algorithms and is competitive against the best ones. [ABSTRACT FROM AUTHOR]

1 This paper proposes an adaptive clustering-based many-objective evolutionary algorithm. 2 A unit hypersurface is estimated to roughly reflect the characteristicsof Pareto fronts. 3 The adaptive clustering can properly fit various Pareto frontsforthe targetproblem. 4 The proposed algorithmimprovestheperformanceondifferentproblemswith various Pareto fronts. This paper proposes an adaptive clustering-based evolutionary algorithm for many-objective optimization problems (MaOPs), called MaOEA/AC. In this algorithm, an adaptive clustering strategy (ACS) is first introduced to divide the population into multiple clusters, which can properly fit various Pareto fronts (PFs) of the target MaOPs. Then, the environmental selection of MaOEA/AC is designed based on these clusters to collect the solutions with balanceable convergence and diversity. To be more detail, the similarity between solutions in ACS is appropriately measured by computing the Euclidean distance between their projections on an adaptive unit hyper-surface, whose curving rate is controlled by a parameter p. A simple yet effective estimation method is proposed to get a suitable value of p based on the distribution of the current non-dominated solution set, so that the estimated unit hyper-surface can roughly reflect the characteristics of PFs in the target MaOPs. The effectiveness of MaOEA/AC is validated by numerous experimental studies on solving test MaOPs with various PFs, which have the characteristics with convex, concave, inverted, disconnected, degenerated, and other mixed or irregular PFs. The experiments also show that MaOEA/AC has the superior performance over several recent many-objective evolutionary algorithms, when solving most of these test MaOPs. [ABSTRACT FROM AUTHOR]

Recently, multi and many-objective evolutionary algorithms (MOEAs) embedded with clustering techniques to enhance their environmental selection show promising performance for tackling multi and many-objective optimization problems (MOPs) with irregular Pareto fronts (PFs). However, the similarity metric used for clustering cannot reflect the diversity of solutions fairly when it is measured based on the direction distances of solutions to an ideal point. Consequently, it may mislead the environmental selection when solving MOPs with convex PFs. To alleviate this issue, this paper suggests an MOEA using clustering with a flexible similarity metric to run the environmental selection. In our approach, we first use a simple yet effective method to roughly predict the concavity or convexity of the target problem. Then, a flexible reference point is set to define the direction distances of solutions, which can properly measure the similarity between solutions and fairly show their diversity for solving MOPs with various PF shapes. After that, we use a hierarchical clustering method with this flexible similarity metric to run the environmental selection on all solutions, which will properly classify them into N clusters (N is the population size). Finally, in each cluster, one solution with the best convergence value will survive to compose the new population. When compared to twenty-seven competitive MOEAs in solving nineteen benchmark MOPs and sixteen real-world engineering MOPs with various PF shapes, the experimental results demonstrate that the proposed algorithm has significant advantages. [ABSTRACT FROM AUTHOR]

Due to the fixed and monotonous search direction, the performance of decomposition-based multiobjective evolutionary algorithms (MOEAs) highly depends on the Pareto front (PF) shape. Recent studies have highlighted the complementary effect of the ideal and nadir points. They roughly employed both as the reference points to diversify the search direction. However, few works investigate whether two points are equally important. This paper thereby proposes a novel decomposition-based MOEA, where the ideal point is consistently considered as the global reference point while the nadir point is conditionally employed as the local one. We show that the nadir point may aid the ideal point in some cases and be recognized as a redundant one in others. More specifically, an assignment strategy is suggested to determine the necessity of using a local reference point for each subproblem, by considering whether the solution found by the nadir point and corresponding weight vector can improve the quality of the population. Experimental results finally verify the effectiveness of the proposed algorithm on 57 benchmark test problems with various PF shapes. In comparison with the state-of-the-art decomposition-based MOEAs, the proposed algorithm is promising to bring a more refined search and prevent redundant search behaviors. [ABSTRACT FROM AUTHOR]

Instance selection, as an important data pre-processing task, is widely used in supervised classification. Recently, a series of instance selection algorithms with different techniques have been suggested. Among them, evolutionary algorithms (EAs) have shown competitive performance. However, when the size of instance set is large, these EA-based algorithms may face great challenges on search efficiency and computational cost. To this end, in this paper, a multi-objective evolutionary algorithm based on length reduction, termed as LRIS, is proposed for large-scale instance selection, where a length reduction strategy is suggested to recursively shorten the length of each individual in the population, and improve the computational efficiency of LRIS greatly. Specifically, in the proposed length reduction strategy of LRIS, each gene in the individuals has a probability of being deleted, whose probability is obtained according to the importance of the corresponding instance in the instance set and the importance of the corresponding gene in the population. Then, two evolutionary operators (e.g. crossover and mutation) based on the length reduction strategy are developed to generate offspring population from the reduced population. In addition, an individual repairing operator is also designed to repair the length of over-reduced individuals. Experimental results on 12 large-scale data sets have demonstrated the efficiency and the effectiveness of the proposed LRIS in comparison with the state-of-the-art EA-based instance selection algorithms. [ABSTRACT FROM AUTHOR]

• A surrogate model based on IRL is suggested, which applies the max-margin method to approximate the reward function. • Under different dynamic environments, IRL learns the reward function and helps accelerate the convergence of the algorithm. • On the basis of learned reward function, IRL-DMOEA generates promising non-dominated solutions during the evolutionary process. Due to the widespread interest in dynamic multiobjective optimization in real-world applications, more and more approaches exploiting machine learning are deployed to tackle this type of problems. Unfortunately, recent works do not make full use of the data obtained during the optimization process, which could be benefit for model training thereby mining the dynamic characteristics of the underlying problem. To address this issue, this paper proposes a dynamic multiobjective evolutionary algorithm driven by inverse reinforcement learning to solve the dynamic multiobjective optimization problems. IRL is widely used to recover the unknown reward function, making it possible to perform at an expert level. The notable features of the proposed algorithm mainly consist of data-driven evolutionary technique, which uses inverse reinforcement learning as a surrogate-assisted model for model training. This design makes full use of the surrogate management strategy based on inverse reinforcement learning to optimize the reward function within a reinforcement learning framework. At the same time, the algorithm can generate a promising policy based on limited training data during the optimization process to achieve better algorithm evolution and guide the search. The experimental results on the benchmark problems validate that the proposed algorithm is effective in dealing with dynamic multiobjective optimization. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

Various evolutionary algorithms have been proposed for tackling many-objective optimization problems over the past three decades. However, these algorithms still suffer from the loss of selection pressures due to the existence of dominance resistance. To tackle this issue, this paper proposes a relative non-dominance matrix, based on which a fitness formula is defined. Empirical analyses show that solutions with smaller fitness values are likely to dominate more other solutions in the future evolutionary process, and play a vital role in enhancing the convergence toward to the true Pareto fronts. Additionally, to further ensure the diversity, k -means clustering strategy is combined with the relative non-dominance matrix for a new design of the environmental selection, where parameter k in the clustering strategy is adjusted adaptively. The proposed algorithm is extensively tested with four state-of-art algorithms on WFG, MaF and DTLZ test suites. Empirical comparisons demonstrate the competitiveness of the proposed algorithm regarding to the convergence, diversity and spread. [ABSTRACT FROM AUTHOR]

Multi-objective optimization problems with interval parameter (IMOPs) are among the most critical optimization problems in practical applications. However, in contrast to deterministic multi-objective optimization, few studies have addressed IMOPs. Moreover, the uncertainty in such problems makes the convergence and diversity of the algorithm more challenging. Therefore, this paper proposes an interval multi-objective optimization algorithm based on elite genetic strategy (EG-IMOEA). First, existing interval dominance relations cannot comprehensively determine which of the two intervals is better when their midpoints are equal but their upper and lower limits are unequal. Therefore, a conditional-based interval confidence dominance relation is proposed that considers both the average level of convergence and value of the minimum lower limit of intervals. The interval crowding distance (ICD) applied to multiple objectives is then defined to evaluate the solutions more completely. Furthermore, an elite genetic strategy for crossover and mutation is proposed to generate better offspring. The proposed algorithm was evaluated on nine benchmark test problems and compared with the typical algorithm as well as state-of-the-art algorithms. The results showed that this algorithm outperformed the comparison algorithms in terms of convergence, diversity, imprecision, and uniform distribution. [ABSTRACT FROM AUTHOR]

• Propose a mechanism combining key features of Linkage Tree Genetic Algorithm (LTGA) and Multifactorial Optimization (MFO). • Propose a method for building the linkage tree based on unified search space to exploit both information between problem variables and transfer knowledge of independent tasks. • Propose an assortative mating mechanism to enhance the compatibility between the main features of MFO and LTGA. • Introduce a crossover operator to keep the key advantages of MFO and LTGA as well as maintain population diversity. • Demonstrate the effectiveness of the proposed algorithm on two benchmark problems. Linkage Tree Genetic Algorithm (LTGA) is an effective Evolutionary Algorithm (EA) to solve complex problems using the linkage information between problem variables. LTGA performs well in various kinds of single-task optimization and yields promising results in comparison with the canonical genetic algorithm. However, LTGA is an unsuitable method for dealing with multi-task optimization problems. On the other hand, Multifactorial Optimization (MFO) can simultaneously solve independent optimization problems, which are encoded in a unified representation to take advantage of the process of knowledge transfer. In this paper, we introduce Genetic Algorithm (MF-LTGA) by combining the main features of both LTGA and MFO. MF-LTGA is able to tackle multiple optimization tasks at the same time, each task learns the dependency between problem variables from the shared representation. This knowledge serves to determine the high-quality partial solutions for supporting other tasks in exploring the search space. Moreover, MF-LTGA speeds up convergence because of knowledge transfer of relevant problems. We demonstrate the effectiveness of the proposed algorithm on two benchmark problems: Clustered Shortest-Path Tree Problem and Deceptive Trap Function. In comparison to LTGA and existing methods, MF-LTGA outperforms in quality of the solution or in computation time. [ABSTRACT FROM AUTHOR]

Many-objective optimization problems take challenges to multi-objective evolutionary algorithms. A number of nondominated solutions in population cause a difficult selection towards the Pareto front. To tackle this issue, a series of indicatorbased multi-objective evolutionary algorithms (MOEAs) have been proposed to guide the evolution progress and shown promising performance. This paper proposes an indicator-based manyobjective evolutionary algorithm called ε-indicator-based shuffled frog leaping algorithm (ε-MaOSFLA), which adopts the shuffled frog leaping algorithm as an evolutionary strategy and a simple and effective ε-indicator as a fitness assignment scheme to press the population towards the Pareto front. Compared with four stateof- the-art MOEAs on several standard test problems with up to 50 objectives, the experimental results show that ε-MaOSFLA outperforms the competitors [ABSTRACT FROM AUTHOR]

Abstract: Differential Evolution (DE) is one of the most popular optimization methods for real-valued problems and a large number of its variants have been proposed so far. However, bringing together different ideas that already led to successful DE versions is rare in the literature. In the present paper a novel DE algorithm is proposed, in which three among the most efficient concepts already applied separately within DE framework are gathered together, namely: (1) the adaptation of algorithm control parameters and probabilities of using different mutation strategies; (2) the use of Nelder–Mead algorithm as a local search method hybridized with DE; and (3) the splitting mutation into Global and Local models, when Local mutation model is based on the concept of neighborhood of individuals organized on a ring topology. The performance of the novel algorithm, called Adaptive Memetic DE with Global and Local neighborhood-based mutation operators is compared with 13 different DE variants on a set of 25 popular problems which include rotated, shifted and hybrid composition functions. It is found that, although none DE algorithm outperforms all the others for the majority of problems, on average the proposed approach perform better than all 13 DE algorithms selected for comparison. The proposed algorithm is another heuristic approach developed to solve optimization problems. The question may arise, whether proposing novel methods is useful as No Free Lunch theorems for optimization state that the expected performance of all possible heuristics on all possible problems is equal. In the last section of the paper the limitations and implications of No Free Lunch theorems are discussed based on rich, but unfortunately frequently neglected literature. A very simple continuous and differentiable minimization problem is proposed, for which it is empirically verified that each among considered 14 DE algorithms perform poorer than random sampling. It is also empirically shown that when all considered DE algorithms search for the maximum of the proposed problem, they found lower minimum than DE algorithms searching for the minimum. Such result is not unexpected according to No Free Lunch theorems and should be considered as a precaution from generalization of good performance of heuristic optimization methods. [Copyright &y& Elsevier]

Abstract: Automatic segmentation of non-stationary signals such as electroencephalogram (EEG), electrocardiogram (ECG) and brightness of galactic objects has many applications. In this paper an improved segmentation method based on fractal dimension (FD) and evolutionary algorithms (EAs) for non-stationary signals is proposed. After using Kalman filter (KF) to reduce existing noises, FD which can detect the changes in both the amplitude and frequency of the signal is applied to reveal segments of the signal. In order to select two acceptable parameters of FD, in this paper two authoritative EAs, namely, genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used. The proposed approach is applied to synthetic multi-component signals, real EEG data, and brightness changes of galactic objects. The proposed methods are compared with some well-known existing algorithms such as improved nonlinear energy operator (INLEO), Varriʼs and wavelet generalized likelihood ratio (WGLR) methods. The simulation results demonstrate that segmentation by using KF, FD, and EAs have greater accuracy which proves the significance of this algorithm. [Copyright &y& Elsevier]

High-order graph matching aims at establishing correspondences between two sets of feature points using high-order constraints. It is usually formulated as an NP-hard problem of maximizing an objective function. This paper introduces a discrete particle swarm optimization algorithm for resolving high-order graph matching problems, which incorporates several re-defined operations, a problem-specific initialization method based on heuristic information, and a problem-specific local search procedure. The proposed algorithm is evaluated on both synthetic and real-world datasets. Its outstanding performance is validated in comparison with three state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Abstract: Capacitated Arc Routing Problem (CARP) has drawn much attention during the last few years. In addition to the goal of minimizing the total cost of all the routes, many real-world applications of CARP also need to balance these routes. The Multi-objective CARP (MO-CARP) commonly exists in practical applications. In order to solve MO-CARP efficiently and accurately, this paper presents a Multi-population Cooperative Coevolutionary Algorithm (MPCCA) for MO-CARP. Firstly, MPCCA applies the divide-and-conquer method to decompose the whole population into multiple subpopulations according to their different direction vectors. These subpopulations evolve separately in each generation and the adjacent subpopulations can share their individuals in the form of cooperative subpopulations. Secondly, multiple subpopulations are used to search different objective subregions simultaneously, so individuals in each subpopulation have a different fitness function, which can be modeled as a Single Objective CARP (SO-CARP). The advanced MAENS approach for single-objective CARP can be used to search each objective subregion. Thirdly, the internal elitism archive is used to construct evolutionary pool for each subregion, which greatly speeds up the convergence. Lastly, the fast nondominated ranking and crowding distance of NSGA-II are used for selecting the offspring and keeping the diversity. MPCCA is tested on 91 CARP benchmarks. The experimental results show that MPCCA obtains better generalization performance over the compared algorithms. [Copyright &y& Elsevier]

Purpose – The purpose of this paper is to report the investigations on the potential of a new evolutionary algorithm based on probabilistic models – the quantum-inspired evolutionary algorithm (QEA) in solving inverse problems. Design/methodology/approach – An improved QEA. Findings – The proposed algorithm is an efficient and robust global optimizer for solving inverse problems. Originality/value – To enhance the convergence speed without compromising the diversity performances of the populations, a new definition of global information sharing is introduced and implemented. To guarantee the balance between exploration and exploitation searches, a different migration strategy and formula, as well as a novel formulation for adaptively updating the rotation angle, are developed. [ABSTRACT FROM AUTHOR]

Abstract: We present a hybrid global–local optimization algorithm for parameter estimation of radial basis function (RBF) networks and the RBF-type autoregressive models without exogenous inputs (RBF-AR) or with exogenous inputs (RBF-ARX). The RBF-AR (X) models are quasi-linear time-varying AR (X) models with Gaussian RBF network-style coefficients, which have been used to effectively model the nonlinear behavior of various complex systems. However, the identification of these models is a difficult optimization problem because of the large number of local minima. A hybrid approach is proposed in this paper to achieve better optimization results for these RBF-type models. The applied hybrid search strategy (EA-SNPOM) is developed by combining an evolutionary algorithm (EA) with a gradient-based algorithm known as the structured nonlinear parameter optimization method (SNPOM). This strategy makes use of the robustness of the EA to cover an entire global search space and the efficiency of the gradient search to converge to a local optimum. Several examples of time series modeling and system identification are presented. The simulation results indicate that the performance of the proposed hybrid approach is better than the performance obtained from using each method (EA or SNPOM) alone. Furthermore, the RBF-AR (X) models estimated by the EA-SNPOM achieve much better modeling accuracy relative to other neural networks or fuzzy models in the simulations. [Copyright &y& Elsevier]

The scarcity of water compared with the abundance of land constitutes the main drawback within agricultural production. Besides the improvement of irrigation techniques a task of primary importance is solving the problem of intra-seasonal irrigation scheduling under limited seasonal water supply. An efficient scheduling algorithm has to take into account the crops' response to water stress at different stages throughout the growing season. Furthermore, for large-scale planning tools compact presentations of the relationship between irrigation practices and grain yield, such as crop water production functions, are often used which also rely on an optimal scheduling of the considered irrigation systems. In this study, two new optimization algorithms for single-crop intraseasonal scheduling of deficit irrigation systems are introduced which are able to operate with general crop growth simulation models. First, a tailored evolutionary optimization technique (EA) searches for optimal schedules over a whole growing season within an open-loop optimization framework. Second, a neuro-dynamic programming technique (NDP) is used for determining optimal irrigation policy. In this paper, different management schemes are considered and crop-yield functions generated with both the EA and the NDP optimization algorithms compared. [ABSTRACT FROM AUTHOR]

Abstract: In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent. [Copyright &y& Elsevier]

Abstract: In this paper, the Poincaré map function as a one-dimensional first-return map is obtained by approximating the scatter plots of inter-peak interval (IPI) during preictal and postictal periods from invasive EEG recordings of nine patients suffering from medically intractable focal epilepsy. Evolutionary Algorithm (EA) is utilized for parameter estimation of the Poincaré map. Bifurcation analyses of the iterated map reveal that as the neuronal activity progresses from preictal state toward the ictal event, the parameter values of the Poincaré map move toward the bifurcation points. However, following the seizure occurrence and in the postictal period, these parameter values move away from the bifurcation points. Both flip and fold bifurcations are analyzed and it is demonstrated that in some cases the flip bifurcation and in other cases the fold bifurcation are the dynamical regime underlying epileptiform events. This information can offer insights into the dynamical nature and variability of the brain signals and consequently could help to predict and control seizure events. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of finding graphs (directed and undirected) maximizing the number of spanning trees among the regular graphs with the same number of nodes and edges. The approach is based on heuristic algorithms such as k-optimal and evolutionary. The emphasis is rather on checking whether these techniques are applicable to solving extremal graph problems than investigating generic structures of optimal graphs. For this reason circulant graphs, for which computationally effective tree counting formulas exist, are discussed first and then the results extended to cover the class of regular graphs. [Copyright &y& Elsevier]