Browsing by Author "Zheng, Jinhua"

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    A dynamic multi-objective evolutionary algorithm based on Niche prediction strategy
    (Elsevier, 2023-07-10) Zheng, Jinhua; Zhang, Bo; Zou, Juan; Yang, Shengxiang; Hu, Yaru
    In reality, many multi-objective optimization problems are dynamic. The Pareto optimal front (PF) or Pareto optimal solution (PS) of these dynamic multi-objective problems (DMOPs) changes as the environment change. Therefore, solving such problems requires an optimization algorithm that can quickly track the PF or PS after an environment change. Prediction-based response mechanism is a common method used to deal with environmental changes, which is commonly known as center point-based prediction. However, if the predicted direction of the center point is inaccurate, the predicted population will be biased towards one side. In this paper, we propose a niche prediction strategy based on center and boundary points (PCPB) to solve the dynamic multi-objective optimization problems, which consists of three steps. After environmental changes are detected, the first step is to divide the niche, dividing different individuals in the PS into different niche populations. The second step is to independently predict different niches, and select individuals with good convergence and distribution in the niche to predict the individuals that will produce the next generation. Finally, some different individuals are randomly generated in the next possible PS area to ensure the diversity of the population. To verify whether our proposed strategy is effective and competitive, PCPB was compared with five state-of-the-art strategies. The experimental results show that PCPB performed competitively in solving dynamic multi-objective optimization problems, which proves that our algorithm has good competitiveness.
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    A dynamic preference-driven evolutionary algorithm for solving dynamic multi-objective problems
    (ACM, 2024-07-01) Wang, Xueqing; Zheng, Jinhua; Zou, Juan; Hou, Zhanglu; Liu, Yuan; Yang, Shengxiang
    Considering the decision-maker's preference information in static multi-objective optimization problems (MOPs) has been extensively studied. However, incorporating dynamic preference information into dynamic MOPs is a relatively less explored area. This paper introduces a preference information-driven DMOEA and proposes a preference-based prediction method. Specifically, a preference-based inverse model is designed to respond to the time-varying preference information, and the model is used to predict an initial population for tracking the changing ROI. Furthermore, a hybrid prediction strategy, that combines a linear prediction model and estimation of population manifolds in the ROI, is proposed to ensure convergence and distribution of population when the preference remain constant. The experimental results show that the proposed algorithm has significant advantages over existing representative DMOEAs through experimental tests on 19 common test problems.
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    A new framework of change response for dynamic multi-objective optimization
    (Elsevier, 2024-02-16) Hu, Yaru; Zou, Juan; Zheng, Jinhua; Jiang, Shouyong; Yang, Shengxiang
    Combining response strategies into multi-objective evolutionary algorithms (MOEAs) for dynamic multi-objective optimization problems (DMOPs) is very popular. However, most of them hardly focus on DMOPs via enhancing the operator’s searching ability of MOEAs. We present a new framework of change response called MOEA/D-HSS. When a change is detected, MOEA/D-HSS updates and assesses saved historical information, computing the intensity of change on the decision variables and the similarity between the current environment and historical ones. Hybrid search strategies (HSS) adaptively adjust the searching range of the population in each generational cycle based on the knowledge above, which has a great chance of discovering new promising regions. HSS is integrated into the variation operator of MOEA based on decomposition (MOEA/D-DE) to enhance its search ability. We take into account that the historical information may be useless references in the later stage of the evolution. Thus, the frequency of HSS usage is gradually decreased in every time interval to balance the population’s convergence and diversity. Experimental results demonstrate that MOEA/S-HSS is very competitive on most benchmark problems compared with other state-of-the-art algorithms.
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    A novel preference-driven dynamic multi-objective evolutionary algorithm for solving dynamic multi-objective problems
    (Elsevier, 2024-06-30) Wang, Xueqing; Zheng, Jinhua; Hou, Zhanglu; Liu, Yuan; Zou, Juan; Xia, Yizhang; Yang, Shengxiang
    Most studies in dynamic multi-objective optimization have predominantly focused on rapidly and accurately tracking changes in the Pareto optimal front (POF) and Pareto optimal set (POS) when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). In particular, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm consists of three key components: an evolutionary direction adjustment strategy based on changing reference points to accommodate shifts in preferences, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy that combines linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in scenarios where preferences remain unchanged. Experimental studies conducted on 30 widely used benchmark problems in which it outperforms contrasting algorithms on 71% of test suits. Empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs.
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    A population hierarchical-based evolutionary algorithm for large-scale many-objective optimization
    (Elsevier, 2024-10-19) Wang, Shiting; Zheng, Jinhua; Zou, Yingjie; Liu, Yuan; Zou, Juan; Yang, Shengxiang
    In large-scale many-objective optimization problems (LMaOPs), the performance of algorithms faces significant challenges as the number of objective functions and decision variables increases. The main challenges in addressing this type of problem are as follows: the large number of decision variables creates an enormous decision space that needs to be explored, leading to slow convergence; and the high-dimensional objective space presents difficulties in selecting dominant individuals within the population. To address this issue, this paper introduces an evolutionary algorithm based on population hierarchy to address LMaOPs. The algorithm employs different strategies for offspring generation at various population levels. Initially, the population is categorized into three levels by fitness value: poorly performing solutions with higher fitness (P_h), better solutions with lower fitness (P_l), and excellent individuals stored in the archive set (P_a). Subsequently, a hierarchical knowledge integration strategy (HKI) guides the evolution of individuals at different levels. Individuals in P_l generate offspring by integrating differential knowledge from P_a and P_h, while individuals in P_h generate offspring by learning prior knowledge from P_a. Finally, using a cluster-based environment selection strategy balances population diversity and convergence. Extensive experiments on LMaOPs with up to 10 objectives and 5000 decision variables validate the algorithm’s effectiveness, demonstrating superior performance.
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    A similarity-detection-based evolutionary algorithm for large-scale multimodal multi-objective optimization
    (Elsevier, 2024-04-09) Long, Si; Zheng, Jinhua; Deng, Qi; Liu, Yuan; Zou, Juan; Yang, Shengxiang
    In recent years, there has been a surge in the development of evolutionary algorithms tailored for multimodal multi-objective optimization problems (MMOPs). These algorithms aim to find multiple equivalent Pareto optimal solution sets (PSs). However, little work has been done on MMOPs with large-scale decision variables, especially when the Pareto optimal solutions are sparse. These problems pose significant challenges due to the dimension curse, the unknown sparsity, and the unknown number of equivalent PSs. In this paper, we propose an evolutionary algorithm based on similarity detection called SD-MMEA to solve large-scale MMOPs with sparse Pareto-optimal solutions. Specifically, it employs a multi-population independent evolution to explore multiple PSs and distinguishes different PSs by double detection of the similarity between subpopulations. Simultaneously, develop online scoring mechanisms for decision variables to guide the subpopulations to explore in different directions. In addition, during the latter stage of evolution, the decision variables of individuals are further optimized by a double-layer grouping process. The proposed algorithm is compared with six state-of-the-art algorithms. Experimental results show that SD-MMEA has significant advantages in solving large-scale MMOPs with sparse solutions.
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    An adaptation reference-point-based multiobjective evolutionary algorithm
    (Elsevier, 2019-03-11) Zou, Juan; Fu, Liuwei; Yang, Shengxiang; Zheng, Jinhua; Ruan, Gan; Pei, Tingrui; Wang, Lei
    It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics.
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    Adaptive neighborhood selection for many-objective optimization problems
    (Elsevier, 2017-12-06) Zou, Juan; Zhang, Yuping; Yang, Shengxiang; Liu, Yuan; Zheng, Jinhua
    It is generally accepted that conflicts between convergence and distribution deteriorate with an increase in the number of objectives. Furthermore, Pareto dominance loses its effectiveness in many-objectives optimization problems (MaOPs), which have more than three objectives. Therefore, a more valid selection method is needed to balance convergence and distribution. This paper presents a many-objective evolutionary algorithm, called Adaptive Neighborhood Selection for Many-objective evolutionary algorithm(ANS-MOEA), to deal with MaOPs. This method defines the performance of each individual by two types of information, convergence information (CI) and distribution information (DI). In the critical layer, a well-converged individual is selected first from the population, and its neighbors, calculated by DI, are pushed into neighbor collection (NC) soon afterwards. Then, the proper distribution of the population is ensured by competition individuals with large DI go back to the population and individuals with small DI remain in the collection. Four state-of-the-art MaOEAs are selected as the competitive algorithms to validate ANS-MOEA. The experimental results show that ANS-MOEA can solve a MaOP and generate a set of remarkable solutions to balance convergence and distribution.
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    An extended fuzzy decision variables framework for solving large-scale multiobjective optimization problems
    (Elsevier, 2023-05-26) Wang, Shiting; Zheng, Jinhua; Liu, Yuan; Zou, Juan; Yang, Shengxiang
    In large-scale multiobjective optimization, the huge search space poses a great challenge to the convergence search of existing evolutionary algorithms. A fuzzy decision variables (FDV) framework for large-scale multiobjective optimization involves a complex parameter tuning process, and the convergence efficiency is moderate. Therefore, we propose an extended fuzzy decision variables (EFDV) framework based on linear search and the non-dominated rate (the proportion of non-dominated individuals in the whole population) to solve large-scale multiobjective optimization problems. First, guiding solutions are sampled from the central region to provide more possible search directions in large-scale decision space. In addition, fuzzy evolution or precise evolution is determined according to the non-dominated rate. When the non-dominated rate is low, the convergence of the whole population is relatively poor. Then a higher degree of fuzzy search is carried out, and the individuals with poor convergence are reversed to increase the population's diversity and enhance the effectiveness of searches. Finally, by comparing experiments on several large-scale multiobjective test suites with 500–5000 decision variables, the efficiency of the EFDV is confirmed. According to experimental results, the EFDV can significantly enhance the performance and computing effectiveness of multiobjective optimizers when used for large-scale multiobjective optimization.
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    A close neighbor mobility method using particle swarm optimizer for solving multimodal optimization problems
    (Elsevier, 2020-05) Zou, Juan; Deng, Qi; Yang, Shengxiang; Zheng, Jinhua
    Niching is an important technique for multimodal optimization. Most existing niching methods require specification of certain niching parameters in order to perform well. But these parameters are usually difficult to set because they depend on the problem. The particle swarm optimization algorithm using the ring neighborhood topology does not require any niche parameters, but the determination of the particle neighborhood in this method is based on the subscript of the particle, and the result fails to achieve the best performance. For better performance, in this paper, a particle swarm optimization algorithm based on the ring neighborhood topology of Euclidean distance between particles is proposed, which is called the close neighbor mobility optimization algorithm. The algorithm mainly includes the following three strategies: elite selection mechanism, close neighbor mobility strategy and modified DE strategy. It mainly uses the Euclidean distance between particles. Each particle forms its own unique niche, evolves in a local scope, and finally locates multiple global optimal solutions with high precision. The algorithm greatly improves the accuracy of the particle. The experimental results show that the close neighbor mobility optimization algorithm has better performance than most single-objective multi-modal algorithms.
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    Combining a hybrid prediction strategy and a mutation strategy for dynamic multiobjective optimization
    (Elsevier, 2022-01-12) Chen, Ying; Zou, Juan; Liu, Yuan; Yang, Shengxiang; Zheng, Jinhua; Huang, Weixiong
    The environments of the dynamic multiobjective optimization problems (DMOPs), such as Pareto optimal front (POF) or Pareto optimal set (POS), usually frequently change with the evolution process. This kind of problem poses a higher challenge for evolutionary algorithms because it requires the population to quickly track (i.e., converge) to the position of a new environment and be widely distributed in the search space. The prediction-based response mechanism is a commonly used method to deal with environmental changes, but it’s only suitable for predictable changes. Moreover, the imbalance of population diversity and convergence in the process of tracking the dynamically changing POF has aggravated. In this paper, we proposed a new change response mechanism that combines a hybrid prediction strategy and a precision controllable mutation strategy (HPPCM) to solve the DMOPs. Specifically, the hybrid prediction strategy coordinates the center point-based prediction and the guiding individual-based prediction to make accurate predictions. Thus, the population can quickly adapt to the predictable environmental changes. Additionally, the precision controllable mutation strategy handles unpredictable environmental changes. It improves the diversity exploration of the population by controlling the variation degree of solutions. In this way, our change response mechanism can adapt to various environmental changes of DMOPs, such as predictable and unpredictable changes. This paper integrates the HPPCM mechanism into a prevalent regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) to optimize DMOPs. The results of comparative experiments with some state-of-the-art algorithms on various test instances have demonstrated the effectiveness and competitiveness of the change response mechanism proposed in this paper.
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    Combining state detection with knowledge transfer for constrained multi-objective optimization
    (IEEE, 0202-04-18) Zheng, Jinhua; Yang, Kaixi; Zou, Juan; Yang, Shengxiang
    The main challenge in studying constrained multi-objective optimization problems (CMOPs) is reasonably balancing convergence, diversity, and feasibility. One of the most successful solutions to this challenge is the co-evolutionary frame-work, an algorithm in which multiple populations cooperate and complement each other, with different but interdependent populations addressing different but related problems. However, the effectiveness of existing algorithms for information exchange between various populations is not apparent. This paper proposes a new algorithm named SDKT using population state detection and knowledge transfer. The method has dual stages (i.e., knowledge acquisition and knowledge reception) and dual populations. Specifically, by restarting the strategy, these two populations (i.e., mainPop and auxPop) first explore more feasible regions with and without constraints. Then, in the knowledge receiving stage, ma i nPop and auxPop provide effective information to promote each other's approach to constrained PF (CPF) and unconstrained PF (UPF), respectively. Extensive experiments on three well-known test suites and three real-world problem studies fully demonstrate that SDKT is more competitive than five state-of-the-art constrained multi-objective evolutionary algorithms.
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    A constrained multi-objective evolutionary strategy based on population state detection
    (Elsevier, 2021-09-14) Tang, Huanrong; Yu, Fan; Zou, Juan; Yang, Shengxiang; Zheng, Jinhua
    The difficulty of solving constrained multi-objective optimization problems (CMOPs) using evolutionary algorithms is to balance constraint satisfaction and objective optimization while fully considering the diversity of the solution set. Many CMOPs with disconnected feasible subregions make it difficult for algorithms to search for all feasible nondominated solutions. To address these issues, we propose a population state detection strategy (PSDS) and a restart scheme to determine whether the environmental selection strategy needs to be changed based on the situation of population. When the population converges in the feasible region, the unconstrained environmental selection allows the population to cross the current feasible region. When the population converging outside the feasible region, all constraints will be considered in the environmental selection to select the population for the feasible region. In addition, the restart scheme will use reinitialization to make the population jump out of unprofitable iterations. The proposed algorithm enhances the search ability through the detection strategy and provides more diversity by reinitializing the population. The experimental results on four constraint test suites with various features have demonstrated that the proposed algorithm had better or competitive performance against other state-of-the-art constrained multi-objective algorithms.
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    Continuous variation operator configuration for decomposition-based evolutionary multi-objective optimization
    (Elsevier, 2024-07-10) Liu, Yuan; Li, Jiazheng; Zou, Juan; Hou, Zhanglu; Yang, Shengxiang; Zheng, Jinhua
    There are various multi-objective evolutionary algorithms (MOEAs) for solving multi-objective optimization problems (MOPs), and the significant difference between them lies in the way they generate offspring, which are the so-called variation operators. Since different variation operators have their own characteristics, it is often tedious to select a suitable EA for a given MOP. Even if the optimal operator is assigned, the fixed operator and hyper-parameters make it difficult to balance exploration and exploitation during the evolutionary process. It is imperative to configure variation operators and hyper-parameters automatically during the evolutionary process, which can improve the efficiency of algorithm search. However, numerous configurations only consider operators or discretize hyper-parameters, making it difficult to achieve satisfactory results. In this paper, we formulate the operator configuration as a continuous Markov Decision Process (MDP) and use a suitable Reinforcement Learning (RL) paradigm to realize the online configuration of EAs. To simplify the deployment of MDP, we adopt a decomposition-based framework and use a one-dimensional vector with a combination of weights and objectives as state spaces. In addition, we take the selection of crossover and mutation operators and the fine-tuning of their hyper-parameters as joint action spaces. With an RL technique, we expect to achieve maximum improvement in the performance of offspring on each preference by selecting an action in a given state. We further explore the effectiveness of the proposed methodology on different characteristic MOPs. Experimental results show that our method is more competitive than other configurations and state-of-the-art EAs.
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    A decision variable classification-based cooperative coevolutionary algorithm for dynamic multiobjective optimization
    (Elsevier, 2021-01-26) Xie, Huipeng; Zou, Juan; Yang, Shengxiang; Zheng, Jinhua; Ou, Junwei; Hu, Yaru
    This paper proposes a new decision variable classification-based cooperative coevolutionary algorithm, which uses the information of decision variable classification to guide the search process, for handling dynamic multiobjective problems. In particular, the decision variables are divided into two groups: convergence variables (CS) and diversity variables (DS), and different strategies are introduced to optimize these groups. Two kinds of subpopulations are used in the proposed algorithm, i.e., the subpopulations that represent DS and the sub-populations that represent CS. In the evolution process, the coevolution of DS and CS is carried out through genetic operators, and subpopulations of CS are gradually merged into DS, which is optimized in the global search space, based on an indicator to avoid becoming trapped in local optimum. Once a change is detected, a prediction method and a diversity introduction approach are adopted for these two kinds of variables to get a promising population with good diversity and convergence in the new environment. The proposed algorithm is tested on 16 benchmark dynamic multiobjective optimization problems, in comparison with state-of-the-art algorithms. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization.
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    Differential evolution based on local grid search for multimodal multiobjective optimization with local Pareto fronts
    (ACM, 2024-07) Zou, Juan; Xie, Tianbin; Deng, Qi; Yu, Xiaozhong; Yang, Shengxiang; Zheng, Jinhua
    Multimodal multiobjective optimization problems (MMOPs) are characterized by multiple Pareto optimal solutions corresponding to the same objective vector. MMOPs with local Pareto fronts (MMOPLs) are common in the real world. However, existing multimodal multiobjective evolutionary algorithms (MMEAs) face significant challenges in finding both global and local Pareto sets (PSs) when dealing with MMOPLs. For this purpose, we propose a differential evolution algorithm based on local grid search, called LGSDE. LGSDE establishes a local grid region for each solution, achieving a balanced distribution by judging the dominant relationship only among solutions within that local region. This approach enables the population to converge towards both global and local PSs. We compare LGSDE with other state-of-the-art MMEAs. Experimental results demonstrate LGSDE exhibits superiority in addressing MMOPLs.
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    A dual-population algorithm based on alternative evolution and degeneration for solving constrained multi-objective optimization problems
    (Elsevier, 2021-07-27) Zou, Juan; Sun, Ruiqing; Yang, Shengxiang; Zheng, Jinhua
    It is challenging to solve constrained multi-objective optimization problems (CMOPs). Different from the traditional multi-objective optimization problem, the feasibility, convergence, and diversity of the population must be considered in the optimization process of a CMOP. How these factors are balanced will affect the performance of the constrained multi-objective optimization algorithm. To solve this problem, we propose a dual-population multi-objective optimization evolutionary algorithm. The proposed algorithm can make good use of its secondary population and alternative between evolution and degeneration according to the state of the secondary population to provide better information for the main population. The test results of three benchmark constrained multi-objective optimization problem suites, and four real-world constrained multi-objective optimization problems show that the algorithm is better than existing dual-population multi-objective optimization, especially when there is a distance between the unconstrained PF and the constrained PF.
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    A dual-population evolutionary algorithm based on adaptive constraint strength for constrained multi-objective optimization
    (Elsevier, 2023-01-19) Yang, Kaixi; Zheng, Jinhua; Zou, Juan; Yu, Fan; Yang, Shengxiang
    It is challenging to balance convergence and diversity while fully satisfying feasibility when dealing with constrained multi-objective optimization problems (CMOPs). Overemphasizing the feasibility optimization of constraint satisfaction may lead to the search falling into local optimum, and overemphasizing the objective optimization of ignoring constraints may cause a lot of computational resources to be wasted in searching for infeasible solutions. This paper proposes a dual-population algorithm called dp-ACS, aiming to seek a balance between constraint satisfaction and objective optimization. The algorithm proposes a dominance relation to speed up the algorithm’s convergence and an adaptive constraint strength strategy to consider the information of excellent infeasible solutions. Specifically, the former defines a new domination relationship to distinguish the pros and cons of nondominated solutions. The population converges faster by selecting better nondominated solutions into the matching pool. The latter is informed by infeasible solutions with good objective values by maintaining two cooperatively complementary populations (i.e., mainPop and auxPop). mainPop uses an adaptive constraint strength function that optimizes the objective of the original problem while satisfying the current constraint strengths. Dynamic adjustment of constraint strength can improve the diversity when the population converges to the boundary of the feasible local region. auxPop optimizes the unconstrained objective of the original problem, which can provide mainPop with favorable information outside the feasible region it explores to guide the evolution of mainPop. Experimental results show that the proposed algorithm was more competitive on four constrained test suites and four real-world CMOPs, compared with seven state-of-the-art CMOEAs.
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    Dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement
    (Elsevier, 2024-06-27) Che, Wang; Zheng, Jinhua; Hu, Yaru; Zou, Juan; Yang, Shengxiang
    Dynamic constrained multi-objective optimization problems (DCMOPs) involve objectives, constraints, and parameters that change over time. This kind of problem presents a greater challenge for evolutionary algorithms because it requires the population to quickly track the changing pareto-optimal set (PS) under constrained conditions while maintaining the feasibility and good distribution of the population. To address these challenges, this paper proposes a dynamic constrained multi-objective optimization algorithm based on co-evolution and diversity enhancement (CEDE), in which we have made improvements to both the static optimization and dynamic response parts, innovatively utilizing the valuable information latent in the optimization process to help the population evolve more comprehensively. The static optimization involves the co-evolution of three populations, through which their mutual synergy can more comprehensively identify potential true PS and provide more useful historical information for dynamic response. Additionally, to prevent the elimination of potentially valuable infeasible individuals (i.e., individuals that are not dominated by feasible individuals) due to pareto domination, we employ an archive set to store and update these individuals. When the environment changes, to effectively enhance population diversity under complex dynamic constraints and help the population to respond quickly to changes, we propose a diversity enhancement strategy, which includes a diversity maintenance strategy and a center point-based exploration strategy. This strategy effectively enhances population diversity in complex and changing environments, helping the population respond quickly to changes. The effectiveness of the algorithm is validated through two test sets. The experimental results show that CEDE can effectively use valuable information to cope with complex dynamic constraint environments. Compared with several of the most advanced algorithms, it is superior in 94% of the test problems, demonstrating strong competitiveness in handling DCMOPs.
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    A dynamic multi-objective evolutionary algorithm based on intensity of environmental change
    (Elsevier, 2020-03-07) Hu, Yaru; Zheng, Jinhua; Zou, Juan; Yang, Shengxiang; Ou, Junwei; Rui, Wang
    This paper proposes a novel evolutionary algorithm based on the intensity of environmental change (IEC) to effectively track the moving Pareto-optimal front (POF) or Pareto-optimal set (POS) in dynamic optimization. The IEC divides each individual into two parts according to the evolutionary information feedback from the POS in the current and former evolutionary environment when an environmental change is detected. Two parts, the micro-changing decision and macro-changing decision, are implemented upon different situations of decision components in order to build an efficient information exchange among dynamic environments. In addition, in our algorithm, if a new evolutionary environment is similar to its historical evolutionary environment, the history information will be used for reference to guide the search towards promising decision regions. In order to verify the availability of our idea, the IEC has been extensively compared with four state-of-the-art algorithms over a range of test suites with different features and difficulties. Experimental results show that the proposed IEC is promising.