Multimodal Evolutionary Algorithms Research Articles

Objective-Constraint Mutual-Guided Surrogate-Based Particle Swarm Optimization for Expensive Constrained Multimodal Problems

Expensive constraint multimodal optimization problems (ECMMOPs) have such characteristics as expensive objectives and constraints, and multiple optimal modalities simultaneously, which pose severe challenges to evolutionary optimization methods. This paper studies an objective-constraint mutual-guided surrogate-assisted particle swarm optimization algorithm for the kind of problem, aiming to discover multiple competing feasible optimal solutions at a lower calculation cost. The algorithm designs firstly a new two-layer cooperative surrogate model framework based on heterogeneous database to effectively adjust the prediction accuracies of objective surrogates and constraint surrogates on different search regions. And, an objective-constraint mutual-guided partial evaluation strategy (O-C-PES) is developed to generate high-quality infilling samples for objective and constraint surrogates respectively, based on which the number of unnecessary real evaluations can be significantly reduced. Moreover, a position feature-guided hybrid update mechanism (PF-HUM) is proposed to find more optimal solutions by searching excellent infeasible and feasible areas at the same time, and a feasible ratio-driven local search (FR-LS) strategy is proposed to improve the algorithm’s exploitation. Compared with four existing surrogate-assisted evolutionary algorithms and one constraint multimodal evolutionary algorithms on 21 benchmark problems and three engineering instances, experiment results show that the proposed algorithm can simultaneously obtain multiple highly-competitive feasible optimal solutions with less computational cost.

Multisurrogate-Assisted Multitasking Particle Swarm Optimization for Expensive Multimodal Problems.

Many real-world applications can be formulated as expensive multimodal optimization problems (EMMOPs). When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face the problem of selecting surrogate models but also need to tackle the problem of discovering and updating multiple modalities. Different optimization problems and different stages of evolutionary algorithms (EAs) generally require different types of surrogate models. To address this issue, in this article, we present a multisurrogate-assisted multitasking particle swarm optimization algorithm to seek multiple optimal solutions of EMMOPs at a low computational cost. The proposed algorithm first transforms an EMMOP into a multitasking optimization problem by integrating various surrogate models, and designs a multitasking niche particle swarm algorithm to solve it. Following that, a surrogate model management strategy based on the skill factor and clustering is developed to effectively balance the number of real function evaluations and the prediction accuracy of candidate optimal solutions. In addition, an adaptive local search strategy based on the trust region is proposed to enhance the capability of swarm in exploiting potential optimal modalities. We compare the proposed algorithm with five state-of-the-art SAEAs and seven multimodal EAs on 19 benchmark functions and the building energy conservation problem and experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.

Large-scale multimodal multiobjective evolutionary optimization based on hybrid hierarchical clustering

Large-scale multimodal multiobjective optimization problems (MMOPs) have different equivalent Pareto optimal solution sets (PSs) for the same Pareto front and contain a great number of decision variables. In particular, when most variables among the Pareto optimal solutions are zero, such problems are termed large-scale MMOPs with sparse Pareto optimal solutions. Due to the multimodal properties of these problems, the curse of dimensionality, and the unknown sparsity of the search space, it is extremely difficult for existing optimizers to solve them. In this study, we propose a multipopulation multimodal evolutionary algorithm based on hybrid hierarchical clustering to solve such problems. The proposed algorithm uses hybrid hierarchical clustering on subpopulations to distinguish the resources of different equivalent PSs and partition them into different subpopulations to achieve efficient cooperative coevolution among multiple subpopulations. Moreover, an adaptive variation method incorporating both local and global guiding information is designed, and an improved environmental selection method based on local guiding information is conducted to improve the convergence in a large search space and introduce diversity to the population. Experimental results verified that the proposed algorithm outperforms the state-of-the-art MOEAs in terms of performance and convergence speed, especially when the number of equivalent PSs is large.

Unsupervised Hyperspectral Band Selection via Multimodal Evolutionary Algorithm and Subspace Decomposition.

Unsupervised band selection is an essential task to search for representative bands in hyperspectral dimension reduction. Most of existing studies utilize the inherent attribute of hyperspectral image (HSI) and acquire single optimal band subset while ignoring the diversity of subsets. Moreover, the ordered property in HSI is expected to be focused in order to avoid choosing redundant bands. In this paper, we proposed an unsupervised band selection method based on the multimodal evolutionary algorithm and subspace decomposition to alleviate the problems. To explore the diversity of band subsets, the multimodal evolutionary algorithm is first employed in spectral subspace decomposition to seek out multiple global or local solutions. Meanwhile, in view of ordered property, we concentrate more on increasing the difference between neighbor band subspaces. Furthermore, to utilize the obtained multiple diverse band subsets, an integrated utilization strategy is adopted to improve the predicted performance. Experimental results on three popular hyperspectral remote sensing datasets and one collected composition prediction dataset show the effectiveness of the proposed method, and the superiority over state-of-the-art methods on predicted accuracy.

A multimodal evolutionary algorithm with multi-niche cooperation

Multimodal optimization problems, which involve multiple global optima, are common in real-world applications. So far, plenty of multimodal evolutionary algorithms (MMEAs) have been proposed, where niching techniques are widely utilized to locate different optima by trying to cover each modality with an exclusive niche. However, most existing MMEAs deal with niches independently without considering their similarity and redundancy, which greatly limits the performance of the algorithms. Directing against this issue, this study proposes a multi-niche cooperation based MMEA, where a knowledge transfer strategy (KTS) and a collaborative search mechanism (CSM) are designed. Specifically, given the high similarity shared by different modalities, KTS cooperatively evolves the corresponding niches by transferring knowledge among them, thereby accelerating their convergence. For niches possibly covering the same modality, CSM explicitly measures the search intensity on the modality and adaptively deactivates redundant niches, so that excessive searches on the modality can be avoided. This study incorporates the above two strategies into a classic MMEA named NEA2, and thus leads to a multi-niche cooperation based NEA (MNC-NEA). Experiments conducted on 20 benchmark functions demonstrate that KTS and CSM are efficient and complementary, and they together endow MNC-NEA with a significant competitive advantage over 11 state-of-the-art MMEAs.

Evolutionary Dual-Ensemble Class Imbalance Learning for Human Activity Recognition

Human activity recognition is an imbalance classification problem in essence since various human actions may occur at different frequencies. Traditional ensemble class imbalance learning methods integrate resampling technique with multi-classifier models, which obtain better generalization than single ones. However, the number of base classifiers is often determined in advance, resulting in the redundant structure of a multi-classifier and larger computational cost. Moreover, various combinations of base classifiers may have similar recognition accuracy, forming a multimodel optimization problem. To address the issue, a dual-ensemble class imbalance learning method is presented, in which two ensemble learning models are nested each other. For each sub-dataset, three heterogeneous sub-classifiers compose of internal ensemble learning model, and the one with the highest recognition accuracy is selected as base classifier. In external ensemble learning model, an optimal combination that contains the smallest number of base classifiers and identifies human actions most exactly is found by multimodal evolutionary algorithms. Based on seven imbalanced activity datasets derived from localization data for person activity, statistical experimental results show that the proposed evolutionary dual-ensemble class imbalance learning method provides the simplest ensemble structure with the best accuracy for imbalanced data that outperforms other five widely-used ensemble classification methods on all metrics.

A two-archive model based evolutionary algorithm for multimodal multi-objective optimization problems

Multimodal multi-objective optimization (MMO) can offer more elegant solutions and provide diverse decisions to decision-makers in real world optimization problems. Many multimodal evolutionary mechanisms have been proposed to explore and exploit two solution spaces (i.e. decision space and objective space) in recent years. However, most existing methods only use single evolutionary operator to generate offsprings and ignore the advantage of using hybrid evolutionary algorithm. Moreover, it is still a great challenge to balance the effectiveness and efficiency simultaneously in the evolutionary process of MMO. In view of this, an efficient Two-Archive model based multimodal evolutionary algorithm is proposed in this paper. Two parallel offspring generation mechanisms based on competitive particle swarm optimizer and differential evolution are applied to expand two solution spaces with different evolutionary requirements. Moreover, niching local search scheme and reverse vector mutation strategy play roles in achieving better convergence and diversity. Finally, 22 MMO test problems are used to validate the superiority of the proposed method by comparing it with 5 state-of-the-art MMO algorithms. The proposed method is also expanded to solve 9 feature selection problems for validating the effectiveness of the proposed method on real world applications.

Multimodal Evolutionary Algorithms for Easing the Complexity of Agent-Based Model Calibration

Multimodal Evolutionary Algorithms for Easing the Complexity of Agent-Based Model Calibration

Dual-Surrogate-Assisted Cooperative Particle Swarm Optimization for Expensive Multimodal Problems

Various real-world applications can be classified as expensive multimodal optimization problems. When surrogate-assisted evolutionary algorithms (SAEAs) are employed to tackle these problems, they not only face a contradiction between the precision of surrogate models and the cost of individual evaluations but also have the difficulty that surrogate models and problem modalities are hard to match. To address this issue, this article studies a dual-surrogate-assisted cooperative particle swarm optimization algorithm to seek multiple optimal solutions. A dual-population cooperative particle swarm optimizer is first developed to simultaneously explore/exploit multiple modalities. Following that, a modal-guided dual-layer cooperative surrogate model, which contains one upper global surrogate model and a group of lower local surrogate models, is constructed with the purpose of reducing the individual evaluation cost. Moreover, a hybrid strategy based on clustering and peak-valley is proposed to detect new modalities. Compared with five existing SAEAs and seven multimodal evolutionary algorithms, the proposed algorithm can simultaneously obtain multiple highly competitive optimal solutions at a low computational cost according to the experimental results of testing both 11 benchmark instances and the building energy conservation problem.

Short-term load forecasting using multimodal evolutionary algorithm and random vector functional link network based ensemble learning

Increasing the accuracy and intelligence of short-term load forecasting system can improve modern power systems management and economic power generation. In recent decades, the optimized machine learning methods have been widely used in load forecasting problems because of their predictability with higher accuracy and robustness. However, most related researches only use evolutionary algorithms for parameters fine-tuning and ignore the evolutionary algorithm based decision-making support and the matching relation between the used evolutionary algorithm and machine learning method, which greatly limit the improvement of forecasting system. To dissolve the above issues, a data-driven evolutionary ensemble learning forecasting model is proposed in this paper. Firstly, a novel multimodal evolutionary algorithm based on comprehensive weighted vector angle and shift-based density estimation is proposed. Secondly, based on the proposed multimodal evolutionary algorithm, an intelligent decision-making support scheme including predictive performance evaluation, model properties analysis, structure and fusion strategy optimization, and optimal model preference selection is designed to improve the random vector functional link network based ensemble learning model and boost the forecasting accuracy. Thirdly, experimental studies on 15 test problems with up to 6000 decision variables are conducted to validate the excellent optimization ability of the proposed evolutionary algorithm. Finally, the proposed evolutionary ensemble learning method is compared with 6 other representative forecast methods on real-world short-term load forecasting datasets from Australia, Great Britain, and Norway. The experiment results verify the superiority and applicability of the proposed method.

Ensemble learning based on fitness Euclidean-distance ratio differential evolution for classification

Ensemble learning is a system that combines a set of base learners to improve the performance in machine learning, where accuracy and diversity of base learners are two important factors. However, these two factors are usually contradictory. To address this problem, in this paper, we propose a novel ensemble learning algorithm based on fitness Euclidean-distance ratio differential evolution, to train the neural network ensemble. FEFERR_ELA employs a multimodal evolutionary algorithm that is capable of producing diverse solutions to search for optimal solutions corresponding to parameters of base learners, where each optimal solution leads to one trained model. A dynamic ensemble selection scheme is applied to select appropriate individuals for the ensemble. The proposed algorithm is evaluated on several benchmark problems and compared with some related ensemble learning models. The experimental results demonstrate that the proposed algorithm outperforms the related works and can produce the neural network ensembles with better generalization.

Evolutionary Algorithms: Multimodal Problems and Spatial Distribution

Over the last few decades, optimization problems have gained special attention in the world of computing, mainly because thanks to them, complex problems, which could only be addressed through approaches, now can be solved. In the wild, biodiversity is manifested by subtle differences in the individuals genetic code and consequently in the evolution of species. This approach is intended to apply to solving optimization problems through multimodal evolutionary algorithms. Standard evolutionary algorithms are not able to find more than a local optimum in the case of multimodal functions due to stochastic errors are committed (an individual randomly move one class to another) and that the population has a finite size (finite diversity). For this reason, in this work, a detailed study of the techniques of solving multimodal problems by using spatial evolutionary algorithms is done. In addition, the design details of new mechanisms for spatial evolutionary algorithms that allow us to reallocate the space of solutions are introduced. Thus, we will be able to deal with the resolution of complex problems with multiple local or global solutions.

Influence Maximization in Social Networks using Deterministic Crowding Algorithm

In a social network the individuals connected to one another become influenced by one another, while some are more influential than others and able to direct groups of individuals towards a move, an idea and an entity. These individuals are named influential users. Attempt is made by the social network researchers to identify such individuals because by changing their behaviors and ideologies due to communications and the high influence on one another would change many others' behaviors and ideologies in a given community. In information diffusion models, at all stages, individuals are influenced by their neighboring people. These influences and impressions thereof are constructive in an information diffusion process. In the Influence Maximization problem, the goal is to finding a subset of individuals in a social network such that by activating them, the spread of influence is maximized. In this work a new algorithm is presented to identify most influential users under the linear threshold diffusion model. It uses explicit multimodal evolutionary algorithms. Four different datasets are used to evaluate the proposed method. The results show that the precision of our method in average is improved 4.8% compare to best known previous works.

Multimodal Evolutionary Algorithm for Multidimensional Scaling with City-Block Distances

Multidimensional scaling with city-block distances is considered in this paper. The technique requires optimization of an objective function which has many local minima and can be non-differentiable at minimum points. This study is aimed at developing a fast and effective global optimization algorithm spanning the whole search domain and providing good solutions. A multimodal evolutionary algorithm is used for global optimization to prevent stagnation at bad local optima. Piecewise quadratic structure of the least squares objective function with city-block distances has been exploited for local improvement. The proposed algorithm has been compared with other algorithms described in literature. Through a comprehensive computational study, it is shown that the proposed algorithm provides the best results. The algorithm with fine-tuned parameters finds the global minimum with a high probability.

Genetic Algorithm with adaptive elitist-population strategies for multimodal function optimization

This paper introduces a new technique called adaptive elitist-population search method. This technique allows unimodal function optimization methods to be extended to efficiently explore multiple optima of multimodal problems. It is based on the concept of adaptively adjusting the population size according to the individuals’ dissimilarity and a novel direction dependent elitist genetic operators. Incorporation of the new multimodal technique in any known evolutionary algorithm leads to a multimodal version of the algorithm. As a case study, we have integrated the new technique into Genetic Algorithms (GAs), yielding an Adaptive Elitist-population based Genetic Algorithm (AEGA). AEGA has been shown to be very efficient and effective in finding multiple solutions of complicated benchmark and real-world multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including rough and stepwise multimodal functions. Empirical results are also compared with other multimodal evolutionary algorithms from the literature, showing that AEGA generally outperforms existing approaches.

Environomic multi-objective optimisation of a district heating network considering centralized and decentralized heat pumps

Concern for the environment has been steadily growing in recent years, and it is becoming more common to include environmental impact and pollution costs in the design problem along with construction, investment and operating costs. To economically respond to the global environmental problems ahead, progress must be made both on more sustainable technologies and on the design methodology, which needs to adopt a more holistic approach. Heat pumps and, in particular systems integrating heat pumps and cogeneration units, offer a significant potential for greenhouse gas reduction. This paper illustrates the application of a multi-objective and multi-modal evolutionary algorithm to facilitate the design and planning of a district heating network based on a combination of centralized and decentralized heat pumps combined with on-site cogeneration. Comparisons are made with an earlier study based on a single objective environomic optimisation of the same overall model.