Improving Estimation of Distribution Algorithm on Multimodal Problems by Detecting Promising Areas

A Memetic Algorithm Based on Probability Learning for Solving the Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a well-known combinatorial optimization problem with many real-life applications. In this article, a memetic algorithm based on probability learning (MA/PL) is proposed to solve MKP. The main highlights of this article are two-fold: 1) problem-dependent heuristics for MKP and 2) a novel framework of MA/PL. For the problem-dependent heuristics, we first propose two kinds of logarithmic utility functions (LUFs) based on the special structure of MKP, in which the profit value and weight vector of each item are considered simultaneously. Then, LUFs are applied to effectively guide the repair operator for infeasible solutions and the local search operator. For the framework of MA/PL, we propose two problem-dependent probability distributions to extract the special knowledge of MKP, that is, the marginal probability distribution (MPD) of each item and the joint probability distribution (JPD) of two conjoint items. Next, learning rules for MPD and JPD, which borrow ideas from competitive learning and binary Markov chain, are proposed. Thereafter, we generate MA/PL's offspring by integrating MPD and JPD, such that the univariate probability information of each item as well as the dependency of conjoint items can be sufficiently used. Results of experiments on 179 benchmark instances and a real-life case study demonstrate the effectiveness and practical values of the proposed MKP.

An Adaptive Covariance Scaling Estimation of Distribution Algorithm

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

Maximizing Lifetime of Range-Adjustable Wireless Sensor Networks: A Neighborhood-Based Estimation of Distribution Algorithm

Sensor activity scheduling is critical for prolonging the lifetime of wireless sensor networks (WSNs). However, most existing methods assume sensors to have one fixed sensing range. Prevalence of sensors with adjustable sensing ranges posts two new challenges to the topic: 1) expanded search space, due to the rise in the number of possible activation modes and 2) more complex energy allocation, as the sensors differ in the energy consumption rate when using different sensing ranges. These two challenges make it hard to directly solve the lifetime maximization problem of WSNs with range-adjustable sensors (LM-RASs). This article proposes a neighborhood-based estimation of distribution algorithm (NEDA) to address it in a recursive manner. In NEDA, each individual represents a coverage scheme in which the sensors are selectively activated to monitor all the targets. A linear programming (LP) model is built to assign activation time to the schemes in the population so that their sum, the network lifetime, can be maximized conditioned on the current population. Using the activation time derived from LP as individual fitness, the NEDA is driven to seek coverage schemes promising for prolonging the network lifetime. The network lifetime is thus optimized by repeating the steps of the coverage scheme evolution and LP model solving. To encourage the search for diverse coverage schemes, a neighborhood sampling strategy is introduced. Besides, a heuristic repair strategy is designed to fine-tune the existing schemes for further improving the search efficiency. Experimental results on WSNs of different scales show that NEDA outperforms state-of-the-art approaches. It is also expected that NEDA can serve as a potential framework for solving other flexible LP problems that share the same structure with LM-RAS.

Triple Archives Particle Swarm Optimization

There are two common challenges in particle swarm optimization (PSO) research, that is, selecting proper exemplars and designing an efficient learning model for a particle. In this article, we propose a triple archives PSO (TAPSO), in which particles in three archives are used to deal with the above two challenges. First, particles who have better fitness (i.e., elites) are recorded in one archive while other particles who offer faster progress, called profiteers in this article, are saved in another archive. Second, when breeding each dimension of a potential exemplar for a particle, we choose a pair of elite and profiteer from corresponding archives as two parents to generate the dimension value by ordinary genetic operators. Third, each particle carries out a specific learning model according to the fitness of its potential exemplars. Furthermore, there is no acceleration coefficient in TAPSO aiming to simplify the learning models. Finally, if an exemplar has excellent performance, it will be regarded as an outstanding exemplar and saved in the third archive, which can be reused by inferior particles aiming to enhance the exploitation and to save computing resources. The experimental results and comparisons between TAPSO and other eight PSOs on 30 benchmark functions and four real applications suggest that TAPSO attains very promising performance in different types of functions, contributing to both higher solution accuracy and faster convergence speed. Furthermore, the effectiveness and efficiency of these new proposed strategies are discussed based on extensive experiments.

Enhancing Gaussian Estimation of Distribution Algorithm by Exploiting Evolution Direction With Archive

As a typical model-based evolutionary algorithm, estimation of distribution algorithm (EDA) possesses unique characteristics and has been widely applied in global optimization. However, the commonly used Gaussian EDA (GEDA) usually suffers from premature convergence, which severely limits its search efficiency. This paper first systematically analyzes the reasons for the deficiency of traditional GEDA, then tries to enhance its performance by exploiting the evolution direction, and finally develops a new GEDA variant named EDA². Instead of only utilizing some good solutions produced in the current generation to estimate the Gaussian model, EDA² preserves a certain number of high-quality solutions generated in the previous generations into an archive and employs these historical solutions to assist estimating the covariance matrix of Gaussian model. By this means, the evolution direction information hidden in the archive is naturally integrated into the estimated model, which in turn can guide EDA² toward more promising solution regions. Moreover, the new estimation method significantly reduces the population size of EDA² since it needs fewer individuals in the current population for model estimation. As a result, a fast convergence can be achieved. To verify the efficiency of EDA², we tested it on a variety of benchmark functions and compared it with several state-of-the-art EAs. The experimental results demonstrate that EDA² is efficient and competitive.

Feature Input Symmetry Algorithm of Multi-Modal Natural Language Library Based on BP Neural Network

When using traditional knowledge retrieval algorithms to analyze whether the feature input of words in multi-modal natural language library is symmetrical, the symmetry of words cannot be analyzed, resulting in inaccurate analysis results. A feature input symmetric algorithm of multi-modal natural language library based on BP (back propagation) neural network is proposed in this paper. A Chinese abstract generation method based on multi-modal neural network is used to extract Chinese abstracts from images in multi-modal natural language library. The Word Sense Disambiguation (WSD) Model is constructed by the BP neural network. After the word or text disambiguation is performed on the Chinese abstract in the multi-modal natural language library, the feature input symmetry problem in the multi-modal natural language library is analyzed according to the sentence similarity. The experimental results show that the proposed algorithm can effectively analyze the eigenvalue symmetry problem of the multi-modal natural language library. The maximum error rate of the analysis algorithm is 7%, the growth rate of the analysis speed is up to 50%, and the average analysis time is 540.56 s. It has the advantages of small error and high efficiency.

Degeneration Recognizing Clonal Selection Algorithm for Multimodal Optimization

In this paper, a computing speed improvement for the clonal selection algorithm (CSA) is proposed based on a degeneration recognizing (DR) method. The degeneration recognizing clonal selection algorithm (DR-CSA) is designed for solving complex engineering multimodal optimization problems. On each iteration of CSA, there is a large amount of eliminated solutions which are usually neglected. But these solutions do contain the knowledge of the nonoptimal area. By storing and utilizing these data, the DR-CSA is aimed to identify part of the new population as degenerated and eliminate them before the evaluation operation, so that a number of evaluation times can be avoided. This pre-elimination operation is able to save computing time because the evaluation is the main reason for the time cost in the complex engineering optimization problem. Experiments on both test function and a real-world engineering optimization problem (wet spinning coagulating process) are conducted. The results show that the proposed DR-CSA is as accurate as regular CSA and is effective in reducing a considerable amount of computing time.

Segment-Based Predominant Learning Swarm Optimizer for Large-Scale Optimization

Large-scale optimization has become a significant yet challenging area in evolutionary computation. To solve this problem, this paper proposes a novel segment-based predominant learning swarm optimizer (SPLSO) swarm optimizer through letting several predominant particles guide the learning of a particle. First, a segment-based learning strategy is proposed to randomly divide the whole dimensions into segments. During update, variables in different segments are evolved by learning from different exemplars while the ones in the same segment are evolved by the same exemplar. Second, to accelerate search speed and enhance search diversity, a predominant learning strategy is also proposed, which lets several predominant particles guide the update of a particle with each predominant particle responsible for one segment of dimensions. By combining these two learning strategies together, SPLSO evolves all dimensions simultaneously and possesses competitive exploration and exploitation abilities. Extensive experiments are conducted on two large-scale benchmark function sets to investigate the influence of each algorithmic component and comparisons with several state-of-the-art meta-heuristic algorithms dealing with large-scale problems demonstrate the competitive efficiency and effectiveness of the proposed optimizer. Further the scalability of the optimizer to solve problems with dimensionality up to 2000 is also verified.

Multimodal Estimation of Distribution Algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima.

An Orthogonal Evolutionary Algorithm With Learning Automata for Multiobjective Optimization

Research on multiobjective optimization problems becomes one of the hottest topics of intelligent computation. In order to improve the search efficiency of an evolutionary algorithm and maintain the diversity of solutions, in this paper, the learning automata (LA) is first used for quantization orthogonal crossover (QOX), and a new fitness function based on decomposition is proposed to achieve these two purposes. Based on these, an orthogonal evolutionary algorithm with LA for complex multiobjective optimization problems with continuous variables is proposed. The experimental results show that in continuous states, the proposed algorithm is able to achieve accurate Pareto-optimal sets and wide Pareto-optimal fronts efficiently. Moreover, the comparison with the several existing well-known algorithms: nondominated sorting genetic algorithm II, decomposition-based multiobjective evolutionary algorithm, decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes, multiobjective optimization by LA, and multiobjective immune algorithm with nondominated neighbor-based selection, on 15 multiobjective benchmark problems, shows that the proposed algorithm is able to find more accurate and evenly distributed Pareto-optimal fronts than the compared ones.

A modified estimation distribution algorithm based on extreme elitism

An existing estimation distribution algorithm (EDA) with univariate marginal Gaussian model was improved by designing and incorporating an extreme elitism selection method. This selection method highlighted the effect of a few top best solutions in the evolution and advanced EDA to form a primary evolution direction and obtain a fast convergence rate. Simultaneously, this selection can also keep the population diversity to make EDA avoid premature convergence. Then the modified EDA was tested by means of benchmark low-dimensional and high-dimensional optimization problems to illustrate the gains in using this extreme elitism selection. Besides, no-free-lunch theorem was implemented in the analysis of the effect of this new selection on EDAs.