Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

A Modular Hybridization of Particle Swarm Optimization and Differential Evolution

In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are implemented, has been introduced to boost the empirical performance. In this paper, we first propose to combine the variants of PSO or DE by modularizing each algorithm and incorporating the variants thereof as different options of the corresponding modules. Then, considering the similarity between the inner workings of PSO and DE, we hybridize the algorithms by creating two populations with variation operators of PSO and DE respectively, and selecting individuals from those two populations. The resulting novel hybridization, called PSODE, encompasses most up-to-date variants from both sides, and more importantly gives rise to an enormous number of unseen swarm algorithms via different instantiations of the modules therein. In detail, we consider 16 different variation operators originating from existing PSO- and DE algorithms, which, combined with 4 different selection operators, allow the hybridization framework to generate 800 novel algorithms. The resulting set of hybrid algorithms, along with the combined 30 PSO- and DE algorithms that can be generated with the considered operators, is tested on the 24 problems from the well-known COCO/BBOB benchmark suite, across multiple function groups and dimensionalities.Comment: 8 pages, 1 figure, to be published in GECCO 2020 Companio

Development of an Entropy-Based Swarm Algorithm for Continuous Dynamic Constrained Optimization

Dynamic constrained optimization problems form a class of problems WHERE the objective function or the constraints can change over time. In static optimization, finding a global optimum is considered as the main goal. In dynamic optimization, the goal is not only to find an optimal solution, but also track its trajectory as closely as possible over time. Changes in the environment must be taken into account during the optimization process in such way that these problems are to be solved online. Many real-world problems can be formulated within this framework. This thesis proposes an entropy-based bare bones particle swarm for solving dynamic constrained optimization problems. The Shannons entropy is established as a phenotypic diversity index and the proposed algorithm uses the Shannons index of diversity to aggregate the global-best and local-best bare bones particle swarm variants. The proposed approach applies the idea of mixture of search directions by using the index of diversity as a factor to balance the influence of the global-best and local-best search directions. High diversity promotes the search guided by the global-best solution, with a normal distribution for exploitation. Low diversity promotes the search guided by the local-best solution, with a heavy-tailed distribution for exploration. A constraint-handling strategy is also proposed, which uses a ranking method with selection based on the technique for order of preference by similarity to ideal solution to obtain the best solution within a specific population of candidate solutions. Mechanisms to detect changes in the environment and to update particles' memories are also implemented into the proposed algorithm. All these strategies do not act independently. They operate related to each other to tackle problems such as: diversity loss due to convergence and outdated memories due to changes in the environment. The combined effect of these strategies provides an algorithm with ability to maintain a proper balance between exploration and exploitation at any stage of the search process without losing the tracking ability to search an optimal solution which is changing over time. An empirical study was carried out to evaluate the performance of the proposed approach. Experimental results show the suitability of the algorithm in terms of effectiveness to find good solutions for the benchmark problems investigated. Finally, an application is developed, WHERE the proposed algorithm is applied to solve the dynamic economic dispatch problem in power systems

Self-adaptive parameter and strategy based particle swarm optimization for large-scale feature selection problems with multiple classifiers

This work was partially supported by the National Natural Science Foundation of China (61403206, 61876089,61876185), the Natural Science Foundation of Jiangsu Province (BK20141005), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (14KJB520025), the Engineering Research Center of Digital Forensics, Ministry of Education, and the Priority Academic Program Development of Jiangsu Higher Education Institutions.Peer reviewedPostprin

Genetic learning particle swarm optimization

Social learning in particle swarm optimization (PSO) helps collective efficiency, whereas individual reproduction in genetic algorithm (GA) facilitates global effectiveness. This observation recently leads to hybridizing PSO with GA for performance enhancement. However, existing work uses a mechanistic parallel superposition and research has shown that construction of superior exemplars in PSO is more effective. Hence, this paper first develops a new framework so as to organically hybridize PSO with another optimization technique for “learning.” This leads to a generalized “learning PSO” paradigm, the *L-PSO. The paradigm is composed of two cascading layers, the first for exemplar generation and the second for particle updates as per a normal PSO algorithm. Using genetic evolution to breed promising exemplars for PSO, a specific novel *L-PSO algorithm is proposed in the paper, termed genetic learning PSO (GL-PSO). In particular, genetic operators are used to generate exemplars from which particles learn and, in turn, historical search information of particles provides guidance to the evolution of the exemplars. By performing crossover, mutation, and selection on the historical information of particles, the constructed exemplars are not only well diversified, but also high qualified. Under such guidance, the global search ability and search efficiency of PSO are both enhanced. The proposed GL-PSO is tested on 42 benchmark functions widely adopted in the literature. Experimental results verify the effectiveness, efficiency, robustness, and scalability of the GL-PSO

Simple and Adaptive Particle Swarms

The substantial advances that have been made to both the theoretical and practical aspects of particle swarm optimization over the past 10 years have taken it far beyond its original intent as a biological swarm simulation. This thesis details and explains these advances in the context of what has been achieved to this point, as well as what has yet to be understood or solidified within the research community. Taking into account the state of the modern field, a standardized PSO algorithm is defined for benchmarking and comparative purposes both within the work, and for the community as a whole. This standard is refined and simplified over several iterations into a form that does away with potentially undesirable properties of the standard algorithm while retaining equivalent or superior performance on the common set of benchmarks. This refinement, referred to as a discrete recombinant swarm (PSODRS) requires only a single user-defined parameter in the positional update equation, and uses minimal additive stochasticity, rather than the multiplicative stochasticity inherent in the standard PSO. After a mathematical analysis of the PSO-DRS algorithm, an adaptive framework is developed and rigorously tested, demonstrating the effects of the tunable particle- and swarm-level parameters. This adaptability shows practical benefit by broadening the range of problems which the PSO-DRS algorithm is wellsuited to optimize