Salp Swarm Algorithm
TL;DR: The qualitative and quantitative results prove the efficiency of SSA and MSSA and demonstrate the merits of the algorithms proposed in solving real-world problems with difficult and unknown search spaces.
About: This article is published in Advances in Engineering Software.The article was published on 2017-12-01. It has received 3027 citations till now. The article focuses on the topics: Multi-swarm optimization & Metaheuristic.
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TL;DR: The statistical results and comparisons show that the HHO algorithm provides very promising and occasionally competitive results compared to well-established metaheuristic techniques.
2,871 citations
TL;DR: The proposed slime mould algorithm has several new features with a unique mathematical model that uses adaptive weights to simulate the process of producing positive and negative feedback of the propagation wave of slime mould based on bio-oscillator to form the optimal path for connecting food with excellent exploratory ability and exploitation propensity.
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TL;DR: Experimental results show that the AOA provides very promising results in solving challenging optimization problems compared with eleven other well-known optimization algorithms.
1,218 citations
Cites methods from "Salp Swarm Algorithm"
...Conventional methods of this group include Krill Herd lgorithm [20], Salp Swarm Algorithm [20], Symbiotic Organisms Search [21], Sine Cosine Algorithm [22], and olphin Echolocation [23]....
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TL;DR: A well-defined “generation rate” term is proved to invigorate EO’s ability in exploration, exploitation, and local minima avoidance, and its performance is statistically similar to SHADE and LSHADE-SPACMA.
Abstract: This paper presents a novel, optimization algorithm called Equilibrium Optimizer (EO), inspired by control volume mass balance models used to estimate both dynamic and equilibrium states. In EO, each particle (solution) with its concentration (position) acts as a search agent. The search agents randomly update their concentration with respect to best-so-far solutions, namely equilibrium candidates, to finally reach to the equilibrium state (optimal result). A well-defined “generation rate” term is proved to invigorate EO’s ability in exploration, exploitation, and local minima avoidance. The proposed algorithm is benchmarked with 58 unimodal, multimodal, and composition functions and three engineering application problems. Results of EO are compared to three categories of existing optimization methods, including: (i) the most well-known meta-heuristics, including Genetic Algorithm (GA), Particle Swarm Optimization (PSO); (ii) recently developed algorithms, including Grey Wolf Optimizer (GWO), Gravitational Search Algorithm (GSA), and Salp Swarm Algorithm (SSA); and (iii) high performance optimizers, including CMA-ES, SHADE, and LSHADE-SPACMA. Using average rank of Friedman test, for all 58 mathematical functions EO is able to outperform PSO, GWO, GA, GSA, SSA, and CMA-ES by 60%, 69%, 94%, 96%, 77%, and 64%, respectively, while it is outperformed by SHADE and LSHADE-SPACMA by 24% and 27%, respectively. The Bonferroni–Dunnand Holm’s tests for all functions showed that EO is significantly a better algorithm than PSO, GWO, GA, GSA, SSA and CMA-ES while its performance is statistically similar to SHADE and LSHADE-SPACMA. The source code of EO is publicly availabe at https://github.com/afshinfaramarzi/Equilibrium-Optimizer , http://built-envi.com/portfolio/equilibrium-optimizer/ and http://www.alimirjalili.com/SourceCodes/EOcode.zip .
1,085 citations
TL;DR: From the experimental results of AO that compared with well-known meta-heuristic methods, the superiority of the developed AO algorithm is observed.
989 citations
References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: This paper suggests a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties, and modify the definition of dominance in order to solve constrained multi-objective problems efficiently.
Abstract: Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN/sup 3/) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN/sup 2/) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed.
37,111 citations
TL;DR: In this article, a new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented, which requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
Abstract: A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
24,053 citations
04 Oct 1995
TL;DR: The optimization of nonlinear functions using particle swarm methodology is described and implementations of two paradigms are discussed and compared, including a recently developed locally oriented paradigm.
Abstract: The optimization of nonlinear functions using particle swarm methodology is described. Implementations of two paradigms are discussed and compared, including a recently developed locally oriented paradigm. Benchmark testing of both paradigms is described, and applications, including neural network training and robot task learning, are proposed. Relationships between particle swarm optimization and both artificial life and evolutionary computation are reviewed.
14,477 citations
"Salp Swarm Algorithm" refers methods in this paper
...Note that the maxi- um archive size for both MSSA and MOPSO are set to 100....
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...The results of MOPSO are very competitive and of ourse better than NSGA-II....
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...SSA outperorms other swarm-based techniques (e.g. PSO, FA , BA , etc.) due to igher exploration during optimization....
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...The results of MOPSO show that this algorithm only converge towards one region of the front and the coverage is low....
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...In PSO-based techniques, finding non-dominated solutions nd updating non-dominated solutions are easy but choosing one f them as the best solution ( gbest or pbest in PSO for instance) nd storing the most distributed ones are challenging [59,60] . any works have been done recently in this area....
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IBM1
TL;DR: A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving and a number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class.
Abstract: A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori "head-to-head" minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems' enforcing of a type of uniformity over all algorithms.
10,771 citations