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 .

Equilibrium optimizer: A novel optimization algorithm

This paper presents a nature-inspired metaheuristic called Marine Predators Algorithm (MPA) and its application in engineering. The main inspiration of MPA is the widespread foraging strategy namely Levy and Brownian movements in ocean predators along with optimal encounter rate policy in biological interaction between predator and prey. MPA follows the rules that naturally govern in optimal foraging strategy and encounters rate policy between predator and prey in marine ecosystems. This paper evaluates the MPA's performance on twenty-nine test functions, test suite of CEC-BC-2017, randomly generated landscape, three engineering benchmarks, and two real-world engineering design problems in the areas of ventilation and building energy performance. MPA is compared with three classes of existing optimization methods, including (1) GA and PSO as the most well-studied metaheuristics, (2) GSA, CS and SSA as almost recently developed algorithms and (3) CMA-ES, SHADE and LSHADE-cnEpSin as high performance optimizers and winners of IEEE CEC competition. Among all methods, MPA gained the second rank and demonstrated very competitive results compared to LSHADE-cnEpSin as the best performing method and one of the winners of CEC 2017 competition. The statistical post hoc analysis revealed that MPA can be nominated as a high-performance optimizer and is a significantly superior algorithm than GA, PSO, GSA, CS, SSA and CMA-ES while its performance is statistically similar to SHADE and LSHADE-cnEpSin. The source code is publicly available at: https://github.com/afshinfaramarzi/Marine-Predators-Algorithm, http://built-envi.com/portfolio/marine-predators-algorithm/, https://www.mathworks.com/matlabcentral/fileexchange/74578-marine-predators-algorithm-mpa, and http://www.alimirjalili.com/MPA.html.

Marine Predators Algorithm: A nature-inspired metaheuristic

In their original versions, nature-inspired search algorithms such as evolutionary algorithms and those based on swarm intelligence, lack a mechanism to deal with the constraints of a numerical optimization problem. Nowadays, however, there exists a considerable amount of research devoted to design techniques for handling constraints within a nature-inspired algorithm. This paper presents an analysis of the most relevant types of constraint-handling techniques that have been adopted with nature-inspired algorithms. From them, the most popular approaches are analyzed in more detail. For each of them, some representative instantiations are further discussed. In the last part of the paper, some of the future trends in the area, which have been only scarcely explored, are briefly discussed and then the conclusions of this paper are presented.

http://www.cs.cinvestav.mx/~constraint/papers/swevo-mezura.pdf

Constraint-Handling in Nature-Inspired Numerical Optimization: Past, Present and Future

Mixed variable structural optimization using Firefly Algorithm

In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.

Bat algorithm for constrained optimization tasks

A parameter-less adaptive penalty scheme for genetic algorithms applied to constrained optimization problems is proposed. Using feedback from the evolutionary process the procedure automatically defines a penalty parameter for each constraint. The user is thus relieved from the burden of having to determine sensitive parameter(s) when dealing with every new constrained optimization problem. The procedure is shown to be effective and robust when applied to test problems from the evolutionary computation literature as well as several optimization problems from the structural engineering literature. Copyright © 2003 John Wiley & Sons, Ltd.

An adaptive penalty scheme for genetic algorithms in structural optimization

A new adaptive penalty scheme for genetic algorithms

A parameter-less adaptive penalty scheme for genetic algorithms applied to constrained optimization problems is proposed. Besides being simple, adaptive and not requiring any parameter, it provides a different penalty parameter for each constraint. The performance of this new scheme is examined using several test-problems from the evolutionary computation literature.

An adaptive penalty scheme in genetic algorithms for constrained optimization problems

A genetic algorithm (GA) is hybridized with an artificial immune system (AIS) as an alternative to tackle constrained optimization problems in engineering. The AIS is inspired in the clonal selection principle and is embedded into a standard GA search engine in order to help move the population into the feasible region. The procedure is applied to mechanical engineering problems available in the literature and compared to other alternative techniques.

A hybrid genetic algorithm for constrained optimization problems in mechanical engineering

PURPOSE The biomechanical behavior of an osseointegrated dental implant plays an important role in its functional longevity inside the bone. Studies of this aspect of dental implants by the finite element method are ongoing. In the present study, a cuneiform-geometry implant was considered with a 3-dimensional model that had a mesh that was finer than in the models commonly found in the literature. MATERIALS AND METHODS A mechanical model of an edentulous mandible was generated from computerized tomography, with the implant placed in the left first premolar region. A 100-N axial load was applied at the implant abutment, and the mandibular boundary conditions were modeled considering the real geometry of its muscle supporting system. The cortical and trabecular bone was assumed to be homogeneous, isotropic, and linearly elastic. RESULTS The stress analysis provided results that were used to plot global and detailed graphics of normal maximum (S1), minimum (S3), and von Mises stress fields. The results obtained were analyzed and compared qualitatively with the literature. DISCUSSION Quantitative comparisons were not performed because of basic differences between the model adopted here and those used by other authors. The stress distribution pattern for the studied geometry was similar to those found in the current literature, but insignificant apical stress concentration occurred. The stress concentration occurred at the neck of the implant, ie, in the cortical bone, which was similar to results for other implant shapes reported in the literature. CONCLUSION The studied geometry showed a smooth stress pattern, with stress concentrated in the cervical region. The values, however, were within the range of values found in the cortical layer far from the implant, caused by the muscular action. No significant stress concentration was found in the apical area.

Afonso C. C. Lemonge

Papers

An adaptive penalty scheme for genetic algorithms in structural optimization

A new adaptive penalty scheme for genetic algorithms

An adaptive penalty scheme in genetic algorithms for constrained optimization problems

A hybrid genetic algorithm for constrained optimization problems in mechanical engineering

Three-dimensional finite element stress analysis of a cuneiform-geometry implant.