An evolutionary based framework for many-objective optimization problems

2018 ◽  
Vol 35 (4) ◽  
pp. 1805-1828 ◽  
Author(s):  
Kimia Bazargan Lari ◽  
Ali Hamzeh
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Fitness Function ◽  
Population Diversity ◽  
Numerical Results ◽  
Superior Performance ◽  
High Dimensional ◽  
Test Problems ◽  
Content Type ◽  
Objective Space

Purpose Recently, many-objective optimization evolutionary algorithms have been the main issue for researchers in the multi-objective optimization community. To deal with many-objective problems (typically for four or more objectives) some modern frameworks are proposed which have the potential of achieving the finest non-dominated solutions in many-objective spaces. The effectiveness of these algorithms deteriorates greatly as the problem’s dimension increases. Diversity reduction in the objective space is the main reason of this phenomenon. Design/methodology/approach To properly deal with this undesirable situation, this work introduces an indicator-based evolutionary framework that can preserve the population diversity by producing a set of discriminated solutions in high-dimensional objective space. This work attempts to diversify the objective space by proposing a fitness function capable of discriminating the chromosomes in high-dimensional space. The numerical results prove the potential of the proposed method, which had superior performance in most of test problems in comparison with state-of-the-art algorithms. Findings The achieved numerical results empirically prove the superiority of the proposed method to state-of-the-art counterparts in the most test problems of a known artificial benchmark. Originality/value This paper provides a new interpretation and important insights into the many-objective optimization realm by emphasizing on preserving the population diversity.

scholarly journals A Novel Angular-Guided Particle Swarm Optimizer for Many-Objective Optimization Problems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Fei Chen ◽  
Shuhuan Wu ◽  
Fang Liu ◽  
Junkai Ji ◽  
Qiuzhen Lin
Keyword(s):  
Optimization Problems ◽  
Particle Swarm ◽  
Superior Performance ◽  
Test Problems ◽  
Particle Swarm Optimizer ◽  
Search Intensity ◽  
External Archive ◽  
Objective Space ◽  
Update Strategy ◽  
Nondominated Sorting

Most multiobjective particle swarm optimizers (MOPSOs) often face the challenges of keeping diversity and achieving convergence on tackling many-objective optimization problems (MaOPs), as they usually use the nondominated sorting method or decomposition-based method to select the local or best particles, which is not so effective in high-dimensional objective space. To better solve MaOPs, this paper presents a novel angular-guided particle swarm optimizer (called AGPSO). A novel velocity update strategy is designed in AGPSO, which aims to enhance the search intensity around the particles selected based on their angular distances. Using an external archive, the local best particles are selected from the surrounding particles with the best convergence, while the global best particles are chosen from the top 20% particles with the better convergence among the entire particle swarm. Moreover, an angular-guided archive update strategy is proposed in AGPSO, which maintains a consistent population with balanceable convergence and diversity. To evaluate the performance of AGPSO, the WFG and MaF test suites with 5 to 10 objectives are adopted. The experimental results indicate that AGPSO shows the superior performance over four current MOPSOs (SMPSO, dMOPSO, NMPSO, and MaPSO) and four competitive evolutionary algorithms (VaEA, θ-DEA, MOEA\D-DD, and SPEA2-SDE), when solving most of the test problems used.

Plasma generation optimization: a new physically-based metaheuristic algorithm for solving constrained optimization problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ali Kaveh ◽  
Hossein Akbari ◽  
Seyed Milad Hosseini
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Optimization Methods ◽  
Test Problems ◽  
Metaheuristic Algorithm ◽  
Constrained Optimization Problems ◽  
Content Type ◽  
Plasma Generation ◽  
Physically Based

Purpose This paper aims to present a new physically inspired meta-heuristic algorithm, which is called Plasma Generation Optimization (PGO). To evaluate the performance and capability of the proposed method in comparison to other optimization methods, two sets of test problems consisting of 13 constrained benchmark functions and 6 benchmark trusses are investigated numerically. The results indicate that the performance of the proposed method is competitive with other considered state-of-the-art optimization methods. Design/methodology/approach In this paper, a new physically-based metaheuristic algorithm called plasma generation optimization (PGO) algorithm is developed for solving constrained optimization problems. PGO is a population-based optimizer inspired by the process of plasma generation. In the proposed algorithm, each agent is considered as an electron. Movement of electrons and changing their energy levels are based on simulating excitation, de-excitation and ionization processes occurring through the plasma generation. In the proposed PGO, the global optimum is obtained when plasma is generated with the highest degree of ionization. Findings A new physically-based metaheuristic algorithm called the PGO algorithm is developed that is inspired from the process of plasma generation. Originality/value The results indicate that the performance of the proposed method is competitive with other state-of-the-art methods.

scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

scholarly journals Investigation of Improved Cooperative Coevolution for Large-Scale Global Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 146
Author(s):  
Aleksei Vakhnin ◽  
Evgenii Sopov
Keyword(s):  
Global Optimization ◽  
Evolutionary Algorithms ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fixed Number ◽  
High Dimensional ◽  
Cooperative Coevolution ◽  
Large Scale Problems

Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

2021 ◽  
Vol 1 (2) ◽  
pp. 1-23
Author(s):  
Arkadiy Dushatskiy ◽  
Tanja Alderliesten ◽  
Peter A. N. Bosman
Keyword(s):  
Boolean Functions ◽  
Surrogate Model ◽  
Optimization Problems ◽  
State Of The Art ◽  
Fitness Function ◽  
Optimal Solution ◽  
Problem Structure ◽  
Novel Approach ◽  
Efficient Learning ◽  
Nk Landscapes

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k -bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O (ℓ log ℓ) function evaluations when the number of subfunctions is O (ℓ) and all subfunctions are k -bounded, outperforming all considered algorithms.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

A New Bio-Inspired Social Spider Algorithm

2021 ◽  
Vol 12 (1) ◽  
pp. 79-93
Author(s):  
Dharmpal Singh
Keyword(s):  
Swarm Intelligence ◽  
Real World ◽  
Optimization Problems ◽  
Fitness Function ◽  
Foraging Strategy ◽  
Superior Performance ◽  
Experimental Result ◽  
Social Spider ◽  
Spider Web ◽  
Social Spider Algorithm

The concept of bio-inspired algorithms is used in real-world problems to search the efficient problem-solving methods. Evolutionary computation and swarm intelligence are outstanding examples of nature-inspired solution techniques of metahuristics. In this paper, an effort has been made to propose a modified social spider algorithm to solve global optimization problems in the real world. Social spiders used the foraging strategy, vibrations on the spider web to determine the positions of prey. The selection of vibration, estimated new position and calculation of the fitness function, has been furnished in details way as compared to different previously proposed swarm intelligence algorithms. Moreover, experimental result has been carried out by modified social spider on series of widely-used benchmark problem with four benchmark algorithms. Furthermore, a modified form of the proposed algorithm has superior performance as compared to other state-of-the-art metaheuristics algorithms.

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

2019 ◽  
Vol 12 (3) ◽  
pp. 389-399
Author(s):  
Saman Babaie-Kafaki ◽  
Saeed Rezaee
Keyword(s):  
Simulated Annealing ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Content Type ◽  
Unconstrained Optimization Problems ◽  
Randomization Scheme ◽  
Enhance Efficiency

PurposeThe purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approachThe well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.FindingsAn adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implicationsThe algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.Originality/valueThe proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

Large-scale economic load dispatch using squirrel search algorithm

2020 ◽  
Vol 14 (6) ◽  
pp. 1351-1380
Author(s):  
Sakthivel V.P. ◽  
Suman M. ◽  
Sathya P.D.
Keyword(s):  
Power Plants ◽  
Large Scale ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Technique ◽  
Research Work ◽  
Superior Performance ◽  
Economic Load Dispatch ◽  
Fuel Cost ◽  
Content Type

Purpose Economic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants. Design/methodology/approach The suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately. Findings Empirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems. Practical implications This study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning. Originality/value To the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.

Multi-Operator Genetic Algorithm for Dynamic Optimization Problems

2017 ◽  
Vol 6 (3) ◽  
pp. 139
Author(s):  
Al-khafaji Amen
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Dynamic Optimization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Population Diversity ◽  
Dynamic Optimization Problems ◽  
Uncertain Environments ◽  
Convergence Problem ◽  
Royal Road

<span lang="EN-US">Maintaining population diversity is the most notable challenge in solving dynamic optimization problems (DOPs). Therefore, the objective of an efficient dynamic optimization algorithm is to track the optimum in these uncertain environments, and to locate the best solution. In this work, we propose a framework that is based on multi operators embedded in genetic algorithms (GA) and these operators are heuristic and arithmetic crossovers operators. The rationale behind this is to address the convergence problem and to maintain the diversity. The performance of the proposed framework is tested on the well-known dynamic optimization functions i.e., OneMax, Plateau, Royal Road and Deceptive. Empirical results show the superiority of the proposed algorithm when compared to state-of-the-art algorithms from the literature.</span>

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