scholarly journals MEEF: A Minimum-Elimination-Escape Function Method for Multimodal Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Lei Fan ◽  
Yuping Wang ◽  
Xiyang Liu ◽  
Liping Jia
Keyword(s):  
Function Method ◽  
Optimization Problems ◽  
Auxiliary Function ◽  
Local Optimum ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Mexican Hat ◽  
Global Optimal ◽  
Elimination Function ◽  
Made In

Auxiliary function methods provide us effective and practical ideas to solve multimodal optimization problems. However, improper parameter settings often cause troublesome effects which might lead to the failure of finding global optimal solutions. In this paper, a minimum-elimination-escape function method is proposed for multimodal optimization problems, aiming at avoiding the troublesome “Mexican hat” effect and reducing the influence of local optimal solutions. In the proposed method, the minimum-elimination function is constructed to decrease the number of local optimum first. Then, a minimum-escape function is proposed based on the minimum-elimination function, in which the current minimal solution will be converted to the unique global maximal solution of the minimum-escape function. The minimum-escape function is insensitive to its unique but easy to adopt parameter. At last, an minimum-elimination-escape function method is designed based on these two functions. Experiments on 19 widely used benchmarks are made, in which influences of the parameter and different initial points are analyzed. Comparisons with 11 existing methods indicate that the performance of the proposed algorithm is positive and effective.

Adaptive Grouping Brain Storm Optimization for Multimodal Optimization Problems

2021 ◽  
Vol 12 (4) ◽  
pp. 81-100
Author(s):  
Yao Peng ◽  
Zepeng Shen ◽  
Shiqi Wang
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Algorithm ◽  
Peak Detection ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Grouping Strategy ◽  
Different Dimensions ◽  
Global Optimal ◽  
Localization Ability

Multimodal optimization problem exists in multiple global and many local optimal solutions. The difficulty of solving these problems is finding as many local optimal peaks as possible on the premise of ensuring global optimal precision. This article presents adaptive grouping brainstorm optimization (AGBSO) for solving these problems. In this article, adaptive grouping strategy is proposed for achieving adaptive grouping without providing any prior knowledge by users. For enhancing the diversity and accuracy of the optimal algorithm, elite reservation strategy is proposed to put central particles into an elite pool, and peak detection strategy is proposed to delete particles far from optimal peaks in the elite pool. Finally, this article uses testing functions with different dimensions to compare the convergence, accuracy, and diversity of AGBSO with BSO. Experiments verify that AGBSO has great localization ability for local optimal solutions while ensuring the accuracy of the global optimal solutions.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

Hypercube-Based Crowding Differential Evolution with Neighborhood Mutation for Multimodal Optimization

2018 ◽  
Vol 9 (2) ◽  
pp. 15-27
Author(s):  
Haihuang Huang ◽  
Liwei Jiang ◽  
Xue Yu ◽  
Dongqing Xie
Keyword(s):  
Differential Evolution ◽  
Euclidean Distance ◽  
Optimization Problems ◽  
Random Search ◽  
Adaptive Method ◽  
Radius Vector ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Reasonable Range ◽  
Neighborhood Mutation

In reality, multiple optimal solutions are often necessary to provide alternative options in different occasions. Thus, multimodal optimization is important as well as challenging to find multiple optimal solutions of a given objective function simultaneously. For solving multimodal optimization problems, various differential evolution (DE) algorithms with niching and neighborhood strategies have been developed. In this article, a hypercube-based crowding DE with neighborhood mutation is proposed for such problems as well. It is characterized by the use of hypercube-based neighborhoods instead of Euclidean-distance-based neighborhoods or other simpler neighborhoods. Moreover, a self-adaptive method is additionally adopted to control the radius vector of a hypercube so as to guarantee the neighborhood size always in a reasonable range. In this way, the algorithm will perform a more accurate search in the sub-regions with dense individuals, but perform a random search in the sub-regions with only sparse individuals. Experiments are conducted in comparison with an outstanding DE with neighborhood mutation, namely NCDE. The results show that the proposed algorithm is promising and computationally inexpensive.

An Adaptive Penalty Function Method for Constrained Optimization with Evolutionary Programming

2000 ◽  
Vol 4 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Baolin Wu
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Optimization Problems ◽  
Evolutionary Programming ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Penalty Function Method ◽  
Adaptive Penalty ◽  
Adaptive Penalty Function

In this paper, we propose a novel adaptive penalty function method for constrained optimization problems using the evolutionary programming technique. This method incorporates an adaptive tuning algorithm that adjusts the penalty parameters according to the population landscape so that it allows fast escape from a local optimum and quick convergence toward a global optimum. The method is simple and computationally effective in the sense that only very few penalty parameters are needed for tuning. Simulation results of five well-known benchmark problems are presented to show the performance of the proposed method.

scholarly journals A bridging method for global optimization

1999 ◽  
Vol 41 (1) ◽  
pp. 41-57 ◽  
Author(s):  
Y. Liu ◽  
K. L. Teo
Keyword(s):  
Global Optimization ◽  
Differentiable Function ◽  
Numerical Solutions ◽  
Finite Interval ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Differentiable Functions ◽  
Global Optimal

AbstractIn this paper a bridging method is introduced for numerical solutions of one-dimensional global optimization problems where a continuously differentiable function is to be minimized over a finite interval which can be given either explicitly or by constraints involving continuously differentiable functions. The concept of a bridged function is introduced. Some properties of the bridged function are given. On this basis, several bridging algorithm are developed for the computation of global optimal solutions. The algorithms are demonstrated by solving several numerical examples.

scholarly journals Solving Bi-Matrix Games Based on Fuzzy Payoffs via Utilizing the Interval Value Function Method

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 469
Author(s):  
Kaisheng Liu ◽  
Yumei Xing
Keyword(s):  
Nonlinear Optimization ◽  
Function Method ◽  
Value Function ◽  
Optimization Problems ◽  
Game Model ◽  
Optimal Solutions ◽  
Equilibrium Solutions ◽  
Matrix Games ◽  
Interval Value

In this article, we introduce a model of bi-matrix games based on crisp parametric payoffs via utilizing the method of interval value function. Then, we get that equilibrium solutions of bi-matrix games on the basis of fuzzy payoffs and equilibrium solutions of the game model are of equal value. Furthermore, it is concluded that equilibrium solutions of the game can be converted to optimal solutions of discrete nonlinear optimization problems with parameters. Lastly, the proposed methodology is illustrated by an example.

Artificial Intelligence Application in Modern Management

2010 ◽  
Vol 37-38 ◽  
pp. 203-206
Author(s):  
Rong Jiang
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Local Optimum ◽  
Efficient Operation ◽  
Modern Management ◽  
Global Optimal ◽  
Annealing Algorithm

Modern management is a science of technology that adopts analysis, test and quantification methods to make a comprehensive arrangement of the limited resources to realize an efficient operation of a practical system. Simulated annealing algorithm has become one of the important tools for solving complex optimization problems, because of its intelligence, widely used and global search ability. Genetic algorithm may prevent effectively searching process from restraining in local optimum, thus it is more possible to obtains the global optimal solution.This paper solves unconstrained programming by simulated annealing algorithm and calculates constrained nonlinear programming by genetic algorithm in modern management. So that optimization process was simplified and the global optimal solution is ensured reliably.

Multimodal Optimization Using a Bi-Objective Evolutionary Algorithm

2012 ◽  
Vol 20 (1) ◽  
pp. 27-62 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Amit Saha
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Space ◽  
Test Problems ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Optimization Task ◽  
Pareto Optimal Set ◽  
Single Objective

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly due to their ability to find and capture multiple solutions within a population in a single simulation run. With the preselection method suggested in 1970, there has been a steady suggestion of new algorithms. Most of these methodologies employed a niching scheme in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are deemphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different strategy in which the single-objective multimodal optimization problem is converted into a suitable bi-objective optimization problem so that all optimal solutions become members of the resulting weak Pareto-optimal set. With the modified definitions of domination and different formulations of an artificially created additional objective function, we present successful results on problems with as large as 500 optima. Most past multimodal EA studies considered problems having only a few variables. In this paper, we have solved up to 16-variable test problems having as many as 48 optimal solutions and for the first time suggested multimodal constrained test problems which are scalable in terms of number of optima, constraints, and variables. The concept of using bi-objective optimization for solving single-objective multimodal optimization problems seems novel and interesting, and more importantly opens up further avenues for research and application.

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