scholarly journals A Hybrid Estimation of Distribution Algorithm and Nelder-Mead Simplex Method for Solving a Class of Nonlinear Bilevel Programming Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Aihong Ren ◽  
Yuping Wang ◽  
Fei Jia
Keyword(s):  
Bilevel Programming ◽  
Simplex Method ◽  
Hybrid Algorithm ◽  
Fitness Function ◽  
Optimal Solution ◽  
Estimation Of Distribution Algorithm ◽  
Test Problems ◽  
Estimation Of Distribution ◽  
Bilevel Programming Problems ◽  
Level Variable

We propose a hybrid algorithm based on estimation of distribution algorithm (EDA) and Nelder-Mead simplex method (NM) to solve a class of nonlinear bilevel programming problems where the follower’s problem is linear with respect to the lower level variable. The bilevel programming is an NP-hard optimization problem, for which EDA-NM is applied as a new tool aiming at obtaining global optimal solutions of such a problem. In fact, EDA-NM is very easy to be implementedsince it does not require gradients information. Moreover, the hybrid algorithm intends to produce faster and more accurate convergence. In the proposed approach, for fixed upper level variable, we make use of the optimality conditions of linear programming to deal with the follower’s problem and obtain its optimal solution. Further, the leader’s objective function is taken as the fitness function. Based on these schemes, the hybrid algorithm is designed by combining EDA with NM. To verify the performance of EDA-NM, simulations on some test problems are made, and the results demonstrate that the proposed algorithm has a better performance than the compared algorithms. Finally, the proposed approach is used to solve a practical example about pollution charges problem.

An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

2010 ◽  
Vol 18 (3) ◽  
pp. 403-449 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ankur Sinha
Keyword(s):  
Problem Solving ◽  
Local Search ◽  
Bilevel Programming ◽  
Optimization Problem ◽  
Practical Importance ◽  
Test Problems ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Bilevel Programming Problems ◽  
Solution Methodology

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

scholarly journals Fast Image Segmentation Using Two-Dimensional Otsu Based on Estimation of Distribution Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Wuli Wang ◽  
Liming Duan ◽  
Yong Wang
Keyword(s):  
Image Segmentation ◽  
Fitness Function ◽  
Probability Model ◽  
Computational Cost ◽  
Estimation Of Distribution Algorithm ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Guided Filtering ◽  
Estimation Of Distribution ◽  
Mean Filtering

Traditional two-dimensional Otsu algorithm has several drawbacks; that is, the sum of probabilities of target and background is approximate to 1 inaccurately, the details of neighborhood image are not obvious, and the computational cost is high. In order to address these problems, a method of fast image segmentation using two-dimensional Otsu based on estimation of distribution algorithm is proposed. Firstly, in order to enhance the performance of image segmentation, the guided filtering is employed to improve neighborhood image template instead of mean filtering. Additionally, the probabilities of target and background in two-dimensional histogram are exactly calculated to get more accurate threshold. Finally, the trace of the interclass dispersion matrix is taken as the fitness function of estimation of distributed algorithm, and the optimal threshold is obtained by constructing and sampling the probability model. Extensive experimental results demonstrate that our method can effectively preserve details of the target, improve the segmentation precision, and reduce the running time of algorithms.

scholarly journals Estimation of Distribution Algorithm Using Correlation between Binary Elements: A New Binary-Code Metaheuristic

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Nantiwat Pholdee ◽  
Sujin Bureerat
Keyword(s):  
Flight Control ◽  
Binary Code ◽  
Marginal Distribution ◽  
Population Based ◽  
Estimation Of Distribution Algorithm ◽  
Design Solution ◽  
Test Problems ◽  
Real World Application ◽  
Estimation Of Distribution ◽  
Comparative Results

A new metaheuristic called estimation of distribution algorithm using correlation between binary elements (EDACE) is proposed. The method searches for optima using a binary string to represent a design solution. A matrix for correlation between binary elements of a design solution is used to represent a binary population. Optimisation search is achieved by iteratively updating such a matrix. The performance assessment is conducted by comparing the new algorithm with existing binary-code metaheuristics including a genetic algorithm, a univariate marginal distribution algorithm, population-based incremental learning, binary particle swarm optimisation, and binary simulated annealing by using the test problems of CEC2015 competition and one real-world application which is an optimal flight control problem. The comparative results show that the new algorithm is competitive with other established binary-code metaheuristics.

scholarly journals Multiobjective Memetic Estimation of Distribution Algorithm Based on an Incremental Tournament Local Searcher

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Kaifeng Yang ◽  
Li Mu ◽  
Dongdong Yang ◽  
Feng Zou ◽  
Lei Wang ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Estimation Of Distribution Algorithm ◽  
Distribution Model ◽  
Test Problems ◽  
Multiobjective Problems ◽  
Estimation Of Distribution ◽  
Distributed Solutions ◽  
Accelerate Convergence ◽  
Low Dimensional

A novel hybrid multiobjective algorithm is presented in this paper, which combines a new multiobjective estimation of distribution algorithm, an efficient local searcher andε-dominance. Besides, two multiobjective problems with variable linkages strictly based on manifold distribution are proposed. The Pareto set to the continuous multiobjective optimization problems, in the decision space, is a piecewise low-dimensional continuous manifold. The regularity by the manifold features just build probability distribution model by globally statistical information from the population, yet, the efficiency of promising individuals is not well exploited, which is not beneficial to search and optimization process. Hereby, an incremental tournament local searcher is designed to exploit local information efficiently and accelerate convergence to the true Pareto-optimal front. Besides, sinceε-dominance is a strategy that can make multiobjective algorithm gain well distributed solutions and has low computational complexity,ε-dominance and the incremental tournament local searcher are combined here. The novel memetic multiobjective estimation of distribution algorithm, MMEDA, was proposed accordingly. The algorithm is validated by experiment on twenty-two test problems with and without variable linkages of diverse complexities. Compared with three state-of-the-art multiobjective optimization algorithms, our algorithm achieves comparable results in terms of convergence and diversity metrics.

scholarly journals Software Defect Prediction Based on Hybrid Swarm Intelligence and Deep Learning

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Zhen Li ◽  
Tong Li ◽  
YuMei Wu ◽  
Liu Yang ◽  
Hong Miao ◽  
...  
Keyword(s):  
Deep Learning ◽  
Swarm Intelligence ◽  
Hybrid Algorithm ◽  
Fitness Function ◽  
Optimal Solution ◽  
Particle Swarm Algorithm ◽  
Hybrid Swarm ◽  
Hyperparameter Optimization ◽  
Advantages And Disadvantages ◽  
Swarm Algorithm

In order to improve software quality and testing efficiency, this paper implements the prediction of software defects based on deep learning. According to the respective advantages and disadvantages of the particle swarm algorithm and the wolf swarm algorithm, the two algorithms are mixed to realize the complementary advantages of the algorithms. At the same time, the hybrid algorithm is used in the search of model hyperparameter optimization, the loss function of the model is used as the fitness function, and the collaborative search ability of the swarm intelligence population is used to find the global optimal solution in multiple local solution spaces. Through the analysis of the experimental results of six data sets, compared with the traditional hyperparameter optimization method and a single swarm intelligence algorithm, the model using the hybrid algorithm has higher and better indicators. And, under the processing of the autoencoder, the performance of the model has been further improved.

AN EFFICIENT AND PRACTICALLY ROBUST HYBRID METAHEURISTIC ALGORITHM FOR SOLVING FUZZY BUS TERMINAL LOCATION PROBLEMS

2012 ◽  
Vol 29 (02) ◽  
pp. 1250009 ◽  
Author(s):  
SAMAN BABAIE-KAFAKI ◽  
REZA GHANBARI ◽  
NEZAM MAHDAVI-AMIRI
Keyword(s):  
Public Transportation ◽  
Hybrid Algorithm ◽  
Large Scale ◽  
Optimal Solution ◽  
Neighborhood Search ◽  
Test Problems ◽  
Nonparametric Statistical Test ◽  
Scale Test ◽  
Nonparametric Statistical ◽  
Fuzzy Parameters

Bus network design is an important problem in public transportation. In practice, some parameters of this problem are uncertain. We propose two models for the bus terminal location problem with fuzzy parameters. In the first formulation, the number of passengers corresponding to each node is a fuzzy number. In the second formulation, an additional assumption of fuzzy neighborhood is considered. These problems being NP-hard, we use a genetic algorithm (GA) and a simulated annealing (SA) algorithm for solving them. We also propose an idea to hybridize these algorithms. In our hybrid algorithm, SA is applied as a neighborhood search procedure of GA on the best individual of the population, which is the best available approximation of the optimal solution, with a varying probability that is gradually increased with the increase in the number of iterations in GA. We then implement GA, SA, our hybrid algorithm, and a recently proposed hybrid algorithm making use of a constant probability for application of SA on all the individuals of the population of GA, and use a nonparametric statistical test to compare their performances on a collection of randomly generated medium to large-scale test problems. Results of computational experiments demonstrating the efficiency and practicability of our proposed algorithm are reported.

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