Multistage Global Search Using Various Scalarization Schemes in Multicriteria Optimization Problems

2019 ◽  
pp. 638-648 ◽  
Author(s):  
Victor Gergel ◽  
Evgeniy Kozinov
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Problems ◽  
Global Search

Assessing the performances of recent global search algorithms using analytic objective functions and seismic optimization problems

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R767-R781 ◽  
Author(s):  
Mattia Aleardi ◽  
Silvio Pierini ◽  
Angelo Sajeva
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Model Space ◽  
Global Search ◽  
Objective Functions ◽  
Swarm Optimization ◽  
Fireworks Algorithm ◽  
Highly Nonlinear ◽  
Whale Optimization

We have compared the performances of six recently developed global optimization algorithms: imperialist competitive algorithm, firefly algorithm (FA), water cycle algorithm (WCA), whale optimization algorithm (WOA), fireworks algorithm (FWA), and quantum particle swarm optimization (QPSO). These methods have been introduced in the past few years and have found very limited or no applications to geophysical exploration problems thus far. We benchmark the algorithms’ results against the particle swarm optimization (PSO), which is a popular and well-established global search method. In particular, we are interested in assessing the exploration and exploitation capabilities of each method as the dimension of the model space increases. First, we test the different algorithms on two multiminima and two convex analytic objective functions. Then, we compare them using the residual statics corrections and 1D elastic full-waveform inversion, which are highly nonlinear geophysical optimization problems. Our results demonstrate that FA, FWA, and WOA are characterized by optimal exploration capabilities because they outperform the other approaches in the case of optimization problems with multiminima objective functions. Differently, QPSO and PSO have good exploitation capabilities because they easily solve ill-conditioned optimizations characterized by a nearly flat valley in the objective function. QPSO, PSO, and WCA offer a good compromise between exploitation and exploration.

scholarly journals Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

2021 ◽  
Author(s):  
Shufen Qin ◽  
Chan Li ◽  
Chaoli Sun ◽  
Guochen Zhang ◽  
Xiaobo Li
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Search ◽  
Model Management ◽  
The Other ◽  
Local Searches ◽  
Fitness Value ◽  
Expensive Problems ◽  
Computationally Expensive

AbstractSurrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

Optimization Problem

2020 ◽  
pp. 276-291
Author(s):  
Albert N. Voronin
Keyword(s):  
Wide Class ◽  
Multicriteria Optimization ◽  
System Approach ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Systemic Approach ◽  
Multicriteria Decision ◽  
Multicriteria Problems ◽  
Linear Scheme ◽  
Non Linear

A systemic approach to solving multicriteria optimization problems is proposed. The system approach allowed uniting the models of individual schemes of compromises into a single integrated structure that adapts to the situation of adopting a multi-criteria solution. The advantage of the concept of non-linear scheme of compromises is the possibility of making a multicriteria decision formally, without the direct participation of a person. The apparatus of the non-linear scheme of compromises, developed as a formalized tool for the study of control systems with conflicting criteria, makes it possible to solve practically multicriteria problems of a wide class.

Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables

2009 ◽  
Vol 71 (12) ◽  
pp. e109-e117 ◽  
Author(s):  
Roman Statnikov ◽  
Alex Bordetsky ◽  
Josef Matusov ◽  
Il’ya Sobol’ ◽  
Alexander Statnikov
Keyword(s):  
Multicriteria Optimization ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Solution Set ◽  
Mixed Design ◽  
Design Variables ◽  
Definition Of ◽  
Mixed Design Variables

scholarly journals Improvement Analysis and Application of Real-Coded Genetic Algorithm for Solving Constrained Optimization Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Jiquan Wang ◽  
Zhiwen Cheng ◽  
Okan K. Ersoy ◽  
Panli Zhang ◽  
Weiting Dai ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Local Search ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Global Search ◽  
Single Mutation ◽  
Constrained Optimization Problems ◽  
Fitness Value ◽  
Steering Mechanism ◽  
Real Coded Genetic Algorithm

An improved real-coded genetic algorithm (IRCGA) is proposed to solve constrained optimization problems. First, a sorting grouping selection method is given with the advantage of easy realization and not needing to calculate the fitness value. Secondly, a heuristic normal distribution crossover (HNDX) operator is proposed. It can guarantee the cross-generated offsprings to locate closer to the better one among the two parents and the crossover direction to be very close to the optimal crossover direction or to be consistent with the optimal crossover direction. In this way, HNDX can ensure that there is a great chance of generating better offsprings. Thirdly, since the GA in the existing literature has many iterations, the same individuals are likely to appear in the population, thereby making the diversity of the population worse. In IRCGA, substitution operation is added after the crossover operation so that the population does not have the same individuals, and the diversity of the population is rich, thereby helping avoid premature convergence. Finally, aiming at the shortcoming of a single mutation operator which cannot simultaneously take into account local search and global search, this paper proposes a combinational mutation method, which makes the mutation operation take into account both local search and global search. The computational results with nine examples show that the IRCGA has fast convergence speed. As an example application, the optimization model of the steering mechanism of vehicles is formulated and the IRCGA is used to optimize the parameters of the steering trapezoidal mechanism of three vehicle types, with better results than the other methods used.

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