AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems

2020 ◽  
Author(s):  
Victor Reyes ◽  
Ignacio Araya
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Continuous Global Optimization

scholarly journals A DE-Based Scatter Search for Global Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kun Li ◽  
Huixin Tian
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Scatter Search ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Candidate Mutation ◽  
Mutation Operators ◽  
Reference Set ◽  
Solution Generation ◽  
Continuous Global Optimization

This paper proposes a hybrid scatter search (SS) algorithm for continuous global optimization problems by incorporating the evolution mechanism of differential evolution (DE) into the reference set updated procedure of SS to act as the new solution generation method. This hybrid algorithm is called a DE-based SS (SSDE) algorithm. Since different kinds of mutation operators of DE have been proposed in the literature and they have shown different search abilities for different kinds of problems, four traditional mutation operators are adopted in the hybrid SSDE algorithm. To adaptively select the mutation operator that is most appropriate to the current problem, an adaptive mechanism for the candidate mutation operators is developed. In addition, to enhance the exploration ability of SSDE, a reinitialization method is adopted to create a new population and subsequently construct a new reference set whenever the search process of SSDE is trapped in local optimum. Computational experiments on benchmark problems show that the proposed SSDE is competitive or superior to some state-of-the-art algorithms in the literature.

scholarly journals Influence of a neighborhood shape on the efficiency of continuous variable neighborhood search

2020 ◽  
Vol 30 (1) ◽  
pp. 3-17
Author(s):  
Milan Drazic
Keyword(s):  
Global Optimization ◽  
Variable Neighborhood Search ◽  
Optimization Problems ◽  
Continuous Variable ◽  
Efficient Algorithms ◽  
Geometric Shape ◽  
Neighborhood Search ◽  
High Dimensional ◽  
Neighborhood Structures ◽  
Continuous Global Optimization

The efficiency of a Variable neighborhood search metaheuristic for continuous global optimization problems greatly depends on geometric shape of neighborhood structures used by the algorithm. Among the neighborhoods defined by balls in ?p, 1 ?p ? ? metric, we tested the ?1, ?2, and ?? ball shape neighborhoods, for which there exist efficient algorithms for obtaining uniformly distributed points. On many challenging high-dimensional problems, our exhaustive testings showed that, popular and the easiest for implementation, ?? ball shape of neighborhoods performed the worst, and much better efficiency was obtained with ?1 and ?2.

Convergence analysis of the plant propagation algorithm for continuous global optimization

2018 ◽  
Vol 52 (2) ◽  
pp. 429-438 ◽  
Author(s):  
Nassim Brahimi ◽  
Abdellah Salhi ◽  
Megdouda Ourbih-Tari
Keyword(s):  
Global Optimization ◽  
Convergence Analysis ◽  
Convergence Theorem ◽  
Optimization Problems ◽  
Stochastic Algorithm ◽  
Strawberry Plant ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Continuous Global Optimization ◽  
General Convergence

The Plant Propagation Algorithm (PPA) is a Nature-Inspired stochastic algorithm, which emulates the way plants, in particular the strawberry plant, propagate using runners. It has been experimentally tested both on unconstrained and constrained continuous global optimization problems and was found to be competitive against well established algorithms. This paper is concerned with its convergence analysis. It first puts forward a general convergence theorem for a large class of random algorithms, before the PPA convergence theorem is derived and proved. It then illustrates the results on simple problems.

Constraint Importance Mode Pursuing Sampling for Continuous Global Optimization

2010 ◽  
Author(s):  
Moslem Kazemi ◽  
G. Gary Wang ◽  
Shahryar Rahnamayan ◽  
Kamal Gupta
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Sampling Technique ◽  
Search Space ◽  
Optimization Method ◽  
Mps Method ◽  
Engineering Design Problems ◽  
Forbidden Regions ◽  
Sample Points ◽  
Continuous Global Optimization

Many engineering design problems deal with global optimization of constrained black-box problems which is usually computation-intensive. Ref. [1] proposed a Mode-Pursuing Sampling (MPS) method for global optimization based on a sampling technique which systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire problem domain. In this paper, we propose a novel and more efficient sampling technique which greatly enhances the performance of the MPS method, especially in the presence of expensive constraints. The effective sampling of the search space is attained via biasing the sample points towards feasible regions and being away from the forbidden regions. This is achieved by utilizing the incrementally obtained information about the constraints, hence, it is called Constraint-importance Mode Pursuing Sampling (CiMPS). According to intensive comparisons and experimental verifications, the new sampling technique is found to be more efficient in solving constrained optimization problems compared to the original MPS method. To the best of our knowledge, this is the first metamodel-based global optimization method that directly aims at reducing the number of function evaluations for both expensive objective functions and constraints.

Convergence of taboo search in continuous global optimization

2006 ◽  
Vol 462 (2071) ◽  
pp. 2077-2084 ◽  
Author(s):  
Mingjun Ji ◽  
Jacek Klinowski
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Convergence Properties ◽  
Taboo Search ◽  
Optimal Value ◽  
Global Optimal ◽  
Objective Value ◽  
Continuous Global Optimization ◽  
Continuous Optimization Problems

While taboo search (TS), a method of global optimization, has successfully solved many optimization problems, little is known about its convergence properties, especially for continuous optimization tasks. We consider the global convergence of the original TS for solving continuous optimization problems, and give a condition which guarantees the convergence of the objective value sequence of the method. We also prove that the minimum objective value sequence converges to the vicinity of the global optimal value with probability 1.

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