scholarly journals On Local Convergence of Stochastic Global Optimization Algorithms

2021 ◽  
pp. 456-472
Author(s):  
Eligius M. T. Hendrix ◽  
Ana Maria A. C. Rocha
Keyword(s):  
Global Optimization ◽  
Local Search ◽  
Minimum Point ◽  
Convergence Criterion ◽  
Continuous Variables ◽  
Local Optima ◽  
Stochastic Global Optimization ◽  
Global Behaviour ◽  
Objective Function Values ◽  
Global And Local

AbstractIn engineering optimization with continuous variables, the use of Stochastic Global Optimization (SGO) algorithms is popular due to the easy availability of codes. All algorithms have a global and local search character, where the global behaviour tries to avoid getting trapped in local optima and the local behaviour intends to reach the lowest objective function values. As the algorithm parameter set includes a final convergence criterion, the algorithm might be running for a while around a reached minimum point. Our question deals with the local search behaviour after the algorithm reached the final stage. How fast do practical SGO algorithms actually converge to the minimum point? To investigate this question, we run implementations of well known SGO algorithms in a final local phase stage.

scholarly journals Delayed improvement local search

2021 ◽  
Author(s):  
Heber F. Amaral ◽  
Sebastián Urrutia ◽  
Lars M. Hvattum
Keyword(s):  
Local Search ◽  
Heuristic Algorithms ◽  
Travelling Salesman Problem ◽  
Computation Time ◽  
The Novel ◽  
Local Optima ◽  
New Strategy ◽  
Max Cut Problem ◽  
Novel Method ◽  
Similar Solutions

AbstractLocal search is a fundamental tool in the development of heuristic algorithms. A neighborhood operator takes a current solution and returns a set of similar solutions, denoted as neighbors. In best improvement local search, the best of the neighboring solutions replaces the current solution in each iteration. On the other hand, in first improvement local search, the neighborhood is only explored until any improving solution is found, which then replaces the current solution. In this work we propose a new strategy for local search that attempts to avoid low-quality local optima by selecting in each iteration the improving neighbor that has the fewest possible attributes in common with local optima. To this end, it uses inequalities previously used as optimality cuts in the context of integer linear programming. The novel method, referred to as delayed improvement local search, is implemented and evaluated using the travelling salesman problem with the 2-opt neighborhood and the max-cut problem with the 1-flip neighborhood as test cases. Computational results show that the new strategy, while slower, obtains better local optima compared to the traditional local search strategies. The comparison is favourable to the new strategy in experiments with fixed computation time or with a fixed target.

On hybridization of stochastic global optimization algorithms taking into account the features of their architecture

2021 ◽  
Vol 1 ◽  
pp. 113-117
Author(s):  
Dmitry Syedin ◽  
Keyword(s):  
Global Optimization ◽  
Stochastic Optimization ◽  
Optimization Algorithms ◽  
Stochastic Global Optimization ◽  
Stochastic Optimization Algorithms ◽  
Pca Algorithm

The work is devoted to the hybridization of stochastic global optimization algorithms depending on their architecture. The main methods of hybridization of stochastic optimization algorithms are listed. An example of hybridization of the algorithm is given, the modification of which became possible due to taking into account the characteristic architecture of the M-PCA algorithm.

Identification of the Optimal Product Configuration and Parameters for Improving Manufacturability

1996 ◽  
Author(s):  
Deyi Xue
Keyword(s):  
Global Optimization ◽  
Optimization Methods ◽  
Product Configuration ◽  
Design System ◽  
Optimization Approach ◽  
Continuous Variables ◽  
Integer Variables ◽  
System A ◽  
Global Optimization Methods

Abstract A global optimization approach for identifying the optimal product configuration and parameters is proposed to improve manufacturability measures including feasibility, cost, and time of production. Different product configurations, including alternative design candidates and production processes, are represented by an AND/OR graph. Product parameters are described by variables including continuous variables, integer variables, Boolean variables, and discrete variables. Two global optimization methods, genetic algorithm and simulated annealing, are employed for identifying the optimal product configuration and parameters. The introduced approach serves as a key component in an integrated concurrent design system. A case study example is given to show how the proposed method is used for solving the engineering problems.

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