scholarly journals Solving Constrained Global Optimization Problems by Using Hybrid Evolutionary Computing and Artificial Life Approaches

2012 ◽  
Vol 2012 ◽  
pp. 1-36 ◽  
Author(s):  
Jui-Yu Wu
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Pso Algorithm ◽  
Global Optimum ◽  
Constrained Global Optimization ◽  
Generalized Polynomial ◽  
Real Coded Genetic Algorithm ◽  
Constriction Coefficient ◽  
Optimum Solution

This work presents a hybrid real-coded genetic algorithm with a particle swarm optimization (RGA-PSO) algorithm and a hybrid artificial immune algorithm with a PSO (AIA-PSO) algorithm for solving 13 constrained global optimization (CGO) problems, including six nonlinear programming and seven generalized polynomial programming optimization problems. External RGA and AIA approaches are used to optimize the constriction coefficient, cognitive parameter, social parameter, penalty parameter, and mutation probability of an internal PSO algorithm. CGO problems are then solved using the internal PSO algorithm. The performances of the proposed RGA-PSO and AIA-PSO algorithms are evaluated using 13 CGO problems. Moreover, numerical results obtained using the proposed RGA-PSO and AIA-PSO algorithms are compared with those obtained using published individual GA and AIA approaches. Experimental results indicate that the proposed RGA-PSO and AIA-PSO algorithms converge to a global optimum solution to a CGO problem. Furthermore, the optimum parameter settings of the internal PSO algorithm can be obtained using the external RGA and AIA approaches. Also, the proposed RGA-PSO and AIA-PSO algorithms outperform some published individual GA and AIA approaches. Therefore, the proposed RGA-PSO and AIA-PSO algorithms are highly promising stochastic global optimization methods for solving CGO problems.

scholarly journals Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Jui-Yu Wu
Keyword(s):  
Global Optimization ◽  
Swarm Intelligence ◽  
Optimization Problems ◽  
Pso Algorithm ◽  
Hybrid Swarm ◽  
Real Coded Genetic Algorithm ◽  
And Performance ◽  
Constriction Coefficient ◽  
Nonlinear Programming Methods ◽  
Algorithm Implementation

Stochastic global optimization (SGO) algorithms such as the particle swarm optimization (PSO) approach have become popular for solving unconstrained global optimization (UGO) problems. The PSO approach, which belongs to the swarm intelligence domain, does not require gradient information, enabling it to overcome this limitation of traditional nonlinear programming methods. Unfortunately, PSO algorithm implementation and performance depend on several parameters, such as cognitive parameter, social parameter, and constriction coefficient. These parameters are tuned by using trial and error. To reduce the parametrization of a PSO method, this work presents two efficient hybrid SGO approaches, namely, a real-coded genetic algorithm-based PSO (RGA-PSO) method and an artificial immune algorithm-based PSO (AIA-PSO) method. The specific parameters of the internal PSO algorithm are optimized using the external RGA and AIA approaches, and then the internal PSO algorithm is applied to solve UGO problems. The performances of the proposed RGA-PSO and AIA-PSO algorithms are then evaluated using a set of benchmark UGO problems. Numerical results indicate that, besides their ability to converge to a global minimum for each test UGO problem, the proposed RGA-PSO and AIA-PSO algorithms outperform many hybrid SGO algorithms. Thus, the RGA-PSO and AIA-PSO approaches can be considered alternative SGO approaches for solving standard-dimensional UGO problems.

A New Global Optimization Method for Simultaneous Computation on Expensive Black-Box Functions

2003 ◽  
Author(s):  
Liqun Wang ◽  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Global Optimum ◽  
Black Box ◽  
Efficient Global Optimization ◽  
Global Optimization Method ◽  
Global Optimization Methods

The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This work proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling (MPS) method which systematically generates more sample points in the neighborhood of the function mode while statistically covers the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitation of the method is also identified and discussed.

scholarly journals SOLVING THE NONLINEAR TRANSPORTATION PROBLEM BY GLOBAL OPTIMIZATION

Transport ◽  
2010 ◽  
Vol 25 (3) ◽  
pp. 314-324 ◽  
Author(s):  
Uroš Klanšek ◽  
Mirko Pšunder
Keyword(s):  
Global Optimization ◽  
Transportation Problem ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Branch And Cut ◽  
Cut Method ◽  
Global Optimization Methods ◽  
Optimum Solution ◽  
Global And Local ◽  
Branch And Cut Method

The aim of this paper is to present the suitability of three different global optimization methods for specifically the exact optimum solution of the nonlinear transportation problem (NTP). The evaluated global optimization methods include the branch and reduce method, the branch and cut method and the combination of global and local search strategies. The considered global optimization methods were applied to solve NTPs with reference to literature. NTPs were formulated as nonlinear programming (NLP) optimization problems. The obtained optimal results were compared with those got from literature. A comparative evaluation of global optimization methods is presented at the end of the paper to show their suitability for solving NTPs.

scholarly journals APPLICATION OF HYBRID RANDOM SEARCH METHOD TO OPTIMISATION OF ENGINEERING SYSTEMS’ PARAMETERS

2018 ◽  
Vol 21 (3) ◽  
pp. 139-149
Author(s):  
A. V. Panteleev ◽  
D. A. Rodionova
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Random Search ◽  
Operating Time ◽  
Optimization Methods ◽  
Search Method ◽  
Function Optimization ◽  
Constrained Global Optimization ◽  
Engineering Systems ◽  
Random Search Method

This paper presents a modification of the Luus-Jaakola global optimization method, which belongs to the class of metaheuristic algorithms. A hybrid method is suggested, using a combination of random search methods: Luus-Jaakola method, adaptive random search method and best trial method. The obtained method is applied to the optimization of parameters of different engineering systems. This class of problems appears during the design of aerospace and aeronautical structures; its goal is the cost or weight minimization of the construction. These problems belong to the class of constrained global optimization problems, where the level surface of the objective function has uneven relief and there is a large number of variables. This means that the classical optimization methods prove to be inefficient and these problems should be solved using metaheuristic optimization methods, which provide sufficient accuracy at reasonable operating time. In this paper, the constrained global optimization problem is solved using the penalty method. Thus, the problem of exterior penalty function optimization is considered, where the penalty coefficients are chosen in such a way as to avoid the violation of the constraints. Two applied problems are considered in the paper: the determination of the high-pressure vessel parameters and the anti rattle spring parameters determination. Using the suggested algorithm, a software complex was developed, which allows us to solve engineering optimization problems. The results obtained using the suggested methods were compared with the results obtained using the non-modified Luus-Jaakola method in order to demonstrate the efficiency of the suggested hybrid random search method.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

Improved Particle Swarm Optimizer with Dynamically Adjusted Search Space and Velocity Limits for Global Optimization

2015 ◽  
Vol 24 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Aderemi Oluyinka Adewumi ◽  
Akugbe Martins Arasomwan
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Search Space ◽  
Particle Swarm Optimizer ◽  
Search Range ◽  
Original Algorithm ◽  
Inertia Weight ◽  
And Performance

This paper presents an improved particle swarm optimization (PSO) technique for global optimization. Many variants of the technique have been proposed in literature. However, two major things characterize many of these variants namely, static search space and velocity limits, which bound their flexibilities in obtaining optimal solutions for many optimization problems. Furthermore, the problem of premature convergence persists in many variants despite the introduction of additional parameters such as inertia weight and extra computation ability. This paper proposes an improved PSO algorithm without inertia weight. The proposed algorithm dynamically adjusts the search space and velocity limits for the swarm in each iteration by picking the highest and lowest values among all the dimensions of the particles, calculates their absolute values and then uses the higher of the two values to define a new search range and velocity limits for next iteration. The efficiency and performance of the proposed algorithm was shown using popular benchmark global optimization problems with low and high dimensions. Results obtained demonstrate better convergence speed and precision, stability, robustness with better global search ability when compared with six recent variants of the original algorithm.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

Hookes-Jeeves-Based Variant of Memetic Algorithm

2016 ◽  
pp. 450-475
Author(s):  
Dipti Singh ◽  
Kusum Deep
Keyword(s):  
Genetic Algorithms ◽  
Memetic Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Memetic Algorithms ◽  
Global Optimum ◽  
Benchmark Problems ◽  
New Variant ◽  
Optimum Solution ◽  
Global Optimum Solution

Due to their wide applicability and easy implementation, Genetic algorithms (GAs) are preferred to solve many optimization problems over other techniques. When a local search (LS) has been included in Genetic algorithms, it is known as Memetic algorithms. In this chapter, a new variant of single-meme Memetic Algorithm is proposed to improve the efficiency of GA. Though GAs are efficient at finding the global optimum solution of nonlinear optimization problems but usually converge slow and sometimes arrive at premature convergence. On the other hand, LS algorithms are fast but are poor global searchers. To exploit the good qualities of both techniques, they are combined in a way that maximum benefits of both the approaches are reaped. It lets the population of individuals evolve using GA and then applies LS to get the optimal solution. To validate our claims, it is tested on five benchmark problems of dimension 10, 30 and 50 and a comparison between GA and MA has been made.

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