An Efficient Kriging-Based Constrained Optimization Algorithm by Global and Local Sampling in Feasible Region

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Tianzeng Tao ◽  
Guozhong Zhao ◽  
Shanhong Ren
Keyword(s):  
Phase I ◽  
Constrained Optimization ◽  
Objective Function ◽  
Optimization Design ◽  
Optimization Problems ◽  
Phase Iii ◽  
Benchmark Problems ◽  
Feasible Region ◽  
Sample Points ◽  
Local Sampling

Abstract To solve challenging optimization problems with time-consuming objective and constraints, a novel efficient Kriging-based constrained optimization (EKCO) algorithm is proposed in this paper. The EKCO mainly consists of three sampling phases. In phase I of EKCO, considering the significance of constraints, feasible region is constructed via employing a feasible region sampling (FRS) criterion. The FRS criterion can avoid the local clustering phenomenon of sample points. Therefore, phase I is also a global sampling process for the objective function in the feasible region. However, the objective function may be higher-order nonlinear than constraints. In phase II, by maximizing the prediction variance of the surrogate objective, more accurate objective function in the feasible region can be obtained. After global sampling, to accelerate the convergence of EKCO, an objective local sampling criterion is introduced in phase III. The verification of the EKCO algorithm is examined on 18 benchmark problems by several recently published surrogate-based optimization algorithms. The results indicate that the sampling efficiency of EKCO is higher than or comparable with that of the recently published algorithms while maintaining the high accuracy of the optimal solution, and the adaptive ability of the proposed algorithm also be validated. To verify the ability of EKCO to solve practical engineering problems, an optimization design problem of aeronautical structure is presented. The result indicates EKCO can find a better feasible design than the initial design with limited sample points, which demonstrates practicality of EKCO.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals SRIFA: Stochastic Ranking with Improved-Firefly-Algorithm for Constrained Optimization Engineering Design Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 250 ◽  
Author(s):  
Umesh Balande ◽  
Deepti Shrimankar
Keyword(s):  
Constrained Optimization ◽  
Engineering Design ◽  
Real World ◽  
Optimization Design ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Design Problems ◽  
Improved Firefly Algorithm ◽  
Engineering Design Problems ◽  
And Performance

Firefly-Algorithm (FA) is an eminent nature-inspired swarm-based technique for solving numerous real world global optimization problems. This paper presents an overview of the constraint handling techniques. It also includes a hybrid algorithm, namely the Stochastic Ranking with Improved Firefly Algorithm (SRIFA) for solving constrained real-world engineering optimization problems. The stochastic ranking approach is broadly used to maintain balance between penalty and fitness functions. FA is extensively used due to its faster convergence than other metaheuristic algorithms. The basic FA is modified by incorporating opposite-based learning and random-scale factor to improve the diversity and performance. Furthermore, SRIFA uses feasibility based rules to maintain balance between penalty and objective functions. SRIFA is experimented to optimize 24 CEC 2006 standard functions and five well-known engineering constrained-optimization design problems from the literature to evaluate and analyze the effectiveness of SRIFA. It can be seen that the overall computational results of SRIFA are better than those of the basic FA. Statistical outcomes of the SRIFA are significantly superior compared to the other evolutionary algorithms and engineering design problems in its performance, quality and efficiency.

An Adaptive Penalty Function Method for Constrained Optimization with Evolutionary Programming

2000 ◽  
Vol 4 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Baolin Wu
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Optimization Problems ◽  
Evolutionary Programming ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Penalty Function Method ◽  
Adaptive Penalty ◽  
Adaptive Penalty Function

In this paper, we propose a novel adaptive penalty function method for constrained optimization problems using the evolutionary programming technique. This method incorporates an adaptive tuning algorithm that adjusts the penalty parameters according to the population landscape so that it allows fast escape from a local optimum and quick convergence toward a global optimum. The method is simple and computationally effective in the sense that only very few penalty parameters are needed for tuning. Simulation results of five well-known benchmark problems are presented to show the performance of the proposed method.

Flexibility-Based Objective Functions for Constrained Optimization Problems on Structural Damage Detection

2011 ◽  
Vol 186 ◽  
pp. 383-387 ◽  
Author(s):  
Xi Chen ◽  
Ling Yu
Keyword(s):  
Damage Detection ◽  
Constrained Optimization ◽  
Objective Function ◽  
Structural Damage ◽  
Optimization Problems ◽  
Objective Functions ◽  
Structural Damage Detection ◽  
Constrained Optimization Problems ◽  
Modal Assurance Criterion ◽  
Damage Scenarios

Based on concepts of structural modal flexibility and modal assurance criterion (MAC), a new objective function is defined and studied for constrained optimization problems (COP) on structural damage detection (SDD) in this paper. Compared with traditionally objective function, which is defined based on natural frequencies and MAC, effect of objective functions on robustness of SDD calculation is evaluated through numerical simulation of a 2-storey rigid frame. Structural damages are identified by solving the COP on SDD based on an improved particle swarm optimization (IPSO) algorithm. Weak and multiple damage scenarios are mainly considered in various noise conditions. Some illustrated results show that the newly defined objective function is better than the traditional ones. It can be used to identify the damage locations but also to quantify the severity of weak and multiple damages in measurement noise conditions.

HYBRID-FITNESS FUNCTION EVOLUTIONARY ALGORITHM BASED ON SIMPLEX CROSSOVER AND PSO MUTATION FOR CONSTRAINED OPTIMIZATION PROBLEMS

2009 ◽  
Vol 23 (01) ◽  
pp. 115-127 ◽  
Author(s):  
YIBO HU
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Penalty Function ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Fitness Function ◽  
Benchmark Problems ◽  
Crossover Operator ◽  
Hybrid Fitness ◽  
Constrained Optimization Problems

For constrained optimization problems, evolutionary algorithms often utilize a penalty function to deal with constraints, even if it is difficult to control the penalty parameters. To overcome this shortcoming, this paper presents a new penalty function which has no parameter and can effectively handle constraint first, after which a hybrid-fitness function integrating this penalty function into the objective function is designed. The new fitness function can properly evaluate not only feasible solution, but also infeasible one, and distinguish any feasible one from an infeasible one. Meanwhile, a new crossover operator based on simplex crossover operator and a new PSO mutation operator are also proposed, which can produce high quality offspring. Based on these, a new evolutionary algorithm for constrained optimization problems is proposed. The simulations are made on ten widely used benchmark problems, and the results indicate the proposed algorithm is effective.

scholarly journals Characteristic feature analysis of continuous optimization problems based on Variability Map of objective function for optimization algorithm configuration

2020 ◽  
Vol 10 (1) ◽  
pp. 97-111
Author(s):  
Taleh Agasiev
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Landscape Analysis ◽  
Decomposition Approach ◽  
Analysis Methods ◽  
Algorithm Configuration ◽  
Sample Points ◽  
Characteristic Features

AbstractAdvanced optimization algorithms with a variety of configurable parameters become increasingly difficult to apply effectively to solving optimization problems. Appropriate algorithm configuration becomes highly relevant, still remaining a computationally expensive operation. Development of machine learning methods allows to model and predict the efficiency of different solving strategies and algorithm configurations depending on properties of optimization problem to be solved. The paper suggests the Dependency Decomposition approach to reduce computational complexity of modeling the efficiency of optimization algorithm, also considering the amount of computational resources available for optimization problem solving. The approach requires development of explicit Exploratory Landscape Analysis methods to assess a variety of significant characteristic features of optimization problems. The results of feature assessment depend on the number of sample points analyzed and their location in the design space, on top of that some of methods require additional evaluations of objective function. The paper proposes new landscape analysis methods based on given points without the need of any additional objective function evaluations. An algorithm of building a so-called Full Variability Map is suggested based on informativeness criteria formulated for groups of sample points. The paper suggests Generalized Information Content method for analysis of Full Variability Map which allows to get accurate and stable estimations of objective function features. The Sectorization method of Variability Map analysis is proposed to assess characteristic features reflecting such properties of objective function that are critical for optimization algorithm efficiency. The resulting features are invariant to the scale of objective function gradients which positively affects the generalizing ability of problems classification algorithm. The procedure of the comparative study of effectiveness of landscape analysis algorithms is introduced. The results of computational experiments indicate reliability of applying the suggested landscape analysis methods to optimization problem characterization and classification.

An Artificial Evolutionary Approach for Solving the Nonlinear Constrained Optimization Problems

2013 ◽  
Vol 479-480 ◽  
pp. 861-864
Author(s):  
Yi Chih Hsieh ◽  
Peng Sheng You
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Evolutionary Approach ◽  
Benchmark Problems ◽  
Second Phase ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Two Phase ◽  
Nonlinear Constrained Optimization

In this paper, an artificial evolutionary based two-phase approach is proposed for solving the nonlinear constrained optimization problems. In the first phase, an immune based algorithm is applied to solve the nonlinear constrained optimization problem approximately. In the second phase, we present a procedure to improve the solutions obtained by the first phase. Numerical results of two benchmark problems are reported and compared. As shown, the solutions by the new proposed approach are all superior to those best solutions by typical approaches in the literature.

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