scholarly journals Modified Covariance Matrix Adaptation – Evolution Strategy algorithm for constrained optimization under uncertainty, application to rocket design

2015 ◽  
Vol 6 ◽  
pp. A1 ◽  
Author(s):  
Rudy Chocat ◽  
Loïc Brevault ◽  
Mathieu Balesdent ◽  
Sébastien Defoort
Keyword(s):  
Constrained Optimization ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Under Uncertainty ◽  
Constrained Optimization Problem ◽  
Covariance Matrix Adaptation ◽  
Principal Axes ◽  
Adaptation Evolution ◽  
Handling Method

The design of complex systems often induces a constrained optimization problem under uncertainty. An adaptation of CMA-ES(λ, μ) optimization algorithm is proposed in order to efficiently handle the constraints in the presence of noise. The update mechanisms of the parametrized distribution used to generate the candidate solutions are modified. The constraint handling method allows to reduce the semi-principal axes of the probable research ellipsoid in the directions violating the constraints. The proposed approach is compared to existing approaches on three analytic optimization problems to highlight the efficiency and the robustness of the algorithm. The proposed method is used to design a two stage solid propulsion launch vehicle.

scholarly journals An adaptive ES with a ranking based constraint handling strategy

2014 ◽  
Vol 24 (3) ◽  
pp. 307-319
Author(s):  
Ali Kusakci ◽  
Mehmet Can
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Real Life ◽  
Constraint Handling ◽  
Benchmark Problems ◽  
Constrained Optimization Problem ◽  
Improve Performance ◽  
Covariance Matrix Adaptation ◽  
Handling Methods ◽  
Handling Method

To solve a constrained optimization problem, equality constraints can be used to eliminate a problem variable. If it is not feasible, the relations imposed implicitly by the constraints can still be exploited. Most conventional constraint handling methods in Evolutionary Algorithms (EAs) do not consider the correlations between problem variables imposed by the constraints. This paper relies on the idea that a proper search operator, which captures mentioned implicit correlations, can improve performance of evolutionary constrained optimization algorithms. To realize this, an Evolution Strategy (ES) along with a simplified Covariance Matrix Adaptation (CMA) based mutation operator is used with a ranking based constraint-handling method. The proposed algorithm is tested on 13 benchmark problems as well as on a real life design problem. The outperformance of the algorithm is significant when compared with conventional ES-based methods.

An Improved Constrained Optimization Multi-Objective Genetic Algorithm and its Application in Engineering

2014 ◽  
Vol 962-965 ◽  
pp. 2903-2908
Author(s):  
Yun Lian Liu ◽  
Wen Li ◽  
Tie Bin Wu ◽  
Yun Cheng ◽  
Tao Yun Zhou ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Crossover Operator ◽  
Multi Objective Optimization ◽  
Constrained Optimization Problem ◽  
Great Ability ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm

An improved multi-objective genetic algorithm is proposed to solve constrained optimization problems. The constrained optimization problem is converted into a multi-objective optimization problem. In the evolution process, our algorithm is based on multi-objective technique, where the population is divided into dominated and non-dominated subpopulation. Arithmetic crossover operator is utilized for the randomly selected individuals from dominated and non-dominated subpopulation, respectively. The crossover operator can lead gradually the individuals to the extreme point and improve the local searching ability. Diversity mutation operator is introduced for non-dominated subpopulation. Through testing the performance of the proposed algorithm on 3 benchmark functions and 1 engineering optimization problems, and comparing with other meta-heuristics, the result of simulation shows that the proposed algorithm has great ability of global search. Keywords: multi-objective optimization;genetic algorithm;constrained optimization problem;engineering application

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.

A Fast Solver for anH1Regularized PDE-Constrained Optimization Problem

2016 ◽  
Vol 19 (1) ◽  
pp. 143-167 ◽  
Author(s):  
Andrew T. Barker ◽  
Tyrone Rees ◽  
Martin Stoll
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Schur Complement ◽  
Time Dependent ◽  
Constrained Optimization Problem ◽  
Bound Constraints ◽  
Constrained Optimization Problems ◽  
Pde Constrained Optimization ◽  
Fast Solver

AbstractIn this paper we consider PDE-constrained optimization problems which incorporate anH1regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

scholarly journals Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 56
Author(s):  
Wei Li
Keyword(s):  
Covariance Matrix ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Population Diversity ◽  
Evolution Strategy ◽  
Multimodal Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

scholarly journals Superlinear Convergence of a Modified Newton's Method for Convex Optimization Problems With Constraints

2021 ◽  
Vol 13 (2) ◽  
pp. 90
Author(s):  
Bouchta RHANIZAR
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Convex Set ◽  
Optimization Problems ◽  
Descent Direction ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Convex Optimization Problems ◽  
Definition Of ◽  
Bounded Convex

We consider the constrained optimization problem  defined by: $$f (x^*) = \min_{x \in  X} f(x)\eqno (1)$$ where the function  f : \pmb{\mathbb{R}}^{n} → \pmb{\mathbb{R}} is convex  on a closed bounded convex set X. To solve problem (1), most methods transform this problem into a problem without constraints, either by introducing Lagrange multipliers or a projection method. The purpose of this paper is to give a new method to solve some constrained optimization problems, based on the definition of a descent direction and a step while remaining in the X convex domain. A convergence theorem is proven. The paper ends with some numerical examples.

scholarly journals A Novel Penalty Function Approach to Constrained Optimization Problems with Genetic Algorithms

1998 ◽  
Vol 2 (6) ◽  
pp. 208-213 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Weixing Zheng ◽  
Baolin Wu ◽  
Xin Yao ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Function Approach ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Unconstrained Optimization Problem ◽  
Penalty Function Approach

In this paper, a novel penalty function approach is proposed for constrained optimization problems with linear and nonlinear constraints. It is shown that by using a mapping function to "wrap" up the constraints, a constrained optimization problem can be converted to an unconstrained optimization problem. It is also proved mathematically that the best solution of the converted unconstrained optimization problem will approach the best solution of the constrained optimization problem if the tuning parameter for the wrapping function approaches zero. A tailored genetic algorithm incorporating an adaptive tuning method is then used to search for the global optimal solutions of the converted unconstrained optimization problems. Four test examples were used to show the effectiveness of the approach.

scholarly journals Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

2019 ◽  
Vol 7 (6) ◽  
pp. 532-549
Author(s):  
Chun-an Liu ◽  
Huamin Jia
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Imperialist Competitive Algorithm ◽  
Search Space ◽  
Feasible Region ◽  
Constrained Optimization Problem ◽  
Diverse Range ◽  
Nonlinear Constrained Optimization ◽  
Competitive Algorithm

Abstract Nonlinear constrained optimization problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

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