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.

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 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 Filled Function Approach for Nonsmooth Constrained Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Solution Algorithm ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Global Minima ◽  
Constrained Optimization Problem

A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising.

scholarly journals Composite Differential Evolution with Modified Oracle Penalty Method for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Minggang Dong ◽  
Ning Wang ◽  
Xiaohui Cheng ◽  
Chuanxian Jiang
Keyword(s):  
Differential Evolution ◽  
Constrained Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Real Life ◽  
Optimization Criterion ◽  
Constrained Optimization Problems ◽  
Constraints Handling ◽  
Efficient Alternative ◽  
Handling Methods

Motivated by recent advancements in differential evolution and constraints handling methods, this paper presents a novel modified oracle penalty function-based composite differential evolution (MOCoDE) for constrained optimization problems (COPs). More specifically, the original oracle penalty function approach is modified so as to satisfy the optimization criterion of COPs; then the modified oracle penalty function is incorporated in composite DE. Furthermore, in order to solve more complex COPs with discrete, integer, or binary variables, a discrete variable handling technique is introduced into MOCoDE to solve complex COPs with mix variables. This method is assessed on eleven constrained optimization benchmark functions and seven well-studied engineering problems in real life. Experimental results demonstrate that MOCoDE achieves competitive performance with respect to some other state-of-the-art approaches in constrained optimization evolutionary algorithms. Moreover, the strengths of the proposed method include few parameters and its ease of implementation, rendering it applicable to real life. Therefore, MOCoDE can be an efficient alternative to solving constrained optimization problems.

scholarly journals GENO – Optimization for Classical Machine Learning Made Fast and Easy

2020 ◽  
Vol 34 (09) ◽  
pp. 13620-13621
Author(s):  
Sören Laue ◽  
Matthias Mitterreiter ◽  
Joachim Giesen
Keyword(s):  
Machine Learning ◽  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Specific Problem ◽  
Optimization Problems ◽  
Modeling Language ◽  
Large Margin ◽  
Unconstrained Optimization Problem

Most problems from classical machine learning can be cast as an optimization problem. We introduce GENO (GENeric Optimization), a framework that lets the user specify a constrained or unconstrained optimization problem in an easy-to-read modeling language. GENO then generates a solver, i.e., Python code, that can solve this class of optimization problems. The generated solver is usually as fast as hand-written, problem-specific, and well-engineered solvers. Often the solvers generated by GENO are faster by a large margin compared to recently developed solvers that are tailored to a specific problem class.An online interface to our framework can be found at http://www.geno-project.org.

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

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