Mixed-integer Constrained Optimization Problem Research Articles

Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems

Methods which do not use any derivative information are becoming popular among researchers, since they allow to solve many real-world engineering problems. Such problems are frequently characterize...

Reliability optimization in stochastic domain via genetic algorithm

Purpose– The purpose of this paper is to formulate the reliability optimization problem in stochastic and interval domain and also to solve the same under different stochastic set up.Design/methodology/approach– Stochastic programming technique has been used to convert the chance constraints into deterministic form and the corresponding problem is transformed to mixed-integer constrained optimization problem with interval objective. Then the reduced problem has been converted to unconstrained optimization problem with interval objective by Big-M penalty technique. The resulting problem has been solved by advanced real coded genetic algorithm with interval fitness, tournament selection, intermediate crossover and one-neighbourhood mutation.Findings– A new optimization technique has been developed in stochastic domain and the concept of interval valued parameters has been integrated with the stochastic setup so as to increase the applicability of the resultant solution to the interval valued nonlinear optimization problems.Practical implications– The concept of probability distribution with interval valued parameters has been introduced. This concept will motivate the researchers to carry out the research in this new direction.Originality/value– The application of genetic algorithm is extended to solve the reliability optimization problem in stochastic and interval domain.

Supervised Constrained Optimization of Bayesian Nonlocal Means Filter With Sigma Preselection for Despeckling SAR Images

Speckle reduction is an important problem in synthetic aperture radar (SAR) image analysis. Recent years have seen how Bayesian filters emerge as the natural extension of the nonlocal means filters, providing a general framework to deal with multiplicative (speckle) noise. In this paper, we present an easy-to-use software tool applying an evolutionary algorithm to optimize a Bayesian nonlocal means filter with sigma preselection for denoising SAR images. The desired result is a filtered image having a significative reduction in its variance but preserving the original mean value of the noisy image. A mixed-integer constrained optimization problem is stated and solved with the human intervention, where the user assists the evolutionary algorithm to reduce the noisy image variance under the restriction of keeping the mean value of the noisy SAR image within a predetermined interval of acceptance. We apply the methodology to a set of synthetic and real SAR speckle corrupted images. The results through the evaluation of objective global and local quality criteria show the excellent potential of the proposal.

Mixed-Integer Constrained Optimization Based on Memetic Algorithm

Evolutionary algorithms (EAs) are population-based global search methods. They have been successfully applied tomany complex optimization problems. However, EAs are frequently incapable of finding a convergence solution indefault of local search mechanisms. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators withlocal search methods. With global exploration and local exploitation in search space, MAs are capable of obtainingmore high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-basedsearch algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, amemetic algorithm based on MIHDE is developed for solving mixed-integer optimization problems. However, most ofreal-world mixed-integer optimization problems frequently consist of equality and/or inequality constraints. In order toeffectively handle constraints, an evolutionary Lagrange method based on memetic algorithm is developed to solvethe mixed-integer constrained optimization problems. The proposed algorithm is implemented and tested on twobenchmark mixed-integer constrained optimization problems. Experimental results show that the proposed algorithmcan find better optimal solutions compared with some other search algorithms. Therefore, it implies that the proposedmemetic algorithm is a good approach to mixed-integer optimization problems.

A Mixed-Integer Memetic Algorithm Applied to Batch Process Optimization

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a mixed-integer memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and applied to the optimal design of batch processes. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

A Memetic Algorithm for Mixed-Integer Optimization Problems

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and tested on a benchmark mixed-integer constrained optimization problem. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

An Evolutionary Lagrange Method for Mechanical Design

A novel application to mechanical optimal design is presented in this paper. Here, an evolutionary algorithm, called mixed-integer differential evolution (MIHDE), is used to solve general mixed-integer optimization problems. However, most of real-world mixed-integer optimization problems frequently consist of equality and/or inequality constraints. In order to effectively handle constraints, an evolutionary Lagrange method based on MIHDE is implemented to solve the mixed-integer constrained optimization problems. Finally, the evolutionary Lagrange method is applied to a mechanical design problem. The satisfactory results are achieved, and demonstrate that the evolutionary Lagrange method can effectively solve the optimal mechanical design problem.

A real coded genetic algorithm for solving integer and mixed integer optimization problems

In this paper, a real coded genetic algorithm named MI-LXPM is proposed for solving integer and mixed integer constrained optimization problems. The proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm, LXPM, of Deep and Thakur [K. Deep, M. Thakur, A new crossover operator for real coded genetic algorithms, Applied Mathematics and Computation 188 (2007) 895–912; K. Deep, M. Thakur, A new mutation operator for real coded genetic algorithms, Applied Mathematics and Computation 193 (2007) 211–230]. The algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints. Performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature, and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm, RST2ANU, incorporating annealing concept. The proposed MI-LXPM outperforms both the algorithms in most of the cases which are considered.

An application of Genetic Algorithm in solving an inventory model with advance payment and interval valued inventory costs

The purpose of this research is to solve the mixed integer constrained optimization problem with interval coefficient by a real-coded genetic algorithm (RCGA) with ranking selection, whole arithmetical crossover and non-uniform mutation for non-integer decision variables. In the ranking selection, as well as in finding the best solution in each generation of RCGA, recently developed modified definitions of order relations between interval numbers with respect to decision-making are used. Also, for integer decision variables, new types of crossover and mutation are introduced. This methodology is applied to solve a finite time horizon inventory model with constant lead-time, uniform demand rate and a discount by paying an amount of money in advance. Moreover, different inventory costs are considered to be interval valued. According to the consumption of items during lead-time and reorder level, two cases may arise. For each case, the mathematical model becomes a constrained nonlinear mixed integer problem with interval objective. Our objective is to determine the optimal number of cycles in the finite time horizon, lot-size in each cycle and optimal profit. The model is illustrated with some numerical examples and sensitivity analysis has been done graphically with the variation of different inventory parameters.

An Evolutionary Lagrange Method For Mixed-Integer Constrained Optimization Problems

This study proposes a method for solving mixed-integer constrained optimization problems using an evolutionary Lagrange method. In this approach, an augmented Lagrange function is used to transform the mixed-integer constrained optimization problem into an unconstrained min—max problem with decision-variable minimization and Lagrange-multiplier maximization. The mixed-integer hybrid differential evolution (MIHDE) is introduced into the evolutionary min—max algorithm to accomplish the implementation of the evolutionary Lagrange method. MIHDE provides a mixed coding to denote genetic representations of teal and integer variables, and a rounding operation is used to guide the genetic evolution of integer variables. To fulfill global convergence, self-adaptation for penalty parameters is involved in the evolutionary min—max algorithm so that small penalty parameters can be used, not affecting the final search results. Some numerical experiments are tested to evacuate the performance of the proposed method. Numerical experiments demonstrate that the proposed method converges to better solutions than the conventional penalty function method