Mixed-integer Hybrid Differential Evolution Research Articles

An integrated vendor–buyer replenishment policy for deteriorating items with fuzzy environment and resource constraint

Different from previous researches, our study considers a perishable item with collaborative vendor–buyer ordering policy and finite replenishment rate. Furthermore, due to the importance of inventory and capital investment in today’s fuzzy marketing environments, researches in fuzzy collaborative inventory models have become very popular research in recent decades. Therefore, in our integrated model with deteriorating inventory replenishment policy, we construct the crisp/fuzzy models with inventory investment constraints with fuzzy environments. Two different fuzzy decision-making methods are used to formulate the models. Convex fuzzy programming (CFP) method is used to maximize the weighted sum for each achievement level of the joint cost and constraints. An inverse weighted fuzzy non-linear programming (IWFNLP) is then proposed to satisfy the decision-maker’s desirable achievement level of service. A heuristic algorithm with mixed-integer hybrid differential evolution (MIHDE) is developed to solve the crisp/fuzzy models. Numerical examples and sensitivity analysis are developed to investigate the effectiveness of the proposed method in the fuzzy environment. From the numerical analysis, it can be seen that the IWFNLP method is a more efficient decision-making tool than the CFP method.

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.

Fuzzy programming for mixed-integer optimization problems

Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems have inherited a more or less imprecise nature. Under these circumstances, if we take into account the flexibility of the constraints and the fuzziness of the objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer hybrid differential evolution (MIHDE) is an evolutionary search algorithm which has been successfully applied to many complex mixed-integer optimization problems. In this article, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. In addition the MIHDE is introduced to solve the fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that MIHDE can effectively handle fuzzy mixed-integer optimization problems.

Evolutionary Neural Networks with Mixed-Integer Hybrid Differential Evolution

A novel application to the optimization of neural networks is presented in this paper. Here, the weight and architecture optimization of neural networks can be formulated as a mixed-integer optimization problem. And then a mixed-integer evolutionary algorithm (Mixed-Integer Hybrid Differential Evolution, MIHDE) is used to optimize the neural network. Finally, the optimized neural network is applied to the prediction of chaotic time series. The satisfactory results are achieved, and demonstrate that the neural network optimized by MIHDE can effectively predict the chaotic time series.

Computer-aided biocompatible solvent design for an integrated extractive fermentation–separation process

Computer-aided process/solvent design is introduced to find a feasible biocompatible solvent for an extractive fermentation and separation process. The designed biocompatible solvent serves as both the extractant for extractive fermentation and the entrainer for extractive distillation, to yield water-free ethanol. Several goals, such as maximizing production rate and extraction efficiency, and limiting solvent utilization, are simultaneously considered in the optimal solvent design problem. Thus, the design was formulated as a mixed-integer nonlinear optimization problem. A two-phase computational scheme was introduced to solve the problem. The mixed-integer hybrid differential evolution (MIHDE) algorithm was first applied to solve the problem in order to obtain a feasible solution. The feasible solution was then served as an initial starting point for the mixed-integer sequential quadratic programming (MISQP) solver to numerically confirm that the optimal design was achieved. We have compared the crisp and fuzzy approaches to the design problem. The fuzzy goal attainment approach is able to address goal trade-offs and yield an overall satisfactory grade for the problem.

Multi-area hydrothermal coordination using modified mixed integer hybrid differential evolution

This paper presents a novel modified mixed integer hybrid differential evolution (MMIHDE) algorithm, for solving the hydrothermal unit commitment of a multi-area power system. Differential evolution is a global optimisation technique that is exceptionally simple, significantly faster and robust. Hybrid differential evolution (HDE) overcomes the usage of large population, which results in lesser computation time. In case of a power pool that involves several generation areas interconnected by tie lines, the objective is to achieve the most economical generation policy that could supply the local demand without violating tie line capacity constraints. The inclusion of tie line security constraints makes the optimisation highly non-linear. Discrete and dynamic constraints such as unit start-up/shutdown and minimum-up/minimum-down time limits are also included in the multi-area hydrothermal unit commitment. In this paper, modifications are incorporated in the MIHDE algorithm as the basic DE algorithm exhibits difficulties in handling the equality constraints. The performance of the proposed approach is validated by illustration with standard test systems. The results of the proposed approach are compared with those techniques reported in literature. From the numerical results it is found that the MMIHDE based approach is able to provide better solution at a relatively lesser computational effort.

Optimal process/solvent design for ethanol extractive fermentation with cell recycling

In this study, the computer-aided process/solvent design is introduced to find an optimal biocompatible solvent and to maximize the ethanol production rate simultaneously for the single- or double-stage extractive fermentation process with cell recycling. Such a process/solvent design problem is formulated as a mixed-integer nonlinear programming problem that is solved by mixed-integer hybrid differential evolution in order to obtain a global design. The double-stage process can use a smaller amount of fresh solvent to increase ethanol productivity compared with that of the single-stage process, but it will also decrease overall conversion. Comparing the case studies, the simultaneous process/solvent design could yield higher overall ethanol productivity than that of the process design. The maximum ethanol production rate for the double-stage extractive fermentation with cell recycling was about 10-fold higher than that of continuous fermentation and about twofold higher than that of continuous fermentation with cell recycling.

Trade-off optimal design of a biocompatible solvent for an extractive fermentation process

In this study, crisp and flexible optimization approaches are, respectively, introduced to design an optimal biocompatible solvent for an extractive fermentation process. The optimal design problem is formulated as a mixed-integer nonlinear programming model in which performance requirements of the compounds are reflected in the objective and the constraints. In general, the requirements for the objective and constraints are not rigid; consequently, the flexible or fuzzy optimization approach is applied to soften the rigid requirement for maximization of the extraction efficiency and to consider the mass flow rate and biocompatibility of solvent as the softened inequality constraints to the solvent design problem. Having elicited the membership function for the objective function and the constraint, the optimal solvent design problem can be formulated as a flexible goal attainment problem. Mixed-integer hybrid differential evolution is applied to solve the problem in order to find a satisfactory design.

Hydrothermal coordination using modified mixed integer hybrid differential evolution

This work presents a novel modified Mixed Integer Hybrid Differential Evolution (MIHDE) algorithm, for solving the unit commitment problem of a hydrothermal power system. Hydrothermal scheduling involves the optimisation of a non-linear objective function with a set of system and hydraulic constraints. Discrete and dynamic constraints such as unit start-up/shutdown and minimum-up/minimum-downtime limits are also included in the hydro unit commitment. The problem of hydrothermal coordination is a mixed integer non-linear optimisation problem, which is well-suited for the use of MIHDE. In this paper, the MIHDE algorithm is modified in order to handle the reservoir end-volume and load balance constraints in the hydrothermal scheduling. The performance of the proposed approach is validated by illustration with standard test systems. The results of the proposed approach are compared with those techniques reported in literature. From the numerical results, it is found that the modified MIHDE-based approach is able to provide better solution at a relatively lesser computational effort.

A mixed-coding scheme of evolutionary algorithms to solve mixed-integer nonlinear programming problems

In this paper, mixed-integer hybrid differential evolution (MIHDE) is developed to deal with the mixed-integer optimization problems. This hybrid algorithm contains the migration operation to avoid candidate individuals clustering together. We introduce the population diversity measure to inspect when the migration operation should be performed so that the user can use a smaller population size to obtain a global solution. A mixed coding representation and a rounding operation are introduced in MIHDE so that the hybrid algorithm is not only used to solve the mixed-integer nonlinear optimization problems, but also used to solve the real and integer nonlinear optimization problems. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional genetic algorithms.

Network reconfiguration of distribution systems using improved mixed-integer hybrid differential evolution

Network reconfiguration of distribution systems using improved mixed-integer hybrid differential evolution

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

Network Reconfiguration of Distribution Systems Using Improved Mixed-Integer Hybrid Differential Evolution

This study proposes an effective method of network reconfiguration to reduce power loss and enhance the voltage profile by the improved mixed-integer hybrid differential evolution (MIHDE) method for distribution systems. This research aims to recognize beneficial load transfers so that the objective function composed of power losses is minimized and the prescribed voltage limits are satisfied. The proposed method determines the proper system topology that reduces the power loss according to a load pattem. Mathematically, the problem of this research is a mixed-integer combinatorial optimization problem well suited to the application of MIHDE.

Fuzzy decision-making design of chemical plant using mixed-integer hybrid differential evolution

In this study, we have introduced a fuzzy decision-making approach to design a multi-objective optimal design problem of a multiproduct batch chemical plant. In the crisp decision-making approach, the designer is first to solve the multi-objective optimization problem, and then to check whether each optimal objective function value satisfies the rigid preference goal. In real world application, the preference goal for each objective function is an interval bound not a rigid value so that the problem becomes a fuzzy goal optimization problem. A monotonic increasing or decreasing membership function is used to define the degree of satisfaction for each objective function so that the fuzzy goal optimization problem is then represented as an augmented minimax problem formulated as mixed-integer nonlinear programming (MINLP) models. To obtain a unique solution, we have introduced the mixed-integer hybrid differential evolution (MIHDE) to solve the MINLP problems. The MIHDE can straightforwardly solve the problem without any mathematical model transformation. Two examples were used to illustrate the applicability of the proposed interactive algorithm.