Use the Power of a Genetic Algorithm to Maximize and Minimize Cases to Solve Capacity Supplying Optimization and Travelling Salesman in Nested Problems

Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

Ant colony algorithm based on genetic method for continuous optimization problem

A new algorithm is presented by using the ant colony algorithm based on genetic method （ACG） to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of component, trail information and fitness. The ant chooses a seed from the seed set with the possibility determined by trail information and fitness of the seed. The genetic method is used to form new solutions from the solutions got by the ants. Best solutions are selected to update the seeds in the sets and trail information of the seeds. In updating the trail information, a diffusion function is used to achieve the diffuseness of trail information. The new algorithm is tested with 8 different benchmark functions.

A Hybrid Genetic Algorithm for Vehicle Routing Problem with Complex Constraints

Most research on the Vehicle Routing Problem （VRP） is focused on standard conditions, which is not suitable for specific cases. A Hybrid Genetic Algorithm is proposed to solve a Vehicle Routing Problem （VRP） with complex side constraints. A novel coding method is designed especially for side constraints. A greedy algorithm combined with a random algorithm is introduced to enable the diversity of the initial population, as well as a local optimization algorithm employed to improve the searching efficiency. In order to evaluate the performance, this mechanism has been implemented in an oil distribution center, the experimental and executing results show that the near global optimal solution can be easily and quickly obtained by this method, and the solution is definitely satisfactory in the VRP application.

Improved genetic algorithm for nonlinear programming problems

An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.

Solution for integer linear bilevel programming problems using orthogonal genetic algorithm

An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.

Orthogonal genetic algorithm for solving quadratic bilevel programming problems

A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.

Dendritic Cell Algorithm with Grouping Genetic Algorithm for Input Signal Generation

The artificial immune system,an excellent prototype for developingMachine Learning,is inspired by the function of the powerful natural immune system.As one of the prevalent classifiers,the Dendritic Cell Algorithm(DCA)has been widely used to solve binary problems in the real world.The classification of DCA depends on a data preprocessing procedure to generate input signals,where feature selection and signal categorization are themain work.However,the results of these studies also show that the signal generation of DCA is relatively weak,and all of them utilized a filter strategy to remove unimportant attributes.Ignoring filtered features and applying expertise may not produce an optimal classification result.To overcome these limitations,this study models feature selection and signal categorization into feature grouping problems.This study hybridizes Grouping Genetic Algorithm(GGA)with DCA to propose a novel DCA version,GGA-DCA,for accomplishing feature selection and signal categorization in a search process.The GGA-DCA aims to search for the optimal feature grouping scheme without expertise automatically.In this study,the data coding and operators of GGA are redefined for grouping tasks.The experimental results show that the proposed algorithm has significant advantages over the compared DCA expansion algorithms in terms of signal generation.

Learning-Based Metaheuristic Approach for Home Healthcare Optimization Problem

This research focuses on the home health care optimization problem that involves staff routing and scheduling problems.The considered problem is an extension of multiple travelling salesman problem.It consists of finding the shortest path for a set of caregivers visiting a set of patients at their homes in order to perform various tasks during a given horizon.Thus,a mixed-integer linear programming model is proposed to minimize the overall service time performed by all caregivers while respecting the workload balancing constraint.Nevertheless,when the time horizon become large,practical-sized instances become very difficult to solve in a reasonable computational time.Therefore,a new Learning Genetic Algorithm for mTSP(LGA-mTSP)is proposed to solve the problem.LGA-mTSP is composed of a new genetic algorithm for mTSP,combined with a learning approach,called learning curves.Learning refers to that caregivers’productivity increases as they gain more experience.Learning curves approach is considered as a way to save time and costs.Simulation results show the efficiency of the proposed approach and the impact of learning curve strategy to reduce service times.

Niche pseudo-parallel genetic algorithms for path optimization of autonomous mobile robot

A new genetic algorithm named niche pseudo-parallel genetic algorithm （NPPGA） is presented for path evolution and genetic optimization of autonomous mobile robot. The NPPGA is an effective improvement to maintain the population diversity as well for the sake of avoiding premature and strengthen parallelism of the population to accelerate the search process combined with niche genetic algorithms and pseudo-parallel genetic algorithms. The proposed approach is evaluated by robotic path optimization, which is a specific application of traveler salesman problem （TSP）. Experimental results indicated that a shortest path could be obtained in the practical traveling salesman problem named ＂Robot tour around Pekin＂, and the performance conducted by NPPGA is better than simple genetic algorithm （SGA） and distributed paralell genetic algorithms （DPGA）.

APPLICATION OF INTEGER CODING ACCELERATING GENETIC ALGORITHM IN RECTANGULAR CUTTING STOCK PROBLEM

An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm （SGA） to cutting stock problem, but the huge amount of computing of SGA is a serious problem in practical application. Accelerating genetic algorithm （AGA） based on integer coding and AGA＇s detailed steps are developed to reduce the amount of computation, and a new kind of rectangular parts blank layout algorithm is designed for rectangular cutting stock problem. SGA is adopted to produce individuals within given evolution process, and the variation interval of these individuals is taken as initial domain of the next optimization process, thus shrinks searching range intensively and accelerates the evaluation process of SGA. To enhance the diversity of population and to avoid the algorithm stagnates at local optimization result, fixed number of individuals are produced randomly and replace the same number of parents in every evaluation process. According to the computational experiment, it is observed that this improved GA converges much sooner than SGA, and is able to get the balance of good result and high efficiency in the process of optimization for rectangular cutting stock problem.

GREEDY NON-DOMINATED SORTING IN GENETIC ALGORITHM-ⅡFOR VEHICLE ROUTING PROBLEM IN DISTRIBUTION

Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.

A Grafted Genetic Algorithm for the Job-Shop Scheduling Problem

The standard genetic algorithm has limitations of a low convergence rate and premature convergence in solving the job-shop scheduling problem.To overcome these limitations,this paper presents a new improved hybrid genetic algorithm on the basis of the idea of graft in botany.Through the introduction of a grafted population and crossover probability matrix,this algorithm accelerates the convergence rate greatly and also increases the ability to fight premature convergence.Finally,the approach is tested on a set of standard instances taken from the literature and compared with other approaches.The computation results validate the effectiveness of the proposed algorithm.

A Genetic Algorithm for the Flowshop Scheduling Problem

The flowshop scheduling problem is NP complete. To solve it by genetic algorithm, an efficient crossover operator is designed. Compared with another crossover operator, this one often finds a better solution within the same time.

Solution of Combined Heat and Power Economic Dispatch Problem Using Genetic Algorithm

This research proposes a synergistic meta-heuristic algorithm for solving the extreme operational complications of combined heat and power economic dispatch problem towards the advantageous economic outcomes on the cost of generation. The combined heat and power (CHP) is a system that provides electricity and thermal energy concurrently. For its extraordinary efficiency and significant emission reduction, it is considered a promising energy prospect. The broad application of combined heat and power units requires the joint dispatch of power and heating systems, in which the modelling of combined heat and power units plays a vital role. The present research employs the genetic optimization algorithm to evaluate the cost function, heat and power dispatch values encountered in a system with simple cycle cogeneration unit and quadratic cost function. The system was first modeled to determine the various parameters of combined heat and power units towards solving its economic dispatch problem directly. In order for modelling to be done, a general structure of combined heat and power must be defined. The test system considered consists of four units: two conventional power units, one combined heat and power unit and one heat-only unit. The algorithm was applied to test system while taking into account the power and heat units, bounds of the units and feasible operation region of cogeneration unit. Output decision variables of 4-unit test systems plus cost function from Genetic Algorithm (GA), was determined using appropriate codes. The proposed algorithm produced a well spread and diverse optimal solution and also converged reasonably to the actual optimal solution in 51 iterations. The result obtained compared favourably with that obtained with the direct solution algorithm discussed in a previous paper. We conclude that the genetic algorithm is quite efficient in dealing with non-convex and constrained combined heat and power economic dispatch problem.

Solving Hitchcock’s transportation problem by a genetic algorithm

Genetic algorithms (GAs) employ the evolutionary process of Darwin’s nature selection theory to find the solutions of optimization problems. In this paper, an implementation of genetic algorithm is put forward to solve a classical transportation problem, namely the Hitchcock’s Transportation Problem (HTP), and the GA is improved to search for all optimal solutions and identify them automatically. The algorithm is coded with C++ and validated by numerical examples. The computational results show that the algorithm is efficient for solving the Hitchcock’s transportation problem.

A Time-Dependent Vehicle Routing Problem with Time Windows for E-Commerce Supplier Site Pickups Using Genetic Algorithm

The VRP is classified as an NP-hard problem. Hence exact optimization methods may be difficult to solve these problems in acceptable CPU times, when the problem involves real-world data sets that are very large. To get solutions in determining routes which are realistic and very close to the actual solution, we use heuristics and metaheuristics which are of the combinatorial optimization type. A literature review of VRPTW, TDVRP, and a metaheuristic such as the genetic algorithm was conducted. In this paper, the implementation of the VRPTW and its extension, the time-dependent VRPTW (TDVRPTW) has been carried out using the model as well as metaheuristics such as the genetic algorithm (GA). The algorithms were implemented, using Matlab and HeuristicLab optimization software. A plugin was developed using Visual C# and DOT NET framework 4.5. Results were tested using Solomon’s 56 benchmark instances classified into groups such as C1, C2, R1, R2, RC1, RC2, with 100 customer nodes, 25 vehicles and each vehicle capacity of 200. The results were comparable to the earlier algorithms developed and in some cases the current algorithm yielded better results in terms of total distance travelled and the average number of vehicles used.

A New Approach to the Optimization of the CVRP through Genetic Algorithms

This paper presents a new approach to the analysis of complex distribution problems under capacity constraints. These problems are known in the literature as CVRPs (Capacitated Vehicle Routing Problems). The procedure introduced in this paper optimizes a transformed variant of a CVRP. It starts generating feasible clusters and codifies their ordering. In the next stage the procedure feeds this information into a genetic algorithm for its optimization. This makes the algorithm independent of the constraints and improves its performance. Van Breedam problems have been used to test this technique. While the results obtained are similar to those in other works, the processing times are longer.

An Adaptive Strategy-incorporated Integer Genetic Algorithm for Wind Farm Layout Optimization

Energy issues have always been one of the most significant concerns for scientists worldwide.With the ongoing over exploitation and continued outbreaks of wars,traditional energy sources face the threat of depletion.Wind energy is a readily available and sustainable energy source.Wind farm layout optimization problem,through scientifically arranging wind turbines,significantly enhances the efficiency of harnessing wind energy.Meta-heuristic algorithms have been widely employed in wind farm layout optimization.This paper introduces an Adaptive strategy-incorporated Integer Genetic Algorithm,referred to as AIGA,for optimizing wind farm layout problems.The adaptive strategy dynamically adjusts the placement of wind turbines,leading to a substantial improvement in energy utilization efficiency within the wind farm.In this study,AIGA is tested in four different wind conditions,alongside four other classical algorithms,to assess their energy conversion efficiency within the wind farm.Experimental results demonstrate a notable advantage of AIGA.

A Hybrid Immigrants Scheme for Genetic Algorithms in Dynamic Environments

Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution（s） of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.