基于实数编码的免疫遗传算法研究

针对标准遗传算法(SGA)搜索效率低、收敛速度慢等缺陷，在免疫遗传算法的基础上提出了基于实数编码的免疫遗传算法(RIGA)。研究表明，RIGA对SGA的改进是有效可行的，显示出稳健的全局优化、计算量少而解的精度高等特点，具有较高的应用价值。     

A hybrid genetic algorithm for the finite horizon economic lot and delivery scheduling in supply chains

In this paper, we investigate the lot and delivery scheduling problem in a simple supply chain where a single supplier produces multiple components on a flexible flow line (FFL) and delivers them directly to an assembly facility (AF). It is assumed that all of parameters such as demand rates for the components are deterministic and constant over a finite planning horizon. The main objective is to find a lot and delivery schedule that would minimize the average of holding, setup, and transportation costs per unit time for the supply chain. We develop a new mixed integer nonlinear program (MINLP) and an optimal enumeration method to solve the problem. Due to difficulty of obtaining the optimal solution in medium and large-scaled problems, a hybrid genetic algorithm (HGA) is also developed. The proposed HGA incorporates a neighborhood search (NS) into a basic genetic algorithm that enables the algorithm to perform genetic search over the subspace of local optima. The two proposed solution methods are compared on randomly generated problems, and computational results show that the performance of HGA is very promising because it is able to find an optimal or near-optimal solution for majority of the test problems.     

101 Activities for Teaching Creativity and Problem Solving,Arthur B. VanGundy,Pfeiffer, J. Wiley,CA, USA (2004), p. xi + 391, £41.95, ISBN: 0-7879-7402-1

Many web sites (e.g. Hotmail, Yahoo) provide free services to the users while generating revenues from advertising. Advertising revenue is, therefore, critical for these sites. This in turn raises the question, how should advertisements at a web site be scheduled in a planning horizon to maximize revenue. Advertisements on the web are specified by geometry and display frequency and both of these factors need to be considered in developing a solution to the advertisement scheduling problem. Since this problem belongs to the class of NP-hard problems, we first develop a heuristic called LSMF to solve the problem. This heuristic is then combined with a genetic algorithm (GA) to develop a hybrid GA. The hybrid GA solution is first compared with the upper bound obtained by running CPLEX for the integer programming formulation of the problem. It is then also compared with an existing algorithm proposed in the literature. Our computational results show that the hybrid GA performs exceptionally well in the sense that it provides optimal or near optimal solution for a wide range of problem instances of realistic sizes and the improvements over existing algorithm are substantial. Finally we present a case study to illustrate how revenue could be significantly increased with a small improvement in the advertisement schedule. It is the first such study in this setup.     

Project scheduling problem with mixed uncertainty of randomness and fuzziness

Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers project scheduling problem with mixed uncertainty of randomness and fuzziness, where activity duration times are assumed to be random fuzzy variables. Three types of random fuzzy models as expected cost minimization model, (α, β)-cost minimization model and chance maximization model are built to meet different management requirements. Random fuzzy simulations for some uncertain functions are given and embedded into genetic algorithm to design a hybrid intelligent algorithm. Finally, some numerical experiments are given for the sake of illustration of the effectiveness of the algorithm.     

Two-Machine Flow Shop Scheduling with Nonregular Criteria

We consider a two-machine flow shop problem with a common due date where the objective is to minimize the sum of functions which penalize early as well as tardy completion of jobs. Since the problem is NP-hard in the strong sense, we investigate some general properties of optimal schedules for the problem, we develop lower and upper bounds, derive dominance criteria, and propose an enumerative algorithm for finding an optimal schedule. The performance of the proposed algorithm together with the influence of the individual components is thoroughly discussed.     

基于支配强度的NSGA Ⅱ改进算法在研究生招生面试分组中的应用

针对研究生招生面试分组这一NP难问题,提出了一种以分组遗传算法(GGA)和基于支配强度的改进NSGA Ⅱ算法为基础的混合多目标分组遗传算法。通过基于矩阵编码的多交叉/多变异算子、次精英化的初始化种群策略以及改进的帕累托支配关系,解决了经典NSGA Ⅱ算法在该问题中的收敛速度慢、易陷入局部最优的问题。仿真实验结果表明,该方法只需进行较少代数(不超过100代)的进化,即可获得最优解集,满足了快速分组的用户偏好。     

An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters

Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper.     

Integrated production planning and scheduling for a mixed batch job-shop based on alternant iterative genetic algorithm

An integrated optimization production planning and scheduling based on alternant iterative genetic algorithm is proposed here. The operation constraints to ensure batch production successively are determined in the first place. Then an integrated production planning and scheduling model is formulated based on non-linear mixed integer programming. An alternant iterative method by hybrid genetic algorithm (AIHGA) is employed to solve it, which operates by the following steps: a plan is given to find a schedule by hybrid genetic algorithm; in turn, a schedule is given to find a new plan using another hybrid genetic algorithm. Two hybrid genetic algorithms are alternately run to optimize the plan and schedule simultaneously. Finally a comparison is made between AIHGA and a monolithic optimization method based on hybrid genetic algorithm (MOHGA). Computational results show that AIHGA is of higher convergence speed and better performance than MOHGA. And the objective values of the former are an average of 12.2% less than those of the latter in the same running time.     

求解带时间窗车辆路径问题的混合Memetic算法

为提高带时间窗车辆路径问题的求解精度和求解效率,设计了一种混合Memetic算法。采用基于时间窗升序排列的混合插入法构造初始种群,提高解质量的同时兼顾多样性,扩大搜索空间;任意选择组成父代种群,以维持搜索空间;运用简化的变邻域搜索进行局部开发,引入邻域半径减少策略提高开发效率,约束放松机制开放局部空间;以弧为对象,增加种群向当前最优解和全局最优解的后学习过程。实验结果表明,所提出的算法具有较好的寻优精度和稳定性,能搜索到更好的路径长度结果,更新了现有研究在最短路径长度的目标函数上的下限。     

阻塞混流生产机器人制造单元调度问题可行解性质研究

针对阻塞混流生产机器人制造单元调度问题的可行解性质进行研究。首先,定义了机器人活动,将机器人运行排序和工件加工排序转化为机器人活动调度,将二维调度问题转化为一维调度问题;其次,提出了可行机器人活动调度概念,给出了几个等价定义;最后,给出了可行机器人活动调度经过一定变换,仍然是可行调度的条件。这些性质为优化算法的设计提供了理论基础。     

Some properties of optimal schedules for the Johnson problem with preemption

The properties are under study of the optimal schedules for the NP-hard Johnson problem with preemption. The length of an optimal schedule is shown to coincide with the total length of some subset of operations. These properties demonstrate that the optimal schedule of every instance of the problem can be found by a greedy algorithm (for the properly defined priority orders of operations on machines). This yields the first exact algorithm for the problem known since 1978. It is shown that the number of interruptions in a greedy schedule (and therefore, in the optimal schedule) is at most the number of operations, which is significantly better than the available upper bounds on the number of interruptions in the optimal schedule.     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

Heuristic Techniques for Single Line Train Scheduling

Optimising a train schedule on a single line track is known to be NP-Hard with respect to the number of conflicts in the schedule. This makes it difficult to determine optimum solutions to real life problems in reasonable time and raises the need for good heuristic techniques. The heuristics applied and compared in this paper are a local search heuristic with an improved neighbourhood structure, genetic algorithms, tabu search and two hybrid algorithms. When no time constraints are enforced on solution time, the genetic and hybrid algorithms were within five percent of the optimal solution for at least ninety percent of the test problems.     

Optimal coordination of directional over-current relays using informative differential evolution algorithm

Growing interconnection in distribution system creates new problem for protection engineers. Particularly the design of overcurrent relay coordination in such system is an independent area of research. With the availability of new artificial based optimization algorithm relay coordination research gain a new momentum. Well established artificial based optimization algorithm such as genetic and particle swam optimization are successfully applied for such applications. This paper discusses the application of informative differential evolution algorithm with self adaptive re-clustering technique for selection of TDS and PSM for optimal coordination of directional overcurrent relays. Both continuous as well as discrete version of informative differential evolution algorithm are used for optimization of relay setting. Proper combination of backup relays for each primary relay are identified by using LINKNET graph theory approach. Coordination of directional overcurrent is developed for 9 bus and IEEE 30 bus distribution systems. The aim of problem is to minimize the total operating time of primary relays and eliminate the miscoordination among the primary and backup relay pairs. Discrete types of settings for electromechanical types of relay are also discussed in this paper. Moreover, the relay coordination problem is modified for providing optimal coordination time interval between 0.2 and 0.8 s among all primary and backup relays pairs. The results are compared with hybrid of genetic algorithm – nonlinear programming and sequential quadratic programming. Digsilient power factory software is used for verification of result.     

Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system

A Vendor Managed Inventory (VMI) system consists of a manufacturing vendor and a number of retailers. In such a system, it is essential for the vendor to optimally determine retailer selection and other related decisions, such as the product’s replenishment cycle time and the wholesale price, in order to maximize his profit. Meanwhile, each retailer’s decisions on her willingness to enter the system and retail price are simultaneously considered in the retailer selection process. However, the above interactive decision making is complex and the available studies on interactive retailer selection are scarce. In this study, we formulate the retailer selection problem as a Stackelberg game model to help the manufacturer, as a vendor, optimally select his retailers to form a VMI system. This model is non-linear, mixed-integer, game-theoretic, and analytically intractable. Therefore, we further develop a hybrid algorithm for effectively and efficiently solving the developed model. The hybrid algorithm combines dynamic programming (DP), genetic algorithm (GA) and analytical methods. As demonstrated by our numerical studies, the optimal retailer selection can increase the manufacturer’s profit by up to 90% and the selected retailers’ profits significantly compared to non-selection strategy. The proposed hybrid algorithm can solve the model within a minute for a problem with 100 candidate retailers, whereas a pure GA has to take more than 1 h to solve a small sized problem of 20 candidate retailers achieving an objective value no worse than that obtained by the hybrid algorithm.     

New multi-objective method to solve reentrant hybrid flow shop scheduling problem

This paper focuses on the multi-objective resolution of a reentrant hybrid flow shop scheduling problem (RHFS). In our case the two objectives are: the maximization of the utilization rate of the bottleneck and the minimization of the maximum completion time. This problem is solved with a new multi-objective genetic algorithm called L-NSGA which uses the Lorenz dominance relationship. The results of L-NSGA are compared with NSGA2, SPEA2 and an exact method. A stochastic model of the system is proposed and used with a discrete event simulation module. A test protocol is applied to compare the four methods on various configurations of the problem. The comparison is established using two standard multi-objective metrics. The Lorenz dominance relationship provides a stronger selection than the Pareto dominance and gives better results than the latter. The computational tests show that L-NSGA provides better solutions than NSGA2 and SPEA2; moreover, its solutions are closer to the optimal front. The efficiency of our method is verified in an industrial field-experiment.     

Hybrid flow shop scheduling with sequence dependent family setup time and uncertain due dates

This paper studies the scheduling problem in hybrid flow shop (HFS) environment. The sequence dependent family setup time (SDFST) is concerned with minimization of makespan and total tardiness. Production environments in real world include innumerable cases of uncertainty and stochasticity of events and a suitable scheduling model should consider them. Hence, in this paper, due date is assumed to be uncertain and its data follow a normal distribution. Since the proposed problem is NP-hard, two metaheuristic algorithms are presented based on genetic algorithm, namely: Non-dominated Sorting Genetic Algorithm (NSGAII) and Multi Objective Genetic Algorithm (MOGA). The quantitative and qualitative results of these two algorithms have been compared in different dimensions with multi phase genetic algorithm (MPGA) used in literature review. Experimental results indicate that the NSGAII performs very well when compared against MOGA and MPGA in a considerably shorter time.     

A two-stage hybrid optimization for honeycomb-type cellular structures under out-of-plane dynamic impact

Honeycomb structures with better balance between lightweight and crashworthiness have aroused growing attentions. However, structural parameters design by traditional optimization algorithm in small design space is not sufficient to significantly enhance the specific energy absorption (SEA) with the lower peak acceleration (a_max). In this paper, a two-stage hybrid optimization for honeycomb-type cellular parameters is proposed to achieve rapid positioning of design space and significantly increase crashworthiness in a larger variable domain under out-of-plane dynamic impact. In stage I, a Taguchi-based grey correlation discrete optimization, combining Taguchi analysis, grey relational analysis, analysis of variance (ANOVA) with grey entropy measurement, is performed to determine the initial optimal value with a higher robustness and the significant influence variables. In stage II, a multi-objective design technique, namely non-nominated sorting genetic algorithm II based on surrogated model, is adopted to maximize the SEA and minimize the a_max in a relatively small design domain. And it is found that the proposed two-stage hybrid method can broaden the optimal design space compared to that of traditional method attributable to its center point positioned by stage I. And the final optimization based on the proposed strategy is superior to the original structure, i.e., the SEA is increased by 47.55% and the a_max is decreased by 80.8%. Therefore, the proposed algorithm can also be used to solve other more complicated engineering problems in a large design space with insightful design data.     

Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time

This paper considers the problem of scheduling a given number of jobs on a single machine to minimize the sum of maximum earliness and maximum tardiness when sequence-dependent setup times exist (1∣ST _sd ∣ET_max). In this paper, an optimal branch-and-bound algorithm is developed that involves the implementation of lower and upper bounding procedures as well as three dominance rules. For solving problems containing large numbers of jobs, a polynomial time-bounded heuristic algorithm is also proposed. Computational experiments demonstrate the effectiveness of the bounding and dominance rules in achieving optimal solutions in more than 97% of the instances.     

Multiple crane scheduling in a batch annealing process with no-delay constraints for machine unloading

In this work, we focus on the scheduling of multi-crane operations in an iron and steel enterprise for a two-stage batch annealing process. The first stage is the heating process, and the second stage is the cooling process. To start the heating (cooling) stage, a special machine called a furnace (cooler) must be loaded. The real constraints of no-delay machine unloading are defined as follows: once the heating (cooling) is completed, the furnace (cooler) must be unloaded by crane immediately. The goal is to schedule limited machines (furnaces and coolers) operated by multiple cranes to minimize the completion time of the last annealed coil (makespan). We formulate a mixed-integer linear programming model to address this problem. Certain feasible properties are identified to avoid crane conflicts and ensure that the machine unloading no-delay constraints are met. Based on these necessary conditions, we then present a heuristic algorithm with running time in connection with the number of cranes, coils and machines. A lower bound to the problem is also developed. Through theoretical analysis, we show the worst-case bound of our heuristic algorithm. The average performances of the solution approaches are computationally evaluated. The computational results show that the proposed heuristic algorithm is capable of generating good quality solutions.