A memetic algorithm based on a NSGAII scheme for the flexible job-shop scheduling problem

The Flexible Job-Shop Scheduling Problem is concerned with the determination of a sequence of jobs, consisting of many operations, on different machines, satisfying several parallel goals. We introduce a Memetic Algorithm, based on the NSGAII (Non-Dominated Sorting Genetic Algorithm II) acting on two chromosomes, to solve this problem. The algorithm adds, to the genetic stage, a local search procedure (Simulated Annealing). We have assessed its efficiency by running the algorithm on multiple objective instances of the problem. We draw statistics from those runs, which indicate that this Memetic Algorithm yields good and low-cost solutions.     

Solving multi-objective parallel machine scheduling problem by a modified NSGA-II

In this paper, we modify a Multi-Objective Evolutionary Algorithm, known as Nondominated sorting Genetic Algorithm-II (NSGA-II) for a parallel machine scheduling problem with three objectives. The objectives are – (1) minimization of total cost due tardiness, (2) minimization of the deterioration cost and (3) minimization of makespan. The formulated problem has been solved by three Multi-Objective Evolutionary Algorithms which are: (1) the original NSGA-II (Non-dominated Sorting Genetic Algorithm–II), (2) SPEA2 (Strength Pareto Evolutionary Algorithm-2) and (3) a modified version of NSGA-II as proposed in this paper. A new mutation algorithm has also been proposed depending on the type of problem and embedded in the modified NSGA-II. The results of the three algorithms have been compared and conclusions have been drawn. The modified NSGA-II is observed to perform better than the original NSGA-II. Besides, the proposed mutation algorithm also works effectively, as evident from the experimental results.     

New fitness sharing approach for multi-objective genetic algorithms

A novel fitness sharing method for MOGA (Multi-Objective Genetic Algorithm) is proposed by combining a new sharing function and sided degradations in the sharing process, with preference to either of two close solutions. The modified MOGA adopting the new sharing approach is named as MOGAS. Three different variants of MOGAS are tested; MOGASc, MOGASp and MOGASd, favoring children over parents, parents over children and solutions closer to the ideal point, respectively. The variants of MOGAS are compared with MOGA and other state-of-the-art multi-objective evolutionary algorithms such as IBEA, HypE, NSGA-II and SPEA2. The new method shows significant performance improvements from MOGA and is very competitive against other Evolutionary Multi-objective Algorithms (EMOAs) for the ZDT and DTLZ test functions with two and three objectives. Among the three variants MOGASd is found to give the best results for the test problems.     

The use of dynamic programming in genetic algorithms for permutation problems

To deal with computationally hard problems, approximate algorithms are used to provide reasonably good solutions in practical time. Genetic algorithms are an example of the meta-heuristics which were recently introduced and which have been successfully applied to a variety of problems. We propose to use dynamic programming in the process of obtaining new generation solutions in the genetic algorithm, and call it a genetic DP algorithm. To evaluate the effectiveness of this approach, we choose three representative combinatorial optimization problems, the single machine scheduling problem, the optimal linear arrangement problem and the traveling salesman problem, all of which ask to compute optimum permutations of n objects and are known to be NP-hard. Computational results for randomly generated problem instances exhibit encouraging features of genetic DP algorithms.     

Space-time tradeoffs in negative cycle detection - An empirical analysis of the Stressing Algorithm

This paper discusses space-time tradeoffs associated with algorithms for the problem of detecting negative cost cycles in networks (NCCD). NCCD is one of the more ubiquitous problems in computer science and operations research, with applications ranging from program verification and real-time scheduling to image segmentation and shortest path identification. Typical algorithmic analysis, whether theoretical or empirical, focuses almost exclusively on the running time of the algorithm. However, there exist applications in which space is just as important a parameter as time is. This is especially true when the problem instances are very large, as is the case in program verification. Consequently, an algorithm that minimizes running time while ignoring the space overhead may be impractical. In this paper, we analyze a number of the more common algorithms for NCCD from the perspectives of both time and space, with a view towards providing a space-time tradeoff for the practitioner. All the algorithms discussed in this paper (with the exception of Network Simplex) run in O(m·n) time on a network with m arcs and n vertices; however, their space requirements range from O(1) (Stressing Algorithm) to Ω(n) (all the Bellman-Ford and Network Simplex variants). Our empirical results demonstrate that in the cases where space is paramount, the Stressing Algorithm is a useful alternative to the Bellman-Ford variants.     

Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems

In this paper, a novel genetic algorithm is developed by generating artificial chromosomes with probability control to solve the machine scheduling problems. Generating artificial chromosomes for Genetic Algorithm (ACGA) is closely related to Evolutionary Algorithms Based on Probabilistic Models (EAPM). The artificial chromosomes are generated by a probability model that extracts the gene information from current population. ACGA is considered as a hybrid algorithm because both the conventional genetic operators and a probability model are integrated. The ACGA proposed in this paper, further employs the “evaporation concept” applied in Ant Colony Optimization (ACO) to solve the permutation flowshop problem. The “evaporation concept” is used to reduce the effect of past experience and to explore new alternative solutions. In this paper, we propose three different methods for the probability of evaporation. This probability of evaporation is applied as soon as a job is assigned to a position in the permutation flowshop problem. Experimental results show that our ACGA with the evaporation concept gives better performance than some algorithms in the literature.     

Total completion time with makespan constraint in no-wait flowshops with setup times

The m-machine no-wait flowshop scheduling problem with the objective of minimizing total completion time subject to the constraint that the makespan value is not greater than a certain value is addressed in this paper. Setup times are considered non-zero values, and thus, setup times are treated as separate from processing times. Several recent algorithms, an insertion algorithm, two genetic algorithms, three simulated annealing algorithms, two cloud theory-based simulated annealing algorithms, and a differential evolution algorithm are adapted and proposed for the problem. An extensive computational analysis has been conducted for the evaluation of the proposed algorithms. The computational analysis indicates that one of the nine proposed algorithms, one of the simulated annealing algorithms (ISA-2), performs much better than the others under the same computational time. Moreover, the analysis indicates that the algorithm ISA-2 performs significantly better than the earlier existing best algorithm. Specifically, the best performing algorithm, ISA-2, proposed in this paper reduces the error of the existing best algorithm in the literature by at least 90% under the same computational time. All the results have been statistically tested.     

Optimal Design of 2 DOF Parallel Kinematics Machines

The aim of this paper is to show the usefulness of the multicriteria approach to optimize the Parallel Kinematic Machines (PKM). Variations of the kinematic performances index remain not constant throughout workspace. Aiming to deal at the same time with multiple criteria in optimal design of PKM, we have developed a Multi-Objective Genetic Algorithm (MOGA) using concepts of Pareto optimality and niching techniques. The obtained results have shown that the use of MOGA in such kind of optimization problem enhances the quality of the optimization outcome, providing a better and more realistic support for the decision maker. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Managing pharmaceuticals delivery service using a hybrid particle swarm intelligence approach

Medicines or drugs have unique characteristics of short life cycle, small size, light weight, restrictive distribution time and the need of temperature and humidity control (selected items only). Thus, logistics companies often use different types of vehicles with different carrying capacities, and considering fixed and variable costs in service delivery, which make the vehicle assignment and route optimization more complicated. In this study, we formulate the problem to a multi-type vehicle assignment and mixed integer programming route optimization model with fixed fleet size under the constraints of distribution time and carrying capacity. Given non-deterministic polynomial hard and optimal algorithm can only be used to solve small-size problem, a hybrid particle swarm intelligence (PSI) heuristic approach, which adopts the crossover and mutation operators from genetic algorithm and 2-opt local search strategy, is proposed to solve the problem. We also adapt a principle based on cost network and Dijkstra’s algorithm for vehicle scheduling to balance the distribution time limit and the high loading rate. We verify the relative performance of the proposed method against several known optimal or heuristic solutions using a standard data set for heterogeneous fleet vehicle routing problem. Additionally, we compare the relative performance of our proposed Hybrid PSI algorithm with two intelligent-based algorithms, Hybrid Population Heuristic algorithm and Improved Genetic Algorithm, using a real-world data set to illustrate the practical and validity of the model and algorithm.

     

急件订单干扰下虚拟单元重调度

虚拟单元生产中,针对急件订单干扰情况,研究了考虑序位相似性,即尽量保持初始工序的加工次序的虚拟单元重调度问题。为了应对急件订单干扰,设置了各工件工序可用机器集合和相应的加工时间集合,构建了以序位相似性最大和急件订单完工时间、系统总流程时间最短为目标的多目标非线性整数规划模型。针对模型自身特征,采用了遗传—蚁群算法相结合的优化算法求解模型。最后,以船舶实际生产为例,验证了模型的可行和优越性,以及算法的有效性。     

Swarm approach based on gravity for optimizing energy savings in grid systems

Execution time optimization is one of the most important objectives to accomplish for experiments launched on grid environments. However, the computing community is becoming more conscious about energy savings, seeking their optimization. In this work, both execution time and energy consumption are optimized through two swarm and multi-objective algorithms based on both physics and biology fields. On the one hand, multi-objective gravitational search algorithm (MOGSA) is inspired by the gravity forces between the planet masses. On the other hand, Multi-Objective Firefly Algorithm is based on the light attraction between the fireflies. These swarm algorithms are compared with the standard multi-objective algorithm non-dominated sorting genetic algorithm II to study their efficiency as multi-objective algorithms. Moreover, the best algorithm proposed, MOGSA, is compared with MOHEFT (a multi-objective version of one of the most-used algorithms in workflow scheduling, HEFT), and also with two real grid schedulers: Workload Management System and deadline budget constraint. Results show the superior performance of MOGSA regarding the others.     

基于运行时间预测的枢纽内多线路协调调度研究

针对传统调度模型预见性不强的弱点,提出一个基于支持向量机(SVM)的公交车辆到达枢纽时间的预测模型,基于该模型构建以所有乘客节约时间最大为目标的调度模型,动态协调公交车辆从枢纽的发车时间,并基于遗传算法对该模型进行求解。最后,我们以大连市沙河口火车站枢纽为实例,对该模型和算法的可行性进行了检验,结果显示,本文提出的调度方法优于传统调度策略。     

Crossdocking—JIT scheduling with time windows

In this paper, we study a problem central to crossdocking that aims to eliminate or minimize storage and order picking activity using JIT scheduling. The problem is modelled naturally as a machine scheduling problem. As the problem is NP-hard, and for real-time applications, we designed and implemented two heuristics. The first uses Squeaky Wheel Optimization embedded in a Genetic Algorithm and the second uses Linear Programming within a Genetic Algorithm. Both heuristics offer good solutions in experiments where comparisons are made with the CPLEX solver.     

Solving multiobjective,multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

In this paper, we solve instances of the multiobjective multiconstraint (or multidimensional) knapsack problem (MOMCKP) from the literature, with three objective functions and three constraints. We use exact as well as approximate algorithms. The exact algorithm is a properly modified version of the multicriteria branch and bound (MCBB) algorithm, which is further customized by suitable heuristics. Three branching heuristics and a more general purpose composite branching and construction heuristic are devised. Comparison is made to the published results from another exact algorithm, the adaptive ε-constraint method [Laumanns, M., Thiele, L., Zitzler, E., 2006. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169, 932–942], using the same data sets. Furthermore, the same problems are solved using standard multiobjective evolutionary algorithms (MOEA), namely, the SPEA2 and the NSGAII. The results from the exact case show that the branching heuristics greatly improve the performance of the MCBB algorithm, which becomes faster than the adaptive ε -constraint. Regarding the performance of the MOEA algorithms in the specific problems, SPEA2 outperforms NSGAII in the degree of approximation of the Pareto front, as measured by the coverage metric (especially for the largest instance).     

Simulated annealing and genetic algorithms for minimizing mean flow time in an open shop

This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Bräsel et al. [H. Bräsel, A. Herms, M. Mörig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30 000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.     

Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems

The majority of Combinatorial Optimization Problems (COPs) are defined in the discrete space. Hence, proposing an efficient algorithm to solve the problems has become an attractive subject in recent years. In this paper, a meta-heuristic algorithm based on Binary Particle Swarm Algorithm (BPSO) and the governing Newtonian motion laws, so-called Binary Accelerated Particle Swarm Algorithm (BAPSA) is offered for discrete search spaces. The method is presented in two global and local topologies and evaluated on the 0–1 Multidimensional Knapsack Problem (MKP) as a famous problem in the class of COPs and NP-hard problems. Besides, the results are compared with BPSO for both global and local topologies as well as Genetic Algorithm (GA). We applied three methods of Penalty Function (PF) technique, Check-and-Drop (CD) and Improved Check-and-Repair Operator (ICRO) algorithms to solve the problem of infeasible solutions in the 0–1 MKP. Experimental results show that the proposed methods have better performance than BPSO and GA especially when ICRO algorithm is applied to convert infeasible solutions to feasible ones.     

Minimizing the total completion time on a single machine with the learning effect and multiple availability constraints

This paper considers a single machine scheduling problem with the learning effect and multiple availability constraints that minimizes the total completion time. To solve this problem, a new binary integer programming model is presented, and a branch-and-bound algorithm is also developed for solving the given problem optimally. Since the problem is strongly NP-hard, to find the near-optimal solution for large-sized problems within a reasonable time, two meta-heuristics; namely, genetic algorithm and simulated annealing are developed. Finally, the computational results are provided to compare the result of the binary integer programming, branch-and-bound algorithm, genetic algorithm and simulated annealing. Then, the efficiency of the proposed algorithms is discussed.     

Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms

Evolutionary Algorithms (EAs) are emerging as competitive and reliable techniques for several optimization tasks. Juxtapositioning their higher-level and implicit correspondence; it is provocative to query if one optimization algorithm can benefit from another by studying underlying similarities and dissimilarities. This paper establishes a clear and fundamental algorithmic linking between particle swarm optimization (PSO) algorithm and genetic algorithms (GAs). Specifically, we select the task of solving unimodal optimization problems, and demonstrate that key algorithmic features of an effective Generalized Generation Gap based Genetic Algorithm can be introduced into the PSO by leveraging this algorithmic linking while significantly enhance the PSO’s performance. However, the goal of this paper is not to solve unimodal problems, neither is to demonstrate that the modified PSO algorithm resembles a GA, but to highlight the concept of algorithmic linking in an attempt towards designing efficient optimization algorithms. We intend to emphasize that the evolutionary and other optimization researchers should direct more efforts in establishing equivalence between different genetic, evolutionary and other nature-inspired or non-traditional algorithms. In addition to achieving performance gains, such an exercise shall deepen the understanding and scope of various operators from different paradigms in Evolutionary Computation (EC) and other optimization methods.     

EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.     

A Robust Genetic Algorithm for Resource Allocation in Project Scheduling

Genetic algorithms have been applied to many different optimization problems and they are one of the most promising metaheuristics. However, there are few published studies concerning the design of efficient genetic algorithms for resource allocation in project scheduling. In this work we present a robust genetic algorithm for the single-mode resource constrained project scheduling problem. We propose a new representation for the solutions, based on the standard activity list representation and develop new crossover techniques with good performance in a wide sample of projects. Through an extensive computational experiment, using standard sets of project instances, we evaluate our genetic algorithm and demonstrate that our approach outperforms the best algorithms appearing in the literature.