Heuristic framework for the resource constrained multi-project scheduling problem

Real world scheduling problems can be affected by diverse and conflicting goals. Some scheduling problems are bounded with limited resources and represent a considerable challenge to planners. When multiple projects are involved, scheduling problems become even more complex and difficult to resolve. Because of the combinatory explosions and unrealistic assumptions, traditional management sciences techniques such as PERT, CPM, and a host of similar project schedulers are very limited to special cases of scheduling problems. Recent developments of artificial intelligence (AI) and knowledge engineering techniques have made the development of expert systems which can be driven by scheduling heuristics to resolve problems associated with the traditional optimization techniques by giving “better” rather than “best” solutions. This paper presents the conceptual framework and development strategy for an expert system in multi-project scheduling domains. This paper will also present a practical application of the scheduling system.     

基于BS-GA的资源约束多项目调度问题研究

针对资源约束的多项目调度问题(RCMPSP),考虑到项目、项目任务和资源各自之间的差异性,引入项目权重系数、活动质量因子和资源能力系数3个概念,提出了一个工期与质量的均衡优化模型.该模型根据资源的配置计划,确定了项目任务的资源平均能力系数,然后用项目权重系数和活动质量因子计算出多项目的单位工期时间内资源平均能力系数,利...     

Solving multiple processor and multiple resource constrained scheduling problems using a genetic algorithm approach

We consider the multiprocessor scheduling of unit time tasks with precedence constraints and finite set of limited resources. Each task demands some amount of resources for its execution and the total demand for each kind of resources must not exceed a certain limit at any instant of time. Our objective is to find out the minimum time schedule which satisfies the partial orders and the resource usage constraints. We have applied Genetic Algorithm for the present problem. We have shown that the Genetic Algorithm is quite superior to the First Fit Decreasing method.     

Hybrid genetic algorithms for constrained placement problems

When solving real-world problems, often the main task is to find a proper representation for the candidate solutions. Strings of elementary data types with standard genetic operators may tend to create infeasible individuals during the search because of the discrete and often constrained search space. This article introduces a generally applicable representation for 2D combinatorial placement and packing problems. Empirical results are presented for two constrained placement problems, the facility layout problem and the generation of VLSI macro-cell layouts. For multiobjective optimization problems, common approaches often deal with the different objectives in different phases and thus are unable to efficiently solve the global problem. Due to a tree structured genotype representation and hybrid, problem-specific operators, the proposed approach is able to deal with different constraints and objectives in one optimization step     

Multi-operator based evolutionary algorithms for solving constrained optimization problems

Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms.     

Efficient genetic algorithms using discretization scheduling

In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling.     

Modified genetic algorithms for solving fuzzy flow shop scheduling problems and their implementation with CUDA

In this paper we propose an improved algorithm to search optimal solutions to the flow shop scheduling problems with fuzzy processing times and fuzzy due dates. A longest common substring method is proposed to combine with the random key method. Numerical simulation shows that longest common substring method combined with rearranging mating method improves the search efficiency of genetic algorithm in this problem. For application in large-sized problems, we also enhance this modified algorithm by CUDA based parallel computation. Numerical experiments show that the performances of the CUDA program on GPU compare favorably to the traditional programs on CPU. Based on the modified algorithm invoking with CUDA scheme, we can search satisfied solutions to the fuzzy flow shop scheduling problems with high performance.     

Heuristic algorithms for solving earliness-tardiness scheduling problems with machine vacations

The earliness and tardiness (E/T) penalty problem in scheduling gained more importance in part due to its application in Just-In-Time (JIT) production system. Inorder to meet JIT production schedules preventive maintenance plan must be in place. During the maintenance periods machine is not available for processing. The time duration planned for preventive maintenance or meal breaks is called machine vacation. Incorporating E/T penalty and machine vacation a single machine scheduling model is developed. Heuristic methods for solving this problem and computational results are also presented.     

Precast production scheduling using multi-objective genetic algorithms

The goal of production scheduling is to achieve a profitable balance among on-time delivery, short customer lead time, and maximum utilization of resources. However, current practices in precast production scheduling are fairly basic, depending heavily on experience, thereby resulting in inefficient resource utilization and late delivery. Moreover, previous methods ignoring buffer size between stations typically induce unfeasible schedules. Certain computational techniques have been proven effective in scheduling. To enhance precast production scheduling, this research develops a multi-objective precast production scheduling model (MOPPSM). In the model, production resources and buffer size between stations are considered. A multi-objective genetic algorithm is then developed to search for optimum solutions with minimum makespan and tardiness penalties. The performance of the proposed model is validated by using five case studies. The experimental results show that the MOPPSM can successfully search for optimum precast production schedules. Furthermore, considering buffer sizes between stations is crucial for acquiring reasonable and feasible precast production schedules.     

Parallel machine scheduling problems using memetic algorithms

In this paper, we investigate how to apply the hybrid genetic algorithms (the memetic algorithms) to solve the parallel machine scheduling problem. There are two essential issues to be dealt with for all kinds of parallel machine scheduling problems: job partition among machines and job sequence within each machine. The basic idea of the proposed method is that (a) use the genetic algorithms to evolve the job partition and then (b) apply a local optimizer to adjust the job permutation to push each chromosome climb to his local optima. Preliminary computational experiments demonstrate that the hybrid genetic algorithm outperforms the genetic algorithms and the conventional heuristics.     

Multi-level parallel chaotic Jaya optimization algorithms for solving constrained engineering design problems

The Journal of Supercomputing - Several heuristic optimization algorithms have been applied to solve engineering problems. Most of these algorithms are based on populations that evolve according to...     

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

Two-dimensional packing problems using genetic algorithms

This paper presents a technique for applying genetic algorithms for the two-dimensional packing problem. The approach is applicable to not only convex shaped objects, but can also accommodate any type of concave and complex shaped objects including objects with holes. In this approach, a new concept of a two-dimensional genetic chromosome is introduced. The total layout space is divided into a finite number of cells for mapping it into this 2D genetic algorithm chromosome. The mutation and crossover operators have been modified and are applied in conjunction with connectivity analysis for the objects to reduce the creation of faulty generations. A new feature has been added to the Genetic Algorithm (GA) in the form of a new operator called compaction. Several examples of GA-based layout are presented.     

Multi-criteria sequence-dependent job shop scheduling using genetic algorithms

Real world job shops have to contend with jobs due on different days, material ready times that vary, reentrant workflows and sequence-dependent setup times. The problem is even more complex because businesses often judge solution goodness according to multiple competing criteria. Producing an optimal solution would be time consuming to the point of rendering the result meaningless. Commonly used heuristics such as shortest processing time (SPT) and earliest due date (EDD) can be used to calculate a feasible schedule quickly, but usually do not produce schedules that are close to optimal in these job shop environments. We demonstrate that genetic algorithms (GA) can be used to produce solutions in times comparable to common heuristics but closer to optimal. Changing criteria or their relative weights does not affect the running time, nor does it require programming changes. Therefore, a GA can be easily applied and modified for a variety of production optimization criteria in a job shop environment that includes sequence-dependent setup times.     

Dynamic scheduling of manufacturing job shops using genetic algorithms

Most job shop scheduling methods reported in the literature usually address the static scheduling problem. These methods do not consider multiple criteria, nor do they accommodate alternate resources to process a job operation. In this paper, a scheduling method based on genetic algorithms is developed and it addresses all the shortcomings mentioned above. The genetic algorithms approach is a schedule permutation approach that systematically permutes an initial pool of randomly generated schedules to return the best schedule found to date.A dynamic scheduling problem was designed to closely reflect a real job shop scheduling environment. Two performance measures, namely mean job tardiness and mean job cost, were used to demonstrate multiple criteria scheduling. To span a varied job shop environment, three factors were identified and varied between two levels each. The results of this extensive simulation study indicate that the genetic algorithms scheduling approach produces better scheduling performance in comparison to several common dispatching rules.     

Solving decentralized POMDP problems using genetic algorithms

The Decentralized Partially Observable Markov Decision Process (DEC-POMDP) model addresses the multiagent planning problem in partially observable environments. Due to its high computational complexity, in general only very small size problems can be solved exactly and most researchers concentrate on approximate solution algorithms to handle more complex cases. However, many approximate solution techniques can handle large size problems only for small horizons due to their exponential memory requirements for representing the policies and searching the policy space. In this study, we offer an approximate solution algorithm called GA-FSC that uses finite state controllers (FSC) to represent a finite-horizon DEC-POMDP policy and searches the policy space using genetic algorithms. We encode FSCs into chromosomes and we use one exact and one approximate technique to calculate the fitness of the chromosomes. The exact calculation technique helps us to obtain better quality solutions with the cost of more processing time compared to the approximate fitness calculation. Our method is able to replicate the best results reported so far in the literature in most cases and it is also able to extend the reported horizons further in almost all cases when compared to optimal approaches.     

Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. In this paper, we focus on multi-criteria human resource allocation for solving multistage combinatorial optimization problem. Hence we tackle this problem via a multistage decision-making model. A multistage decision-making model is similar to a complex problem solving, in which a suitable sequence of decisions is to be found. The task can be interpreted as a series of interactions between a decision maker and an outside world, at each stage of which some decisions are available and their immediate effect can be easily computed. Eventually, goals would be reached due to the found of optimized variables. In order to obtain a set of Pareto solutions efficiently, we propose a multiobjective hybrid genetic algorithm (mohGA) approach based on the multistage decision-making model for solving combinatorial optimization problems. According to the proposed method, we apply the mohGA to seek feasible solutions for all stages. The effectiveness of the proposed algorithm was validated by its application to an illustrative example dealing with multiobjective resource allocation problem.     

利用遗传算法求解静态与动态背包问题的研究

为了有效处理遗传算法在求解静态与动态背包问题时产生非正常编码个体的问题,在分析已有处理方法不足的基础上,基于贪心策略提出了一种贪心修正算子与贪心优化算子相结合的新方法,并将该方法与遗传算法相融合给出了求解静态与动态背包问题的有效算法.仿真计算结果表明,在求解静态与动态背包问题时,利用所提出的新方法不仅可以解决非正常编码个体的问题,而且还能够显著提高个体所对应的可行解的质量,极大地改善了遗传算法的求解效果.     

Some algorithms of solving minimax multiprocessor scheduling problem

A problem of constructing schedules of minimal length without interrupts and switches is considered for a multiprocessor system, in which the job execution time depends on the processor assigned to the job. To solve this problem, the branch and bound method is developed. The method is based on efficient algorithms for calculating lower and upper bounds of minimal length of the schedule. For the particular case when processors are identical, their number is fixed and the directive deadline is given, a pseudo-polynomial algorithm is proposed for constructing the admissible schedule. The number of processors required for efficient parallelizing of the algorithm is found.