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Solving resource-constrained project scheduling problem by genetic algorithm
Abstract
This paper proposes a genetic algorithm to solve resource constrained project scheduling problem, in which resources are optimally allocated to tasks. Resources are renewable. In RCPSP each activity is executing in single mode. This work employed genetic algorithm to schedule project task to minimize makespan respect to resource constraint and precedence constraint. The Schedule Generation Scheme was used to decode project plan. The approach was tested on a set of standard problem obtained from Project Scheduling Problem Library (PSLIB) and algorithm given in this paper was compared with the existing optimization algorithm, the result reveals that the algorithm is effective for the RCPSP.
... Exact methods can be divided in four different groups: 1) Integer Programming -using large number of binary variables [5], [6] 2) Implicit Enumeration -using enumeration tree and bounds to reduce the space of feasible solutions [7], [8] 3) Branch-and-bound methods -using trees and lower bounds to eliminate nodes in tree that cannot lead to optimal solution [9], [10] 4) Dynamic programming -divide problem on problems with smaller size and solve that problems, and combine the solution [11]. Some of heuristic methods that can be found in literature are: Genetic algorithms [12], [13], Simulated annealing [14], Ant colony [15]. For achieving better results there are attempts of combining different solution methods like hybrid algorithms, memetic algorithms etc. Usually these approaches combine some evolutionary algorithm and local search methods. ...
... If the completion time of the last activity is minimal then the completion time for all activities is minimal too. Constraints (12) and (15) ensure that the activity can be completed exactly in one time period. Constraint (13) ensures that all predecessors of activity A j are completed before it starts with execution, and constraint (14) ensures that in each time period the amount of resources being used is smaller or equal to the available amount of resources. ...
... The GA is a powerful biological mechanism and natural selection theory-based metaheuristic algorithm [28], [29]. Among the population-based meta-heuristics, GA is the most widely applied not only in RCPSP [30], [31] and RCPSPDC [10], but also in others sort of optimization domains [27], [32]- [34]. GA generates good quality solutions with a reasonable time when the problem domain is large [10], [33]. ...
The net present value (NPV)-based resource constrained project scheduling problem (RCPSP) is a well-known scheduling problem in many industries, such as construction, software development, and manufacturing. Over the last five decades, although different approaches have been proposed to solve the problem, no single approach has been shown to achieve satisfactory performances with quality solutions for a wide range of problems. This study presents a hybrid immune genetic algorithm (IGA) to solve NPV-based RCPSPs. Hybridizing a genetic algorithm (GA) with an immune algorithm (IA) enhances the overall performance of their standalone components (i.e., only GA or IA). Performance of the proposed IGA is further improved by applying a variable insertion based local search (VINS) and forward-backward improvement (FBI). A restart mechanism is presented to the algorithm which induces diversity and helps to avoid becoming trapped in local optima. Moreover, an activity move rule (AMR) is implemented to shift the negative cash flow associated activities to further improve the NPV. Taguchi Design of Experiment (DOE) is conducted to investigate the impact of various parameters and to determine the appropriate set of parameters for the proposed IGA. The performances of the proposed algorithms are tested on 17,280 standard benchmark instances ranging from 25 to 100 activities. Comparison with the state-of-art algorithms through extensive numerical experiments reveal the effectiveness of the proposed algorithms. Overall, the proposed algorithm outperforms existing algorithms, particularly the projects with 0% and 100% negative cash flow associated activities, the 75-activity instances, and the projects with two resources usage in terms of a lower value of average percentage deviation.
... Zarrazvand and Shojafar (2012) used fuzzy logic for calculating the cost of information technology projects considering process activity degree, response time and interrupt time. Kadam and Kadam (2014) used genetic algorithm approach for solving resource constraint project scheduling problem. The main objective of the problem was considered as the minimisation of the makespan. ...
... The second class of methods is applied to initial complete solutions with the goal of achieving improvement in terms of a selected criterion. The main representatives of this category are genetic algorithms [19,20], tabu search, simulated annealing [21], ant colony optimization [22] and others. ...
The main task of scheduling is the allocation of limited resources to activities over time periods to optimize one or several criteria. The scheduling algorithms are devised mainly by the experts in the appropriate fields and evaluated over synthetic benchmarks or real-life problem instances. Since many variants of the same scheduling problem may appear in practice, and there are many scheduling algorithms to choose from, the task of designing or selecting an appropriate scheduling algorithm is far from trivial. Recently, hyper-heuristic approaches have been proven useful in many scheduling domains, where machine learning is applied to develop a customized scheduling method. This paper is concerned with the resource constrained project scheduling problem (RCPSP) and the development of scheduling heuristics based on Genetic programming (GP). The results show that this approach is a viable option when there is a need for a customized scheduling method in a dynamic environment, allowing the automated development of a suitable scheduling heuristic.
The resource-constrained project scheduling problem (RCPSP) is one of the scheduling problems that belong to the class of NP-hard problems. Therefore, heuristic approaches are usually used to solve it. One of the most commonly used heuristic approaches are priority rules (PRs). PRs are easy to use, fast and able to respond to system changes, which makes them applicable in a dynamic environment. The disadvantage of PRs is that when applied in a static environment, they do not achieve results of the same quality as heuristic approaches designed for a static environment. Moreover, a new PR must be evolved separately for each optimization criterion, which is a challenging process. Therefore, recently significant effort has been put into the automatic development of PRs. Although PRs are mainly used in a dynamic environment, they are also used in a static environment in situations where speed and simplicity are more important than the quality of the obtained solution. Since PRs evolved for the dynamic environment do not use all the information available in a static environment, this paper analyzes two adaptations for evolving PRs for the RCPSP - iterative priority rules and rollout approach. This paper shows that these approaches achieve better results than the PRs evolved and used without these adaptations. The results of the approaches presented in the paper were also compared with the results obtained with the genetic algorithm as a representative of the heuristic approaches used mainly in the static environment.
Resource constraint project scheduling problem is an NP-hard problem that attracts many researchers because of its complexity and daily use. In literature there are a lot of various solving methods for this problem. The priority rules are one of the prominent methods used in practice. Because of their simplicity, speed, and possibility to react to changes in the system, they can be used in a dynamic environment. In this paper, ensembles of priority rules were created to improve the performance of priority rules created with genetic programming. For ensemble creation, four different methods will be considered: simple ensemble combination, BagGP, BoostGP, and cooperative coevolution. The priority rules that are part of the ensemble will be combined with the sum and vote methods in reaching the final decision. Additionally, the ensemble subset search method will be applied to the created ensembles to find the optimal subset of priority rules. The results achieved in this paper show that ensembles of priority rules can achieve significantly better results than those achieved when using only a single priority rule.
The project scheduling problem is both practically and theoretically of paramount importance. From the practical perspective, improvement of project scheduling as a critical part of project management process can lead to successful project completion and significantly decrease of the relevant costs. From the theoretical perspective, project scheduling is regarded as one of the in-teresting optimization issues, which has attracted the attention of many researchers in the area of operations research. Therefore, the project scheduling issue has been significantly evaluated over time and has been developed from various aspects. In this research, the topics related to Re-source-Constrained Project Scheduling Problem (RCPSP) are reviewed, recent developments in this field are evaluated, and the results are presented for future studies. In this regard, first, the standard problem of RCPSP is expressed and related developments are presented from four as-pects of resources, characteristics of activities, type of objective functions, and availability level of information. Following that, details about 216 articles conducted on RCPSP during 1980-2017 are expressed. At the end, in line with the statistics obtained from the evaluation of previ-ous articles, suggestions are made for the future studies in order to help the development of new issues in this area.
The resource constrained project-scheduling problem (RCPSP) aims to minimize the duration of a project. RCPSP is prevalently used in programming the projects with high number of activities and resources such as construction projects. In this study, 240 projects such as residential, office, school, etc. are designed and programmed under limited resources. The resource amounts of these projects are determined using three priority rules, these are Latest Finish Time, Minimum Slack Time and Maximum Remaining Path Length which have the highest performance according to the literature, in the amounts of 2, 4, 6 and 8. The project times are estimated using artificial neural network (ANN). A correlation coefficient of 0.70 was obtained from the ANN estimation model.
This paper proposes a Genetic Algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). Resources are renewable and there is a unique way to perform the activities. This work employs Genetics Algorithms to schedule project activities to minimize makespan subject to precedence constraints and resources availability. A serial generation scheme is used to obtain the schedule. The algorithm was programmed using Object Oriented programming that allows generating individuals with their own attributes such as activity sequence and makespan. A Genetic Algorithm (GA) is proposed which uses a novel chromosome representation. The issues of the GA parameter tuning are also discussed in this paper. A computer tool that allows the user to define activities, precedence constraints and resource capacity was developed.
Managing multiple projects is a complex task. It involves the integration of varieties of resources and schedules. The researchers have proposed many tools and techniques for single project scheduling. Mathematical programming and heuristics are limited in application. In recent years non-traditional techniques are attempted for scheduling. This paper proposes the use of a heuristic and a genetic algorithm for scheduling a multi-project environment with an objective to minimize the makespan of the projects. The proposed method is validated with numerical examples and is found competent.
The aim of this paper is to present a new genetic algorithm approach for large scale multiple resource-constrained project-scheduling problems (RCPSP). It also presents a heuristic approach to achieve proper solutions for large scale problems. This research area is very common in industry especially when a set of activities needs to be finished as soon as possible subject to two sets of constraints, precedence constraints and resource constraints. The emphasis in this research is on investigating the complexity of scheduling problems and developing a new GA approach to solve this problem in such a way that the advantages of GA are appropriately utilized by applying a novel method to reduce the complexity of the problem. Computational results are also reported for the most famous classical problems taken from the operational research literature.
1 Abstract The Home Care Scheduling Problem (HCSP) involves as-signing nurses to certain people or patients who are in need of support within quite strict time windows at their homes. The assignment is based on particular support requirements and qualifications of the nurses. Each nurse should visit all the assigned patients within the determined time windows to perform the tasks concerning them. During these visits, to-tal traveling time should be minimized and a number of con-straints concerning the nurses' rosters should be handled. HCSP is a combination of two NP-hard problems, namely the Nurse Rostering Problem (NRP) and the Vehicle Rout-ing Problem (VRP). In the literature, we can find plenty of studies related to both problems. However, very limited studies are available about the combined HCSP. A related combined problem that shows similar characteristics under simpler constraints is the Vehicle Routing and Scheduling Problem with Time Window Constraints (VRSPTW) [9]. It is the VRP with time windows that cover the time hori-zon for delivering goods or services to customers. In the HCSP, different nurses with different skills are required, the services delivered are more complicated and more types of tasks are present than in the VRSPTW. There is a limited number of papers about the HCSP in the literature [1, 2, 3, 4, 6, 7, 8]. Fast heuristic approaches are an alternative to solve the HCSP. However, the problem depen-dency of such optimisation strategies is an important issue to be tackled. It is possible to design an algorithm that can find high performance solutions for a specific problem or just an instance of a problem. However, the algorithm may not be successful to solve related problems or different instances or it may require lots of changes or tuning to be adapted to the new problem. Hyper-heuristics are generic search strategies that perform search over a heuristic search space instead of the solution space to clear up this case [5]. In this study, we apply a new improvement hyper-heuristic which chooses the best possible low-level heuristic at each optimization step for the HCSP to show the potential of hyper-heuristics for difficult combined problems.
Project scheduling is concerned with single-item or small batch production where scarce resources have to be allocated to dependent activities over time. Applications can be found in diverse industries such as construction engineering, software development, etc. Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts. Likewise, project scheduling is very attractive for researchers, because the models in this area are rich and, hence, difficult to solve. For instance, the resource-constrained project scheduling problem contains the job shop scheduling problem as a special case. So far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling. Also, a variety of symbols are used by project scheduling researchers in order to denote one and the same subject. Hence, there is a gap between machine scheduling on the one hand and project scheduling on the other with respect to both, viz. a common notation and a classification scheme. As a matter of fact, in project scheduling, an ever growing number of papers is going to be published and it becomes more and more difficult for the scientific community to keep track of what is really new and relevant. One purpose of our paper is to close this gap. That is, we provide a classification scheme, i.e. a description of the resource environment, the activity characteristics, and the objective function, respectively, which is compatible with machine scheduling and which allows to classify the most important models dealt with so far. Also, we propose a unifying notation. The second purpose of this paper is to review some of the recent developments. More specifically, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time–cost tradeoff problem, for problems with minimum and maximum time lags, for problems with other objectives than makespan minimization and, last but not least, for problems with stochastic activity durations.
In this paper we address the resolution of the Ground Station Scheduling problem by Genetic Algorithms. Ground Stations (GS) are required during spacecraft (S/C) operations to provide communications links between operations teams and the S/C systems. Basic communication types, such as telemetry, tele-command and tracking, are all supported by the same satellite and GS systems. The allocation of ground resources to S/C is a highly constrained problem and traditionally has been conducted manually: stations are selected for communication support with certain S/C for certain periods. The manual approach has clear limitations and new modern scheduling approaches are needed to tackle with the complexity of the problem and produce optimal solutions to scheduling operations. We propose the use of Genetic Algorithm, a well-known family of population-based methods, for solving the problem. A series of genetic operators have been designed to find the configuration that outputs the best GA solution for the problem. The proposed GA has been implemented in Matlab and experimentally studied on a set of randomly generated instances. The results of the study showed the effectiveness of the proposed GA algorithm.
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.
An appropriate tabu search implementation is designed to solve the resource constrained project scheduling problem. This approach uses well defined move strategies and a structured neighbourhood, defines appropriate tabu status and tenure and takes account of objective function approximation to speed up the search process. A sound understanding of the problem has helped in many ways in designing and enhancing the tabu search methodology. The method uses diversification, intensification and handles infeasibility via strategic oscillation.
The studied resource-constrained project scheduling problem (RCPSP) is a classical well-known problem which involves resource, precedence, and temporal constraints and has been applied to many applications. However, the RCPSP is confirmed to be an NP-hard combinatorial problem. Restated, it is hard to be solved in a reasonable time. Therefore, there are many metaheuristics-based schemes for finding near optima of RCPSP were proposed. The particle swarm optimization (PSO) is one of the metaheuristics, and has been verified being an efficient nature-inspired algorithm for many optimization problems. For enhancing the PSO efficiency in solving RCPSP, an effective scheme is suggested. The justification technique is combined with PSO as the proposed justification particle swarm optimization (JPSO), which includes other designed mechanisms. The justification technique adjusts the start time of each activity of the yielded schedule to further shorten the makespan. Moreover, schedules are generated by both forward scheduling particle swarm and backward scheduling particle swarm in this work. Additionally, a mapping scheme and a modified communication mechanism among particles with a designed gbest ratio (GR) are also proposed to further improve the efficiency of the proposed JPSO. Simulation results demonstrate that the proposed JPSO provides an effective and efficient approach for solving RCPSP.
The paper presents a fuzzy simulated evolution algorithm for the
public transport driver scheduling problem, which involves solving a set
covering model. The novel scheduling algorithm incorporates the idea of
fuzzy evaluation into simulated evolution, combining the features of
iterative improvement and constructive perturbation, to explore solution
space effectively and obtain superior schedules. Experiments with
benchmark tests using data from the transportation industry demonstrate
the strengths of the proposed algorithm in solving large size real-world
driver scheduling problems. It is suggested that this approach might be
suitable for other large-scale set covering problems
A heuristic approach, ZEST for ESTimator, is developed to analyze bus driver scheduling problems and produce an estimate of the number of drivers required for a bus schedule. Based on the observation that the maximum number of drivers is needed in the morning and afternoon peaks, ZEST divides the driver scheduling problem into morning and afternoon subproblems, solves each subproblem separately, and, finally, combines the solutions. The key techniques in ZEST derive from manual scheduling operations that examine the critical decision points in a bus schedule that are vital for a good driver schedule and use these decision points to develop chains of meal breaks that dovetail one driver's meal break with another driver's. ZEST can be used as a standalone estimator of driver duties or as a component of other driver scheduling approaches
A survey conducted in the United States in 1994 (Icmeli-Tukel and Rom 1998), revealed that the issues Project Managers (PMs) face today are more complicated than those studied in the project scheduling literature. The study indicates that for over 90% of PMs the objective is to maximize the quality of projects and their outcomes. They usually measure quality by the degree to which a project’s outcome conforms to the customer’s requirements and the degree to which the project completes within budget and on schedule. In order to achieve these goals, PMs are trying to eliminate the rework associated with non-conforming activities. A job is considered to be non-conforming when it fails to meet customer/design requirements and therefore needs some rework (Ireland 1991). Non-conformities usually result in increased project implementation time and cost. In the traditional Resource Constrained Project Scheduling Problem (RCPSP) formulations, however, the general assumption is that work will be done as scheduled and that rework will not be required. This assumption clearly makes the RCPSP models more amenable to solution yet less realistic. PMs report (Icmeli-Tukel and Rom 1998) that most of the projects they implement have at least one non-conforming activity which needs to be reworked before the project moves to the next stage. Because of these reworks, they have a difficult time anticipating delays and cost overruns when using traditional techniques. If an activity is (partially) reworked to satisfy customer requirements, then the start time of all immediately succeeding activities are delayed, which, in turn might delay the project completion time. This in turn contributes to the consistently poor record of project performance (Cooper 1994).
The Resource Constrained Project Scheduling Problem (RCPSP) can formulate many scheduling problems including jobshop and flowshop scheduling problems. In this paper, we extend the definition of RCPSP further so that various complicated constraints and objective functions arising in practice can be handled; for example, each activity can be processed in one of the selectable modes, the available amounts of renewable resources may vary depending on the periods, setup activities can be dealt with, and complex objective functions can be handled. Then, we develop a tabu search based heuristic algorithm, which contains elaborations in representing solutions and in constructing neighborhood. Our code was tested for many benchmarks of RCPSP, and also for some problems from real applications. For a number of RCPSP instances, we found better solutions than the best ones found so far. These computational results indicate the effectiveness and usefulness of our approach.
We present a set of benchmark instances for the evaluation of solution procedures for single- and multi-mode resource-constrained project scheduling problems. The instances have been systematically generated by the standard project generator ProGen. They are characterized by the input-parameters of ProGen. The entire benchmark set including its detailed characterization and the best solutions known so-far are available on a public ftp-site. Hence, researchers can download the benchmark sets they need for the evaluation of their algorithms. Additionally, they can make available new results. Depending on the progress made in the field, the instance library will be continuously enlarged and new results will be made accessible. This should be a valuable and driving source for further improvements in the area of project type scheduling.
The Ground Station Scheduling is one of the most important problems in the field of Satellite-Scheduling. This problem consists in planning feasible planning of communications between satellites or spacecraft (SC) and operations teams of Ground Station (GS). The information received in these communications is usually basic information such as telemetry, tracking information or tasks to perform, so usually the time required for communication is usually quite smaller than the window of visibility. Typically, the assignment of the Ground Stations to Spacecraft is a very limited and small enough to make a manual planning, defined by short periods of time. However, resource allocation of a ground station on a mission has a high cost, and automation of this process provides many benefits not only in terms of management, but in economic terms as well. The problem is known for its high complexity and is an over-constrained problem. In this paper, we present the resolution of the problem through Struggle Genetic Algorithms. Struggle GA is a version of GAs that distinguishes for its efficiency in maintaining the diversity of the population through genetic evolution. We present some computational results for the case of the multi-ground stations scheduling obtained with Struggle GA using the STK simulation toolkit.
This paper addresses methods for formulating and solving a general class of nonpreemptive resource-constrained project scheduling problems in which job durations are discrete functions of committed renewable, nonrenewable and doubly-constrained resources (multi-mode time resource tradeoff). We present a stochastic scheduling method which solves these problems to sub-optimality in an efficient way. Computational results demonstrate that this method is highly superior to other well-known existing deterministic scheduling rules. Extensions to problems in which job-specific (demand) resource profiles are varying with time, in addition to time-varying supply resource profiles, are discussed as well.
The resource-constrained project scheduling problem (RCPSP) can be given as follows. A single project consists of a set J = {0,1,…, n, n +1} of activities which have to be processed. Fictitious activities 0 and n + 1 correspond to the “project start” and to the “project end”, respectively. The activities are interrelated by two kinds of constraints. First, precedence constraints force activity j not to be started before all its immediate predecessor activities comprised in the set P
j
have been finished. Second, performing the activities requires resources with limited capacities. We have k resource types, given by the set K = {1,…,K}. While being processed, activity j requires r
j,k
units of resource type k ∈ K during every period of its non-preemptable duration p
j
. Resource type k has a limited capacity of R
k
at any point in time. The parameters pj,r
j,k
, and R
k
are assumed to be deterministic; for the project start and end activities we have pj = 0 and r
j,k
= 0 for all k ∈ K. The objective of the RCPSP is to find precedence and resource feasible completion times for all activities such that the makespan of the project is minimized. Figure 7:1 gives an example of a project comprising n = 6 activities which have to be scheduled subject to K = 1 renewable resource type with a capacity of 4 units. A feasible schedule with an optimal makespan of 13 periods is represented in Figure 7:2.
Genetic algorithms have successfully been used to solve real timetabling problems. Satisfactory solutions, focused on the elimination of open periods and isolated classes, allowed the "Escola Estadual Padre Rog?rio Abdala" to process automatization for 2004 and 2005 school terms consecutively. In this paper, a hybrid variation is proposed (memetic algorithm) in order to improve the algorithm robustness. The comparative analysis through statistical methods (t-test and confidence interval) indicates that hybridization increased the robustness and the quality of the results, presenting more appropriate solutions to that real problem.
In this paper we develop a heuristic algorithm, based on Scatter Search, for project scheduling problems under partially renewable
resources. This new type of resource can be viewed as a generalization of renewable and non-renewable resources, and is very
helpful in modelling conditions that do no fit into classical models, but which appear in real timetabling and labor scheduling
problems. The Scatter Search algorithm is tested on existing test instances and obtains the best results known so far.
This paper proposes an effective algorithm to solve a nurse scheduling problem by using genetic algorithm (GA). In hospitals, nurses are assigned to any section such as the internal medicine department or the pediatrics department. In generally, 15-30 nurses belong to a section. A clinical director of the department has to make a duty schedule of all nurses of the department every month. It is very complex task to create the nurse schedule. To improve this problem, we propose an effective algorithm to create and optimize the nurse schedule. Our algorithm is based on the cooperative GA. In conventional ways using the cooperative GA for the nurse scheduling, a crossover operator is only applied to optimize the schedule, because it keeps validity between chromosomes. As the first proposal of this paper, we apply a new mutation operator to the cooperative GA, which does not fail validity of the schedule. Although the cooperative GA with the crossover and mutation operators optimizes the nurse schedule better than the conventional GA, the optimization mostly stagnates at the middle game or the endgame. We consider that this stagnation is caused that the optimization is caught in a local minimum area of a solution space. To escape from the local minimum and to find better solution, we apply a mountain-climbing operator to the cooperative GA. Effectiveness of these two new operators are shown by practical experiments
A novel hybrid meta-heuristic algorithm, entitled as RCPSPGSA, is proposed for solving the resource-constrained project scheduling problem (RCPSP) in this paper. The algorithm incorporates the simulated annealing algorithm (SA) into genetic algorithm in order to improve local searching performance and boost up evolution capability. In each evolution iteration GA generates a new temporary population, and after that SA is used for improving every individual in it and at the mean time the next gap population is generated. For the sake of keeping the same convergence direction and speed of GA and SA, the cooling procedure occurs at the end of each evolution iteration. Simulation experiments are performed on the standard project instance sets of PSPLIB, and orthogonal experiment method is introduced to solve the parameter selection problem. Parameter combinations selected by this method are proved to be outperformed. Experimental results show that RCPSPGSA improves solution quality for J30, J60, J90 sets and not bad for J120.
With the development of the global business and logisticspsila a container terminal (CT) system becomes more and more busy. Therefore, the available resources in the sea port get scarcer than before. In order to increase the operating efficiency of CT system, the resources planning problem has become a critical issue in the fields of operations research and logistics. In this paper, we introduce the berth allocation planning problem and formulate a mathematical model considered each berth for container ship with different number of quay cranes (QCs). In order to solve this quay crane scheduling in berth allocation planning problem, we also propose a hybrid genetic algorithm (HGA) approach with the priority-based encoding method. To demonstrate the effectiveness of proposed HGA approach, numerical experiment is carried out, and the best solution to the problem is obtained.
The Educational timetabling problem is a common and hard problem inside every educative institution, this problem tries to coordinate Students, Teachers, Classrooms and Timeslots under certain constrains that dependent in many cases the policies of each educational institution. The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. This paper presents several strategies to improve a GA-based method that produces general hyper heuristics for the educational timetabling design problem using API-Carpio methodology. The GA uses static-length representation, witch involves the complete encoding of a solution algorithm capable to solve schedule design instances. This hyper-heuristic is achieved by learning and testing phases using real instances from Leon Institute of Technology (LIT) producing encouraging results for most of the instances. Finally we analyze the quality of our hyper-heuristic in the context of real Academic Timetabling Design problem against past Investigations.
This paper presents a search method that combines elements from evolutionary and local search paradigms by the systematic use of crossover operations, generally used as structured exchange of genes between a series of solutions in genetic algorithms. Crossover operations here are particularly utilized as a systematic means to generate several possible solutions from two superior solutions. To test the effectiveness of the method, it has been applied to the resource-constrained project scheduling problem. The computational experiments show that the application of the method to this problem is promising.
This paper presents the novel application of a collaborative population-based meta-heuristic technique called Particle Swarm Optimization (PSO) to the scheduling of home care workers. The technique is applied to a genuine situation arising in the UK, where the provision of community care service is a responsibility of the local authorities. Within this provision, optimization routes for each care worker are determined in order to minimize the distance traveled providing that the capacity and service time window constraints are not violated. The objectives of this paper are twofold; first to exploit a systematic approach to improve the existing schedule of home care workers, second to develop the methodology to enable the continuous PSO algorithm to be efficiently applied to this type of problem and all classes of similar problems. For this problem, a particle is defined as a multi-dimensional point in space which represents the corresponding care activities and assignment priority. The Heuristic Assignment scheme is specially designed to transform the continuous PSO algorithm to the discrete job schedule. The Earliest Start Time Priority with Minimum Distance Assignment (ESTPMDA) technique is developed for generating an initial solution which guides the search direction of the particle. Local improvement procedures (LIP), i.e. insertion and swap, are embedded in the PSO algorithm in order to further improve the solution quality. The proposed methodology is implemented, tested, and compared with existing solutions on a variety of real problem instances.
Military course of action planning involves time and space synchronization as well as resource and asset allocation. A mission could be seen as a defined set of logical ordered tasks with time and space constraints. The resources to task rules require that available assets should be allocated to each task. A combination of assets might be required to execute a given task. The couple (task, resources) constitutes an action. This problem is formulated as a multi-objectives scheduling and resource allocation problem. Any solution is assessed based on a number of conflicting and heterogeneous objectives. In fact, military planning officers should keep perfecting the plan based on the Commander’s criteria for success. The scheduling problem and resource allocation problem are considered as NP-Hard Problems [A. Guitouni, B. Urli, J.-M. Martel, Course of action planning: A project based modelling, Working Paper, Faculté des sciences de l’ administration, Université Laval, Québec, 2005]. This paper is concerned with the multi-objectives resource allocation problem. Our objective is to find adequate resource allocation for given courses of action schedule. To optimize this problem, this paper investigates non-exact solution methods, like meta-heuristic methods for finding potential efficient solutions. A progressive resource allocation methodology is proposed based on Tabu Search and multi-objectives concepts. This technique explores the search space so as to find a set of potential efficient solutions without aggregating the objectives into a single objective function. It is guided by the principle of maximizing the usage of any resource before considering a replacement resource. Thus, a given resource is allocated to the maximum number of tasks for a given courses of action schedule. A good allocation is a potential efficient solution. These solutions are retained by applying a combination of a dominance rule and a multi-criteria filtering method. The performance of the proposed Pareto-based approach is compared to two aggregation approaches: weighted-sum and the lexicographic techniques. The result shows that a Pareto-based approach is providing better solutions and allowing more flexibility to the decision-maker.
This paper describes new simulated annealing (SA) algorithms for the resource-constrained project scheduling problem (RCPSP) and its multiple mode version (MRCPSP). The objective function considered is minimisation of the makespan. The conventional SA search scheme is replaced by a new design that takes into account the specificity of the solution space of project scheduling problems. For RCPSP, the search was based on an alternated activity and time incrementing process, and all parameters were set after preliminary statistical experiments done on test instances. For MRCPSP, we introduced an original approach using two embedded search loops alternating activity and mode neighbourhood exploration. The performance evaluation done on the benchmark instances available in the literature proved the efficiency of both adaptations that are currently among the most competitive algorithms for these problems.
We review recent advances in dealing with the resource-constrained project scheduling problem using an efficient depth-first branch-and-bound procedure, elaborating on the branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive conclusions from the research on optimal solution procedures for the basic problem and subsequently illustrate extensions to a rich and realistic variety of related problems involving activity preemption, the use of ready times and deadlines, variable resource requirements and availabilities, generalized precedence relations, time/cost, time/resource and resource/resource trade-offs and non-regular objective functions.
We develop a heuristic procedure for solving the discrete time/resource trade-off problem in the field of project scheduling. In this problem, a project contains activities interrelated by finish-start-type precedence constraints with a time lag of zero, which require one or more constrained renewable resources. Each activity has a specified work content and can be performed in different modes, i.e. with different durations and resource requirements, as long as the required work content is met. The objective is to schedule each activity in one of its modes in order to minimize the project makespan. We use a scatter search algorithm to tackle this problem, using path relinking methodology as a solution combination method. Computational results on randomly generated problem sets are compared with the best available results indicating the efficiency of the proposed algorithm.
There have been many survey papers in the area of project scheduling in recent years. These papers have primarily emphasized modeling and algorithmic contributions for specific classes of project scheduling problems, such as net present value (NPV) maximization and makespan minimization, with and without resource constraints. Paralleling these developments has been the research in the area of project scheduling decision support, with its emphasis on data sets, data generation methods, and so on, that are essential to benchmark, evaluate, and compare the new models, algorithms and heuristic techniques. These investigations have extended the frontiers of research and application in all areas of project scheduling and management. In this paper, we survey the vast literature in this area with a perspective that integrates models, data, and optimal and heuristic algorithms, for the major classes of project scheduling problems. We also include recent surveys that have compared commercial project scheduling systems. Finally, we present an overview of web-based decision support systems and discuss the potential of this technology in enabling and facilitating researchers and practitioners in identifying new areas of inquiry and application.
In the last few decades, several effective algorithms for solving the resource-constrained project scheduling problem have been proposed. However, the challenging nature of this problem, summarised in its strongly NP-hard status, restricts the effectiveness of exact optimisation to relatively small instances. In this paper, we present a new meta-heuristic for this problem, able to provide near-optimal heuristic solutions for relatively large instances. The procedure combines elements from scatter search, a generic population-based evolutionary search method, and from a recently introduced heuristic method for the optimisation of unconstrained continuous functions based on an analogy with electromagnetism theory. We present computational experiments on standard benchmark datasets, compare the results with current state-of-the-art heuristics, and show that the procedure is capable of producing consistently good results for challenging instances of the resource-constrained project scheduling problem. We also demonstrate that the algorithm outperforms state-of-the-art existing heuristics.
In deterministic sequencing and scheduling problems, jobs are to be processed on machines of limited capacity. We consider an extension of this class of problems, in which the jobs require the use of additional scarce resources during their execution. A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification. Models involving parallel machines, unit-time jobs and the maximum completion time criterion are studied in detail; other models are briefly discussed.
The Earth observation satellites scheduling problem (SMS) involves scheduling tasks to be performed by a satellite, where new task requests can arrive at any time, non-deterministically, and must be scheduled in real-time. This paper describes a new satellite mission scheduling algorithm based on constraint satisfaction problem (CPP). We describe the dynamic scheduling problem as a dynamic weighted maximal CSP in which constraints can be changed dynamically. It is usually undesirable to drastically modify the previous schedule in the re-scheduling process. This paper presents a new satellite mission scheduling problem based on constraint satisfaction problem (SMSCSP). The simulation results show that the proposed approach is effective and efficient in applications to the real problems.
The paper describes an implementation of an evolution program for
a resource constrained project scheduling problem, which is much more
complex than other scheduling problems. The traditional order-based
crossover operators are not well suited for this problem without
modification. The approach adopted is based on the augmentation of the
evolution program with domain-specific knowledge. It undertakes the
burden of devising appropriate genetic operators for this problem to
guarantee a feasible schedule. A new discipline is addressed for
designing the genetic operators. In the implementation, crossover is
designed to perform blind search to explore the area beyond local
optima, and mutation is designed to perform intensive search to produce
an improved solution. The proposed approach has been tested on two
standard test problems and the results show that it can find the known
optimum very rapidly and is superior to existing heuristic techniques.
The suggested approach can significantly improve the performance of
evolution program both in terms of speed and accuracy and can be applied
to other difficult combinatorial optimization problems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1996. Includes bibliographical references (p. 57-60). by Matthew Bartschi Wall. Ph.D.
The resource-constrained project scheduling problem (RCPSP) is one of the most challenging problems in project scheduling. During the last couple of years many heuristic procedures have been developed for this problem, but still these procedures often fail in finding near-optimal solutions for more challenging problem instances. In this paper, we present a new genetic algorithm (GA) that, in contrast of a conventional GA, makes use of two separate populations. This bi-population genetic algorithm (BPGA) operates on both a population of left-justified schedules and a population of right-justified schedules in order to fully exploit the features of the iterative forward/backward local search scheduling technique. Comparative computational results reveal that this procedure can be considered as today’s best performing RCPSP heuristic. Note
This paper discusses the problem of scheduling quay cranes (QCs), the most important equipment in port terminals. A mixed-integer programming model, which considers various constraints related to the operation of QCs, was formulated. This study proposes a branch and bound (B & B) method to obtain the optimal solution of the QC scheduling problem and a heuristic search algorithm, called greedy randomized adaptive search procedure (GRASP), to overcome the computational difficulty of the B & B method. The performance of GRASP is compared with that of the B & B method.
Nurse scheduling is the process of allocating shifts for nurses by specifying the sequence of shifts for each nurse in the scheduling period. Generating good schedules for nurses is a very difficult and tedious problem due to the operational of hospital that runs 24 hours a day and 7 days a week. Schedule that has work shifts is a big influence on the level of stress and fatigue for nurses, as well as on the quality of social relationship and family. In this paper, a brief overview of three stages Tabu Search heuristic for nurse-scheduling problem (NSP) is presented. The problem is approached via the goal programming method. The goal programming (GP) model for the nurse scheduling problem of this paper focuses on both hospital objectives and nurses’ preferences.
The Software Development Project Scheduling Problem is similar to the well-known Resource-Constrained Multi-Project Scheduling Problem (RCMPSP). It consists in determining a schedule of tasks taking into consideration resource availabilities and precedence constraints, while optimizing an objective. Like RCMPSP, it is an NP-hard problem. In this paper, a task segmentation scheme to schedule a software development project is proposed and the average duration of the multiple concurrent projects is minimized using the Particle Swarm Optimization (PSO) meta-heuristic. PSO is a recent meta-heuristic algorithm, known for its simplicity in programming and its rapid convergence. A series of experiments show optimum results for several software development schedule scenarios.
In this paper the competitive Hopfield neural network method for finding a broadcasting schedule in the satellite system will be described. The satellite broadcast scheduling (SBS) problem is known as an NP-complete problem. Communication links between satellites and ground terminals are provided in a repetition of time slots. The goal of the proposed algorithm is to find the broadcasting schedule of satellites with the maximum number of broadcasting time slots under the constraints. A competitive learning rule provides a highly effective means for obtaining a resonance solution and is capable of reducing the time-consuming effort to obtain coefficients. The proposed method can always satisfy the problem constraints and guarantee the viability of the solutions for the SBS problem. The competitive mechanism simplifies the network complexity. The proposed method is greatly suitable for implementation on a digital machine. Furthermore, the competitive Hopfield neural network method permits temporary energy increases to escape from local minima. Simulation results show that the competitive Hopfield neural network method can improve system performance and with fast convergence and high reliability.
This paper presents an ant colony optimization (ACO) approach to solve the resource-constrained project scheduling problem (RCPSP) with generalized precedence relations (RCPSP-GPR) with the objective of minimizing the project duration. The general ACO is improved by using the ants with backtracking capabilities and several kinds of heuristic information for solution construction. The combination of direct and summation pheromone evaluation methods and the pseudo-random-proportional action choice rule is also used. The ACO algorithm is tested efficient by using a set of benchmark problems generated by the project generator ProGen/max and performs the best on average among several other heuristic methods.
The Nurse Scheduling Problem (NSP) is a problem of allocating
shifts (day and night shifts, holidays, and so on) for nurses under
various constraints. Generally, NSP has a lot of constraints. As a
result, it needs a lot of knowledge and experience to construct the
scheduling table with its constraints, and it is usually done by the
head nurse or the authority in hospitals. Some research on NSP using
genetic algorithms (GA) is reported. Conventional methods take the
constraints into the fitness function. However, if it reduces the
fitness value a lot to the parts of solution against the constraints, it
causes useless search, because most of the chromosomes are selected in
the initial population or in the change by the genetic operations. If it
doesn't reduce the fitness value so much, the final solution has some
parts against the constraints. Some of them are established by the Labor
Standards Act or the Labor Union Act, so the solution has to be
modified. As a result, it is difficult to acquire an effective
scheduling table automatically. The paper studies the method of coding
and genetic operations with their constraints for NSP. The exchange of
shifts is done to satisfy the constraints in the coding and after the
genetic operations. We apply this method to NSP using actual shifts and
constraints being used in a hospital. It shows that an effective
scheduling table satisfying the constraints is acquired by this method
In this paper we consider the resource-constrained project scheduling problem (RCPSP) with makespan minimization as objective. We propose a new genetic algorithm approach to solve this problem. Subsequently, we compare it to two genetic algorithm concepts from the literature. While our approach makes use of a permutation based genetic encoding that contains problem-specific knowledge, the other two procedures employ a priority value based and a priority rule based representation, respectively. Then we present the results of our thorough computational study for which a standard set of project instances has been used. The outcome reveals that our procedure is the most promising genetic algorithm to solve the RCPSP. Finally, a priority rule based random sampling procedure known from the literature serves as a further benchmark. We show that our genetic algorithm yields better results than this sampling approach. Keywords: Project Management and Scheduling, Resource-Constraints, Genetic A...
Nuevos Metodos de Resolucion de Problema de Secuenciocion de Proyectos con Recursos Limitados
- F Ballostin
A Random KeyBased Genetic Algorithm for the RCPSP
- J De Jorge
- M Mendes
- J F Goncalves
- M G C Resende
Swarm Intelligence in the Optimization of Software Development Project Schedule
- T Gonsalves
- A Ito
- R Kawabta
- K Itoh