A Hybrid Approach to Decision Support for Resource-Constrained Scheduling Problems

Constrained scheduling problems are quite common in project management, manufacturing, distribution, transportation, logistics, supply chain management, software engineering, and computer networks etc. The need to use integer and binary decision variables representing the allocation of different resources to many activities and numerous specific, universal and additional constraints on these decision variables are typical components of the resource-constrained scheduling problems (RCSPs) modeling. It is often necessary to model additional resources and constraints. For these reasons, models are becoming computationally demanding. This is particularly noticeable when methods of operations research (mathematical programing (MP), network programing, and dynamic programming) are used. On the other hand, most RCPSs can be easily modeled as instances of the constraint satisfaction problems (CSPs) and solved using constraint programming (CP) methods. In contrast to the MP-based environment, the CP-based environment methods deal well with binary constraints but worse in optimization. Therefore, the hybrid approach based on integration mathematical programming and constraint logic programming to optimization resource-constrained scheduling problems has been proposed. To evaluate the applicability and computational efficiency of the proposed approach and its implementation programming framework, the illustrative examples of optimization resource-constrained scheduling problems are implemented separately for mathematical programming and hybrid method.

Constrained scheduling problems are common in manufacturing, project management, transportation, supply chain management, software engineering, computer networks etc. Multiple binary and integer decision variables representing the allocation of resources to activities and numerous specific constraints on these variables are typical components of the constraint scheduling problem modeling. With their increased computational complexity, the models are more demanding, particularly when methods of operations research (mathematical programming, network programming, dynamic programming) are used. By contrast, most resource-constrained scheduling problems can be easily modeled as instances of the constraint satisfaction problems (CSPs) and solved using constraint programming (CP) or others methods. In the CP-based environment the problem definition is separated from the methods and algorithms used to solve the problem. Therefore, a constraint-based approach to resource-constrained scheduling problems that combines an OR-based approach for problem solving and a CP-based approach for problem modeling is proposed. To evaluate the applicability and efficiency of this approach and its implementation framework, illustrative examples of resource-constrained scheduling problems are implemented separately for different environments.

Contributors

Study on the number of decision variables in design and optimization of Varicol process

A Simplex Crossover based evolutionary algorithm including the genetic diversity as objective

Stochastic inventory control in multi-echelon systems poses hard problems in optimisation under uncertainty. Stochastic programming can solve small instances optimally, and approximately solve large instances via scenario reduction techniques, but it cannot handle arbitrary nonlinear constraints or other non-standard features. Simulation optimisation is an alternative approach that has recently been applied to such problems, using policies that require only a few decision variables to be determined. However, to find optimal or near-optimal solutions we must consider exponentially large scenario trees with a corresponding number of decision variables. We propose a neuroevolutionary approach: using an artificial neural network to approximate the scenario tree, and training the network by a simulation-based evolutionary algorithm. We show experimentally that this method can quickly find good plans.KeywordsHide UnitPenalty CostInventory ControlScenario TreeOptimal PlanThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Han-Powell algorithm has proved to be extremely fast and robust for small Optimum Power Problems [1]. There is every reason to believe its performance could be extended to large problems, provided its one serious disadvantage is eliminated. This disadvantage stems from its use of nonsparse approximations to certain Hessian matrices. These matrices are of dimension (m x m) where m is the number of decision variables. Since all the network variables are retained by the algorithm as decision variables, the Hessians quickly get too big to be conveniently accommodated. One remedy is to add a variable-reduction-procedure. Berna, Locke and Westerberg [2] have developed one such procedure. It helps but does not completely eliminate the difficulties. This paper develops another reduction procedure with concepts borrowed from the fields of network dissection and parallel processing. The computations are arranged in two nested loops. The inner loop eliminates n < m of the variables by satisfying the problem's n equality constraints to a tolerance that is tightened as the problem's solution is approached. The outer loop applies the Han-Powell algorithm to the reduced problem. Besides eliminating the need for dealing with unwieldly Hessians, this "reduced method" appears to be as robust as the original Han-Powell algorithm and converges at least as fast for small problems. The method has not yet been tested on large problems, but it is reasonable to expect that it will perform as well on them.

The design of a multipurpose hydro plant requires the analysis of several subjects related to the hydrological, meteorological, environmental, geological, topographical, structural, electrical, mechanical, operational, social, economic and financial aspects. Once a feasible site and a base scheme are identified, the values of the most significant design decision variables must be found. For under pressure schemes they are usually: dam height; type of turbine; number of units; installed power of each unit; diameters of tunnels and pipes and pipe thicknesses. Due to the considerable number of decision variables and constraints, approaches using mathematical programming optimization techniques have been considered. Yet, from our point of view, these approaches do not fully incorporate the financial aspects. As we believe that these aspects are of great importance in the design optimization process, we have developed an optimization model that performs a financial analysis that takes into account the risk associated with the hydrologic and market variability, the promoter’s capital, the loan interest rate, the repayment period, and the fiscal expenses. Research was done using real data from a Portuguese hydro plant. From the examples in this paper, it can be shown that the financial aspects can have a considerable impact on the optimum multipurpose hydro plant design.

Many applications involve the concepts of scheduling, such as communications, packet routing, production planning [Zhai et al., 2006], classroom arrangement [Mathaisel & Comm, 1991], aircrew scheduling [Chang, 2002], nurse scheduling [Ohki et al., 2006], food industrial [Simeonov & Simeonovova, 2002], control system [Fleming & Fonseca, 1993], resource-constrained scheduling problem [Chen, 2007] and grid computing. There are many different types of scheduling problems such as real-time, job-shop, permutation flow-shop, project scheduling and other scheduling problems have been studied intensively. However, in this work, the studied grid task scheduling problem is much more complex than above stated classic task scheduling problems. Restated, a grid application is regarded as a task scheduling problem involving tasks with inter-communication and distributed homogeneous or heterogeneous resources, and can be represented by a task interaction graph (TIG). Grid is a service for sharing computing power and data storage capacity over the Internet. The grid systems outperform simple communication between computers and aims ultimately to turn the global network of computers into one vast computational resource. Grid computing can be adopted in many applications, such as high-performance applications, large-output applications, data-intensive applications and community-centric applications. These applications major concern to efficiently schedule tasks over the available multi-processor environment provided by the grid. A grid is a collaborative environment in which one or more tasks can be submitted without knowing where the resources are or even who owns the resources [Foster et al., 2001]. The efficiency and effectiveness of grid resource management greatly depend on the scheduling algorithm [Lee et al., 2007]. Generally, in the grid environment, these resources are different over time, and such changes will affect the performance of the tasks running on the grid. In grid computing, tasks are assigned among grid system [Salman, 2002]. The purpose of task scheduling in grid is to find optimal task-processor assignment and hence minimize application completion time (total cost). Most scheduling problems in these applications are categorized into the class of NP-complete problems. This implies that it would take amount of computation time to obtain an optimal solution, especially for a large-scale scheduling problem. A variety of approaches have been applied to solve scheduling problems, such as

Classical approaches for the resolution of combinatorial problems are of two kinds: exact methods or approximate ones. Scheduling problems enter in this framework. Up to now, operational research tools were proposed to consider such problems. Recently, new resolution methods were developed. This is the case for the family of stochastic methods or genetic algorithms. But, real life problem that come from the industrial environment require more flexible tools. This is the purpose of constraint logic programming approach. It allows one to ally versatility and efficiency. We will show in this paper, why this new generation of tools seems to be interesting for solving scheduling problems.

A Hybrid Multi-agent Approach to the Solving Supply Chain Problems

This paper describes a new method for modeling and solving different scheduling and resource assignment problems that are common in high-level synthesis (HLS) and system-level synthesis. It addresses assignment of resources for operations and tasks as well as their static, off-line scheduling. Different heterogeneous constraints are considered for these problems. These constraints can be grouped into two classes: problem-specific constraints and design-oriented constraints. They are uniformly modeled, in our approach, by finite domain (FD) constraints and solved using related constrained programming (CP) techniques. This provides a way to improve quality of final solutions. We have developed in Java a constraint solver engine, JaCoP ( Ja va Co nstraint P rogramming), to evaluate this approach. This solver and a related framework make it possible to model different resource assignment and scheduling problems, and handle them uniformly. The JaCoP prototype system has been extensively evaluated on a number of HLS and system-level synthesis benchmarks. We have been able to obtain optimal results together with related proofs of optimality for all HLS scheduling benchmarks and for all explored design styles (except one functional pipeline design). Many system-level benchmarks can also be solved optimally. For large randomly generated task graphs, we have used heuristic search methods and obtained results that are 1--3% worse than lower bounds or optimal results. These experiments have proved the feasibility of the presented approach.

Combination of local search and CLP in the vehicle-fleet scheduling problem

The job-shop scheduling problem is one of the hardest problems (NP-complete problem) {Garey and Johnson 1979, Computer and Intractability: A Guide to the Theory of NP-completeness (San Francisco: Freeman)}. In lots of cases, the combination of goals and resources exponentially increases the search space, and the generation of consistent and satisfying schedules is more and more difficult. This article shows the coupling of three approaches in order to contribute to the solving of the job-shop scheduling problem: genetic algorithms (GAs); constraint logic programming (CLP); and multi-criteria decision-making (MCDM). The GAs are searching algorithms based on the mechanics of natural selection. They employ a probabilistic search for locating the globally optimal solution. They start with an initial population often randomly generated. The difficulty holds in the creation of this initial population which is considered an important parameter of GAs. CLP is a concept based on operation research (OR) and artificial intelligence (AI). It tends to rid itself of their drawbacks and to regroup their advantages. It aims at providing a set of solutions to a problem expressed in term of constraints. A MCDM approach aims at providing an analysis of a set of possible alternatives according to a set of conflicting criteria in order to help the user. This article explains first how to use the CLP to generate a first population. Second it describes the application of GAs to provide a set of job-shop scheduling minimizing the global makespan. Among the set of job-shop scheduling minimizing the global makespan, it is then possible for the decision-maker to select the most satisfying scheduling according to other criteria, e.g. balance of workload or makespan of each manufacturing order. A large-sized example illustrates clearly the advantages of our hybrid method.

Optimal reactive power dispatch using self-adaptive real coded genetic algorithm