Scheduling problem using genetic algorithm,simulated annealing and the effects of parameter values on GA performance

Genetics algorithms have been designed as general purpose optimisation methods. Simulated annealing simulates the cooling process of solid materials-known as annealing. However this analogy is limited to the physical movement of the molecules without involving complex thermodynamic systems. Physical annealing refers to the process of cooling a solid material so that it reaches a low energy state. Initially the solid is heated up to the melting point. Then it is cooled very slowly, allowing it is to come to thermal equilibrium at each temperature. This process of slow cooling is called annealing. The goal is to find the best arrangement of molecules that minimises the energy of the system, which is referred to as the ground state of the solid material. If the cooling process is fast, the solid will not attain the ground state, but a locally optimal structure. In this paper presents a general purpose schedule optimiser for manufacturing shop scheduling using genetic algorithms and simulated annealing. Then, the ‘uniform order-based’ crossover and mutation operators and novel general effects of parameter values on minimised objective value are presented.     

一种求解延迟工件数最小的混合流水车间调度问题的模拟退火算法

针对延迟工件数最小的混合流水车间调度问题,给出了一种改进的模拟退火求解算法. 该算法首先给出一个启发式算法来获得初始解,然后用模拟退火算法对初始解改进. 通过交换工件在第一阶段的排序来获得一个新的解,采用最先空闲设备分配规则和先到先被加工规则,对工件在剩余各级的工序进行调度. 实验仿真表明算法是可行有效的.     

Scheduling surgical procedures

The scheduling of surgical procedures in hospitals is examined in the context of an optimisation problem. The solution procedure proposed uses simulated annealing to find improved solutions. An assessment of current practice reveals that customising of any automated procedure will be necessary as the constraints used to describe the problem are often hospital specific.     

A Distributed Evolutionary Simulated Annealing Algorithm for Combinatorial Optimisation Problems

In this paper, the Evolutionary Simulated Annealing (ESA) algorithm, its distributed implementation (dESA) and its application to two combinatorial problems are presented. ESA consists of a population, a simulated annealing operator, instead of the more usual reproduction operators used in evolutionary algorithms, and a selection operator. The implementation is based on a multi island (agent) system running on the Distributed Resource Machine (DRM), which is a novel, scalable, distributed virtual machine based on Java technology. As WAN/LAN systems are the most common multi-machine systems, dESA implementation is based on them rather than any other parallel machine. The problems tackled are well-known combinatorial optimisation problems, namely, the classical job-shop scheduling problem and the uncapacitated facility location problem. They are difficult benchmarks, widely used to measure the efficiency of metaheuristics with respect to both the quality of the solutions and the central processing unit (CPU) time spent. Both applications show that dESA solves problems finding either the optimum or a very near optimum solution within a reasonable time outperforming the recent reported approaches for each one allowing the faster solution of existing problems and the solution of larger problems.     

A priority list based heuristic for the job shop problem

A priority list for the job shop scheduling problem is defined to be any permutation of a set of symbols where the symbol for each job appears as many times as the number of its operations. Every priority list can be associated in a natural way with a feasible schedule, and every feasible schedule arises in this way. Priority lists are therefore a representation of feasible schedules that avoid the problems normally associated with schedule infeasibility. As a result, the three ingredients of local search heuristics, namely picking initial starting schedules, constructing search neighbourhoods and computing makespans, become faster and easier when performed in the space of priority lists rather than in the space of feasible schedules. As an illustration of their usefulness, a priority list based simulated annealing heuristic is presented, which, although simple, is competitive with the current leading schedule based simulated annealing and tabu search heuristics.     

Investigation of temperature parallel simulated annealing for optimizing continuous functions with application to hyperspectral tomography

The simulated annealing (SA) algorithm is a well-established optimization technique which has found applications in many research areas. However, the SA algorithm is limited in its application due to the high computational cost and the difficulties in determining the annealing schedule. This paper demonstrates that the temperature parallel simulated annealing (TPSA) algorithm, a parallel implementation of the SA algorithm, shows great promise to overcome these limitations when applied to continuous functions. The TPSA algorithm greatly reduces the computational time due to its parallel nature, and avoids the determination of the annealing schedule by fixing the temperatures during the annealing process. The main contributions of this paper are threefold. First, this paper explains a simple and effective way to determine the temperatures by applying the concept of critical temperature (T_C). Second, this paper presents systematic tests of the TPSA algorithm on various continuous functions, demonstrating comparable performance as well-established sequential SA algorithms. Third, this paper demonstrates the application of the TPSA algorithm on a difficult practical inverse problem, namely the hyperspectral tomography problem. The results and conclusions presented in this work provide are expected to be useful for the further development and expanded applications of the TPSA algorithm.     

Construction of factory schedules using reverse simulation

A real-world, multi-stage, industrial scheduling problem is presented. An algorithm is described that converts a sequence of jobs into a complete schedule. Backward simulation is used to determine minimum storage requirements when scheduling each job, and to calculate the minimum amount of delay required. Combining this algorithm with a metaheuristic, such as simulated annealing, results in an effective algorithm for schedule optimization.     

Design method using hybrid of line-type and circular-type routes for transit network system optimization

Transit network design is a very important problem. In particular, it has a great influence on passenger satisfaction with the whole transit network system. The present research proposes a simulated annealing (SA) method for optimizing a transit network design. In the algorithm, the strategy to search for neighborhood solutions provides the chance to find the best hybrid of line-type and circular-type routes. The proposed SA method is also compared with other methods. The results show that the proposed SA model is a good alternative for transit network design, particularly as it provides the scope to design hybrids of line-type and circular-type routes.     

Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem

This paper describes serial and parallel implementations of two different search techniques applied to the traveling salesman problem. A novel approach has been taken to parallelize simulated annealing and the results are compared with the traditional annealing algorithm. This approach uses abbreviated cooling schedule and achieves a superlinear speedup. Also a new search technique, called tabu search, has been adapted to execute in a parallel computing environment. Comparison between simulated annealing and tabu search indicate that tabu search consistently outperforms simulated annealing with respect to computation time while giving comparable solutions. Examples include 25, 33, 42, 50, 57, 75 and 100 city problems.     

Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.     

Order planning for networked make-to-order enterprises—a case study

From the general trend towards global markets and a growing customer orientation, new concepts and forms of organisation are emerging, such as distributed or networked enterprises. One key requirement of these new paradigms is the availability of models and tools to support order negotiation with the optimisation of manufacturing routes and logistics and ensuring the co-ordination of all participating entities. We address the problem of planning an incoming customer order to be produced in a distributed (multi-site) and multi-stage production system. In particular, we have used as a case study the industry of semiconductors (in the business area of application specific integrated circuits). The problem is tackled in a hierarchical model, in two levels: there is a global network planning procedure, and a set of local capacity models associated to the different production units reflecting their particular features. An approach based on simulated annealing is presented, as well as a specially designed constructive heuristic, that takes into account many of the real world constraints and complexities. The general performance of the simulated annealing algorithm is assessed through some preliminary computational experiments. Finally, some concluding remarks and current directions of research are presented.     

Traditional heuristic versus Hopfield neural network approaches to a car sequencing problem

This paper considers the problem of optimally sequencing different car models along an assembly line according to some contiguity constraints, while ensuring that the demands for each of the models are satisfied. This car sequencing problem (CSP) is a practical NP-hard combinatorial optimisation problem. The CSP is formulated as a nonlinear integer programming problem and it is shown that exact solutions to the problem are difficult to obtain due to the indefinite quadratic form of the CSP objective function. Two traditional heuristics (steepest descent and simulated annealing) are employed to solve the CSP approximately. Several Hopfield neural network (HNN) approaches are also presented. The process of mapping an optimisation problem onto a HNN is demonstrated explicitly, and modifications to the existing neural approaches are presented which guarantee feasibility of solutions. Further modifications are proposed to improve the solution quality by permitting escape from local minima in an attempt to locate the global optimum. Results from all solutions techniques are compared on a set of instances of the CSP, and conclusions drawn.     

A simulated annealing algorithm for resource constrained project scheduling problems

This paper presents a simulated annealing algorithm for resource constrained project scheduling problems with the objective of minimising makespan. In the search algorithm, a solution is represented with a priority list, a vector of numbers each of which denotes the priority of each activity. In the algorithm, a priority scheduling method is used for making a complete schedule from a given priority list (and hence a project schedule is defined by a priority list). The search algorithm is applied to find a priority list which corresponds to a good project schedule. Unlike most of priority scheduling methods, in the suggested algorithm some activities are delayed on purpose so as to extend search space. Solutions can be further improved by delaying certain activities, since non-delay schedules are not dominant in the problem (the set of non-delay schedules does not always include an optimal solution). The suggested algorithm is flexible in that it can be easily applied to problems with an objective function of a general form and/or complex constraints. The performance of the simulated annealing algorithm is compared with existing heuristics on problems prepared by Patterson and randomly generated test problems. Computational results showed that the suggested algorithm outperformed existing ones.     

Analytical and stochastic modelling techniques

In mining supply chains, large combinatorial optimization problems arise. These are NP-hard and typically require a large number of computing resources to solve them. In particular, the run-time overheads can become increasingly prohibitive with increasing problem sizes. Parallel methods provide a way to manage such run-time issues by utilising several processors in independent or shared memory architectures. However it is not obvious how to adapt serial optimisation algorithms to perform best in a parallel environment. Here, we consider a resource constrained scheduling problem which is motivated in mining supply chains and present two popular meta-heuristics, ant colony optimization (ACO) and simulated annealing and investigate how best to parallelize these methods on a shared memory architecture consisting of several cores. ACO’s solution construction framework is inherently parallel allowing a relatively straightforward parallel implementation. However, for best performance, ACO needs an element of local search. This significantly complicates the paralellization. Several alternative schemes for parallel ACO with elements of local search are considered and evaluated empirically. We find that ACO with local search is the most effective single-threaded algorithm. The best parallel implementation can obtain similar quality results to the serial method in significantly less elapsed time.     

A comparison of acceptance criteria for the adaptive large neighbourhood search metaheuristic

Adaptive large neighborhood search (ALNS) is a useful framework for solving difficult combinatorial optimisation problems. As a metaheuristic, it consists of some components that must be tailored to the specific optimisation problem that is being solved, while other components are problem independent. The literature is sparse with respect to studies that aim to evaluate the relative merit of different alternatives for specific problem independent components. This paper investigates one such component, the move acceptance criterion in ALNS, and compares a range of alternatives. Through extensive computational testing, the alternative move acceptance criteria are ranked in three groups, depending on the performance of the resulting ALNS implementations. Among the best variants, we find versions of criteria based on simulated annealing, threshold acceptance, and record-to-record travel, with a version of the latter being consistently undominated by the others. Additional analyses focus on the search behavior, and multiple linear regression is used to identify characteristics of search behavior that are associated with good search performance.     

An analytically derived cooling schedule for simulated annealing

We present an analytically derived cooling schedule for a simulated annealing algorithm applicable to both continuous and discrete global optimization problems. An adaptive search algorithm is used to model an idealized version of simulated annealing which is viewed as consisting of a series of Boltzmann distributed sample points. Our choice of cooling schedule ensures linearity in the expected number of sample points needed to become arbitrarily close to a global optimum.     

Performance Analysis of Cyclical Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms for addressing intractable discrete optimization problems. Measures for assessing the finite-time performance of GHC algorithms have been developed using this framework, including the expected number of iterations to visit a predetermined objective function value level. This paper analyzes how the expected number of iterations to visit a predetermined objective function value level can be estimated for cyclical simulated annealing. Cyclical simulated annealing uses a cooling schedule that cycles through a set of temperature values. Computational results with traveling salesman problem instances taken from TSPLIB show how the expected number of iterations to visit solutions with predetermined objective function levels can be estimated for cyclical simulated annealing.AMS 2000 Subject Classification 90-08 Computational Methods: Local Search, 90C59 Heuristics: Simulated Annealing     

A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect

This paper considers a scheduling model involving two agents, job release times, and the sum-of-processing-times-based learning effect. The sum-of-processing-times-based learning effect means that the actual processing time of a job of either agent is a decreasing function of the sum of the processing times of the jobs already scheduled in a given schedule. The goal is to seek for an optimal schedule that minimizes the total weighted completion time of the first agent, subject to no tardy job for the second agent. We first provide a branch-and-bound method to solve the problem. We then develop an approach that combines genetic algorithm and simulated annealing to seek for approximate solutions for the problem. We carry on extensive computational tests to assess the performance of the proposed algorithms.     

A Two Stage Search Heuristic for Scheduling Payments in Projects

When the Net Present Value (NPV) of a project is used as a measure of its financial performance, effective management of cash flows over the duration of the project is critical for improved profitability. Progress payments are a major component of project cash flows. In many project environments, the contractor can negotiate payment terms. Payments are typically tied to completion of project activities and therefore have significant impact on the schedule of activities and the timing of the payments. In this paper, we consider the problem of simultaneously determining the amount, timing and location of progress payments in projects to maximize NPV. Due to the combinatorial nature of the problem, heuristics are a practical approach to solving the problem. We propose a two-stage heuristic where simulated annealing is used in the first stage to determine a set of payments. In the second stage, activities are rescheduled to improve project NPV. We compare the performance of this general purpose heuristic with other problem-dependent heuristics from the literature. Our results indicate that the simulated annealing heuristic significantly outperforms the parameter-based heuristics. Although rescheduling in the second stage improves NPV, increases are relatively small in magnitude. While the specific parameters settings suggested by the simulated annealing heuristic in this study may have limited generalizability at this time due to the narrow range of problems tested, our analysis suggests that a pure simulated annealing approach is a very attractive alternative for obtaining good heuristic solutions to the complex problem of scheduling payments in projects.