Scheduling for Schools

. The industrial and commercial worlds are increasingly competitive, requiring companies to be more productiveand more responsive to market changes (e.g. globalisation and privatisation). As a consequence, there is a strong need for solutions to large scale optimization problems, in domains such as production scheduling, transport, finance and network management. This means that more experts in constraint programming and optimization technology are required to develop adequate software. Given the computational complexity of Large Scale Combinatorial Optimization problems, a key question is how to help/guide in the tackling of LSCO problems in industry. Optimization technology is certainly reaching a level of maturity. Having emerged in the 50s within the Operational Research community, it has evolved and comprises new paradigms such as constraint programming and stochastic search techniques. There is a practical need, i.e. efficiency, scalability and tractability, to integrate techniques from the different paradigms. This adds complexity to the design of LSCO models and solutions. Various forms of guidance are available in the literature in terms of 1) case studies that map powerful algorithms to problem instances, and 2) visualization and programming tools that ease the modelling and solving of LSCOs. However, there is little guidance to address the process of building applications for new LSCO problems (independently of any language). This article gives an overview of the CHIC-2 methodology which aims at filling a gap in this direction. In particular, we describe some management issues specific to LSCOs such as risk management and team structures, and focus on the technical development guidance for scoping, designing and implementing LSCO appl...

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

Ant colony optimization(ACO) provides an effective way to solve combinatorial optimization problem. However, with the complexity of the problem increasing, the ACO algorithm needs considerable computational time and resources to improve the good quality of solution, and this rarely satisfies the requirement of real-time computing in M&S (Modeling and Simulation) area. Parallel implementation of ACO can reduce the computational time obviously for the large scale combinatorial optimization problem, and much of the previous work in this field focuses on parallel implementation using MPI which is executed on clusters. Meanwhile, great emphasis is placed on multi-core computing technology with the development of multi-processor architecture and multi-core architecture. A new parallel ant colony optimization (PACO) algorithm is proposed, which applies two kinds of typical multi-core computing technologies, the well-known OpenMP and the recently introduced TBB (Threading Building Blocks) library by Intel Corporation, to solve target assignment problem(TAP). Effectiveness and efficiency of proposed algorithm is validated by studying the convergence speed, problem size scalability and thread size scalability of it.

Optimal placement of the water quality sensor refers to the arrangement of best water quality sensor deployment in water distribution systems to test the accidental or intentional contaminant. The optimization problem is essentially a kind of large scale combinatorial optimization problem and it needs the highly reliable and highly scalable resources to solve the problem. Traditional methods to solve this kind of problems are usually using MPI. But it can't meet the demand of QoS (quality of service) which contains reliability, scalability and flexibility. In order to solve this problem, we have developed a solution which is parallel and we use the Map/Reduce computation model in Clouds, namely the parallel GA. It uses Map/Reduce framework to parallelize the process. A middle-sized water distribution network is tested by the proposed algorithm, and the results indicate that the parallel GA with Map/Reduce can cut the computing time and deliver a high performance.

As pointed out in the introduction (chapter 1) there exists a clear analogy between the annealing of solids and the problem of solving large combinatorial optimization problems. The physical annealing process can be successfully modelled by using computer simulation methods from condensed matter physics [BAR76], [WOOD68]. These methods in turn are based on the theory of statistical mechanics which can be viewed as the central discipline of condensed matter physics [BIN78], [TOD83]. Starting off with the first paper on simulated annealing by Kirkpatrick et al. [KIR82], a number of authors elaborate on the relation between combinatorial optimization and statistical mechanics, either because of a phenomenological interest in the analogy (Bernasconi [BER87], Bonomi and Lutton [BON84], Kirkpatrick et al. [KIR82], [KIR83], [KIR85] and Mezard and Parisi [MEZ85], [MEZ86]) or because of a possible framework to model the convergence and the corresponding control of the simulated annealing algorithm (Aarts and Van Laarhoven [AAR85a], [AAR88a], Grest et al. [GRES86], Kirkpatrick et al. [KIR82], [KIR83], Otten and Van Ginneken [OTT84], Randelman and Grest [RAN86] and White [WHI84]). In this chapter a number of quantities are discussed that are defined in the theory of statistical mechanics for the description of a physical many-particle system at equilibrium and it will be elucidated how these quantities are related to the problem of solving large combinatorial optimization problems.

Given a schedule of trains, the locomotive planning (or scheduling) problem (LPP) is to determine the minimum cost assignment of locomotive types to trains that satisfies a number of business and operational constraints. Once this is done, the railroad has to determine the sequence of trains to which each locomotive is assigned by unit number so that it can be fueled and serviced as necessary. We refer to this problem as the locomotive routing problem (LRP). The LRP is a very large scale combinatorial optimization problem, and the general version that we consider has previously been unstudied and unsolved in the research literature. In this paper, we develop robust optimization methods to solve the LRP. There are two major sets of constraints that need to be satisfied by each locomotive route: (1) locomotive fueling constraints, which require that every unit visit a fueling station at least once for every F miles of travel, and (2) locomotive servicing constraints, which require that every unit visit a service station at least once for every S miles of travel. The output of the LPP is not directly implementable because the LPP does not consider these fueling and servicing constraints. The LRP considers these constraints, and its output is therefore implementable. We model the LRP by considering alternative fueling and servicing friendly train paths (or strings) between servicing stations on the network. We formulate the LRP as an integer programming problem on a suitably constructed space-time network and show that this problem is NP-Complete. This integer programming problem has millions of decision variables. We develop a fast aggregation-disaggregation based algorithm to solve the problem within a few minutes of computational time to near optimality. Finally, we present computational results and extensive case studies of our algorithms on real data provided by a major Class I U.S. railroad.

In recent years, the integration of techniques from Artificial Intelligence and Operations Research has shown to improve the solutions of complex and large scale combinatorial optimization problems, in terms of efficiency, scalability and optimality. In this context, Constraint Programming is an emerging discipline situated at the confluence of the two fields that has been recognized as a suitable environment for achieving such an integration. This paper briefly presents the integration directions explored in the literature, and provides some pointers to relevant work in these directions.

Finding the Right Hybrid Algorithm - A Combinatorial Meta-Problem

This article proposes a novel method for solving traffic signal coordination problem under over-saturated conditions. This problem is a large combinatorial optimization problem formulated as a dynamic optimization problem. The algorithm derives optimal green times for a network consisting of 20 interconnected signals using termite spatial correlation optimization (TSCO) algorithm. The algorithm tries to do so by incorporating proper queue dissipation along with maximizing number of vehicles precessed by the network in the congestion period. The resulted green times and fitness values have been compared with those derived using Genetic Algorithm (GA) and Ant Colony Optimization (ACO). TSCO is shown to outperform GA and ACO in terms of fitness value as well as overall function evaluations.

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.

Simulated annealing is a probabilistic algorithm for approximately solving large combinatorial optimization problems. The algorithm can mathematically be described as the generation of a series of Markov chains, in which each Markov chain can be viewed as the outcome of a random experiment with unknown parameters (the probability of sampling a cost function value). Assuming a probability distribution on the values of the unknown parameters (the prior distribution) and given the sequence of configurations resulting from the generation of a Markov chain, we use Bayes's theorem to derive the posterior distribution on the values of the parameters. Numerical experiments are described which show that the posterior distribution can be used to predict accurately the behavior of the algorithm corresponding to the next Markov chain. This information is also used to derive optimal rules for choosing some of the parameters governing the convergence of the algorithm.

Simulated annealing is an effective method for solving large combinatorial optimisation problems. Because of its iterative nature the annealing process requires substantial amount of computation time. A new parallel implementation based on the concurrency control theory of database systems is presented; the parallelised annealing process is serialisable. Concurrent updates to the base solution are allowed provided that they do not have data conflict. Using the travelling salesman problem as the example application, the parallel simulated annealing algorithm is implemented on a Motorola Delta 3000 shared-memory multiprocessor system with eight processors. With a moderate problem size of 400 cities, a speedup efficiency of over 90% is achieved at high annealing temperature and close to 100% at low annealing temperature.

There are many problems in the real world that can be modeled as large scale global optimization problems. Usually, large scale global optimization problems are global optimization problems where the dimensions are greater than or equal to 1000. In this research, we propose a genetic algorithm that can be used to solve large scale optimization problems with dimensions up to 100000. To measure the capabilities of the proposed genetic algorithm, we use five different test functions. Based on the results obtained, it can be inferred that the proposed genetic algorithm can find a good solution in a fairly short time.

Self organizing migrating algorithm with quadratic interpolation for solving large scale global optimization problems

Many real life problems that play a major role in human lives are mostly optimization problems and need to be solved in order to judiciously utilize vital resources. The vast solution space consists of a large number of feasible solutions. Solving these problems requires finding the most optimal solution while satisfying the constraints imposed (if any). Vehicle Routing is a real life problem originated primarily in the logistics industry where the consignments are to be delivered to the clients in such a way, that there is minimal usage of resources like fuel, and time. In addition, the consignments are to be successfully delivered to the clients through the shortest route and utilizing the maximum capacity of each vehicle. Automation is the key to solve such large problems while reducing effort and complexity of the solution. Literature reveals that nature inspired algorithms have proved their ability for solving such large complex optimization problems. These algorithms are inspired from various natural phenomena and are supported by their successful survival. This paper proposes a hybrid framework to solve Vehicle Routing Problem (VRP) utilizing Differential Evolution and Marine Predators algorithm. We have considered the variant called Capacitated Vehicle Routing Problem (CVRP) to conduct experiments and compared the results to evaluate the performance of proposed hybrid approach DEMPA with Differential Evolution (DE). Results indicate the superiority of the proposed approach over Differential Evolution.