Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

Adaptive firefly algorithm for hierarchical text clustering

Text clustering is essentially used by search engines to increase the recall and precision in information retrieval. As search engine operates on Internet content that is constantly being updated, there is a need for a clustering algorithm that offers automatic grouping of items without prior knowledge on the collection. Existing clustering methods have problems in determining optimal number of clusters and producing compact clusters. In this research, an adaptive hierarchical text clustering algorithm is proposed based on Firefly Algorithm. The proposed Adaptive Firefly Algorithm (AFA) consists of three components: document clustering, cluster refining, and cluster merging. The first component introduces Weight-based Firefly Algorithm (WFA) that automatically identifies initial centers and their clusters for any given text collection. In order to refine the obtained clusters, a second algorithm, termed as Weight-based Firefly Algorithm with Relocate (WFAR), is proposed. Such an approach allows the relocation of a pre-assigned document into a newly created cluster. The third component, Weight-based Firefly Algorithm with Relocate and Merging (WFARM), aims to reduce the number of produced clusters by merging nonpure clusters into the pure ones. Experiments were conducted to compare the proposed algorithms against seven existing methods. The percentage of success in obtaining optimal number of clusters by AFA is 100% with purity and f-measure of 83% higher than the benchmarked methods. As for entropy measure, the AFA produced the lowest value (0.78) when compared to existing methods. The result indicates that Adaptive Firefly Algorithm can produce compact clusters. This research contributes to the text mining domain as hierarchical text clustering facilitates the indexing of documents and information retrieval processes

Parallelizing a solution of multicriteria optimization problem for the conditions of a chemical reaction based on CUDA technology

In this work, the task of multicriteria optimization for the conditions of the reaction of alcohols with dimethyl carbonate in the presence of a catalyst for cobalt carbonyl or tungsten carbonyl was solved. The criteria of optimality re considered - the output of the target product and the profitability of the process. Implemented calculation of attainable program in the space of optimality criteria and approximating the Pareto front, the Pareto set. The results of the parallelization efficiency of the computing process are presented

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.Support from the Mathematical Institute, Serbian Academy of Sciences and Arts, are acknowledged for this research

Optimisation des systèmes de stockage de conteneurs dans les terminaux maritimes automatisés

AIn our study, we consider two optimization problems in automated container terminals at import; the first is the vehicle scheduling problem; and the second is the integrated problem of location assignment and vehicle scheduling. In the first part of our study, we propose different traffic layout adapted to the two studied problems and to every kind of automated container terminal. We also introduce relevant reviews of literature treating the optimization of container handling systems at maritime terminal, the optimization of general automated guided vehicle system and the multi-objective optimization in general, and in particular context of maritime container terminals. In the second part, we resolve the planning of QC-AV-ASC (Quay Cranes-Automated Vehicles - Automated Stacking Cranes). We present an effective model for every kind of traffic layout. Moreover, we propose an efficient bi-objective model which is important to determine the optimal storage time and the minimal number of required AVs. CPLEX resolutions are used to prove the efficiency of our modelling approach. In the third part of this thesis, we explore a problem which has not been sufficiently studied: the integrated problem of location assignment and vehicle scheduling (IPLAVS), in Maritime Automated Container Terminal (MACT) at import. This part represents a new and realistic approach of MACT optimization considering mono-objective and multi-objective aspect.Notre travail s’intéresse à un cas très particulier des terminaux à conteneurs, il s’agit des terminaux à conteneurs automatisés, qui en plus des véhicules autoguidés, sont équipés de grues de quai et de grues de stockage automatiques (grues de cour), ce qui pousse souvent les scientifiques à considérer les problèmes d’ordonnancement intégré dans les terminaux automatisés ou semi-automatisés. Nous traitons dans ce travail l’optimisation de plusieurs objectifs pour stocker les conteneurs d'une manière efficace et réaliste. Nous traitons le problème d’ordonnancement intégré considérant les trois équipements d’un terminal à conteneurs automatisé soient: les véhicules autoguidés, les grues de quai et les grues de baie (éventuellement). L’objectif principal de cette étude est la minimisation du coût opérationnel de stockage de conteneurs dans un terminal maritime automatis

Cooperative Models of Particle Swarm Optimizers

Particle Swarm Optimization (PSO) is one of the most effFective optimization tools, which emerged in the last decade. Although, the original aim was to simulate the behavior of a group of birds or a school of fish looking for food, it was quickly realized that it could be applied in optimization problems. Different directions have been taken to analyze the PSO behavior as well as improving its performance. One approach is the introduction of the concept of cooperation. This thesis focuses on studying this concept in PSO by investigating the different design decisions that influence the cooperative PSO models' performance and introducing new approaches for information exchange. Firstly, a comprehensive survey of all the cooperative PSO models proposed in the literature is compiled and a definition of what is meant by a cooperative PSO model is introduced. A taxonomy for classifying the different surveyed cooperative PSO models is given. This taxonomy classifies the cooperative models based on two different aspects: the approach the model uses for decomposing the problem search space and the method used for placing the particles into the different cooperating swarms. The taxonomy helps in gathering all the proposed models under one roof and understanding the similarities and differences between these models. Secondly, a number of parameters that control the performance of cooperative PSO models are identified. These parameters give answers to the four questions: Which information to share? When to share it? Whom to share it with? and What to do with it? A complete empirical study is conducted on one of the cooperative PSO models in order to understand how the performance changes under the influence of these parameters. Thirdly, a new heterogeneous cooperative PSO model is proposed, which is based on the exchange of probability models rather than the classical migration of particles. The model uses two swarms that combine the ideas of PSO and Estimation of Distribution Algorithms (EDAs) and is considered heterogeneous since the cooperating swarms use different approaches to sample the search space. The model is tested using different PSO models to ensure that the performance is robust against changing the underlying population topology. The experiments show that the model is able to produce better results than its components in many cases. The model also proves to be highly competitive when compared to a number of state-of-the-art cooperative PSO algorithms. Finally, two different versions of the PSO algorithm are applied in the FPGA placement problem. One version is applied entirely in the discrete domain, which is the first attempt to solve this problem in this domain using a discrete PSO (DPSO). Another version is implemented in the continuous domain. The PSO algorithms are applied to several well-known FPGA benchmark problems with increasing dimensionality. The results are compared to those obtained by the academic Versatile Place and Route (VPR) placement tool, which is based on Simulated Annealing (SA). The results show that these methods are competitive for small and medium-sized problems. For higher-sized problems, the methods provide very close results. The work also proposes the use of different cooperative PSO approaches using the two versions and their performances are compared to the single swarm performance

Optimised search heuristics: combining metaheuristics and exact methods to solve scheduling problems

Tese dout., Matemática, Investigação Operacional, Universidade do Algarve, 2009Scheduling problems have many real life applications, from automotive industry to air traffic control. These problems are defined by the need of processing a set of jobs on a shared set of resources. For most scheduling problems there is no known deterministic procedure that can solve them in polynomial time. This is the reason why researchers study methods that can provide a good solution in a reasonable amount of time. Much attention was given to the mathematical formulation of scheduling problems and the algebraic characterisation of the space of feasible solutions when exact algorithms were being developed; but exact methods proved inefficient to solve real sized instances. Local search based heuristics were developed that managed to quickly find good solutions, starting from feasible solutions produced by constructive heuristics. Local search algorithms have the disadvantage of stopping at the first local optimum they find when searching the feasible region. Research evolved to the design of metaheuristics, procedures that guide the search beyond the entrapment of local optima. Recently a new class of hybrid procedures, that combine local search based (meta) heuristics and exact algorithms of the operations research field, have been designed to find solutions for combinatorial optimisation problems, scheduling problems included. In this thesis we study the algebraic structure of scheduling problems; we address the existent hybrid procedures that combine exact methods with metaheuristics and produce a mapping of type of combination versus application and finally we develop new innovative metaheuristics and apply them to solve scheduling problems. These new methods developed include some combinatorial optimisation algorithms as components to guide the search in the solution space using the knowledge of the algebraic structure of the problem being solved. Namely we develop two new methods: a simple method that combines a GRASP procedure with a branch-and-bound algorithm; and a more elaborated procedure that combines the verification of the violation of valid inequalities with a tabu search. We focus on the job-shop scheduling problem

Cardinality constraints and dimensionality reduction in optimization problems

Tesis doctoral inédita. Universidad Autónoma de Madrid, Escuela Politécnica Superior, junio de 201