3D packing of balls in different containers by VNS

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityIn real world applications such as the transporting of goods products, packing is a major issue. Goods products need to be packed such that the smallest space is wasted to achieve the maximum transportation efficiency. Packing becomes more challenging and complex when the product is circular/spherical. This thesis focuses on the best way to pack three-dimensional unit spheres into the smallest spherical and cubical space. Unit spheres are considered in lieu of non-identical spheres because the search mechanisms are more difficult in the latter set up and any improvements will be due to the search mechanism not to the ordering of the spheres. The two-unit sphere packing problems are solved by approximately using a variable neighborhood search (VNS) hybrid heuristic. A general search framework belonging to the Artificial Intelligence domain, the VNS offers a diversification of the search space by changing neighborhood structures and intensification by thoroughly investigating each neighborhood. It is exible, easy to implement, adaptable to both continuous and discrete optimization problems and has been use to solve a variety of problems including large-sized real-life problems. Its runtime is usually lower than other meta heuristic techniques. A tutorial on the VNS and its variants along with recent applications and areas of applicability of each variant. Subsequently, this thesis considers several variations of VNS heuristics for the two problems at hand, discusses their individual efficiencies and effectiveness, their convergence rates and studies their robustness. It highlights the importance of the hybridization which yields near global optima with high precision and accuracy, improving many best- known solutions indicate matching some, and improving the precision and accuracy of others. Keywords: variable neighborhood search, sphere packing, three-dimensional packing, meta heuristic, hybrid heuristics, multiple start heuristics

Metaheuristic approach for solving scheduling and financial derivative problems

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe objective of this thesis is to implement metaheuristic approaches to solve di erent types of combinatorial problems. The thesis is focused on neighborhood heuristic optimisation techniques such as Variable Neighborhood Search (VNS) and Ant Colony Optimisation (ACO) algorithms. The thesis will focus on two diverse combinatorial problems. A job shop scheduling problem, and a nancial derivative matching problem. The rst is a NP-hard 2-stage assembly problem, where we will be focussing on the rst stage. It consists of sequencing a set of jobs having multiple components to be processed. Each job has to be worked on independently on a speci c machine. We consider these jobs to form a vector of tasks. Our objective is to schedule jobs on the particular machines in order to minimise the completion time before the second stage starts. In this thesis, we have constructed a new hybrid metaheuristic approach to solve this unique job shop scheduling problem. The second problem has arisen in the nancial sector, where the nancial regulators collects transaction data across regulated assets classes. Our focus is to identify any unhedged derivative, Contract for Di erence (CFD), with its corresponding underlying asset that has been reported to the corresponding component authorities. The underlying asset and CFD transaction contain di erent variables, like volume and price. Therefore, we are looking for a combination of underlying asset variables that may hedge the equivalent CFD variables. Our aim is to identify unhedged or unmatched CFD's with their corresponding underlying asset. This problem closely relates to the goal programming problem with variable parameters. We have developed two new local search methods and embedded the newly constructed local search methods with basic VNS, to attain a new modi ed variant of the VNS algorithm. We then used these newly constructed VNS variants to solve this nancial matching problem. In tackling the Vector Job Scheduling problem, we developed a new hybrid optimisation heuristic algorithm by combining VNS and ACO. We then compared the results of this hybrid algorithm with VNS and ACO on their own. We found that the hybrid algorithm performance is better than the other two independent heuristic algorithms. In tackling the nancial derivative problem, our objective is to match the CFD trades with their corresponding underlying equity trades. Our goal is to identify the mismatched CFD trades while optimising the search process. We have developed two new local search techniques and we have implemented a VNS algorithm with the newly developed local search techniques to attain better solutions

Variable Formulation and Neighborhood Search Methods for the Maximum Clique Problem in Graph

Doktorska disertacija se bavi temama rešavanja računarski teških problema kombinatorne optimizacije. Istaknut je problem maksimalne klike kao predstavnik određenih struktura u grafovima. Problem maksimalne klike i sa njim povezani problemi su formulisani kao nelinearne funkcije. Rešavani su sa ciljem otkrivanja novih metoda koje pronalaze dobre aproksimacije rešenja za neko razumno vreme. Predložene su varijante Metode promenljivih okolina na rešavanje maksimalne klike u grafu. Povezani problemi na grafovima se mogu primeniti na pretragu informacija, raspoređivanje, procesiranje signala, teoriju klasifikacije, teoriju kodiranja, itd. Svi algoritmi su implementirani i uspešno testirani na brojnim različitim primerima.This Ph.D. thesis addresses topics NP hard problem solving approaches in combinatorial optimization and according to that it is highlighted maximum clique problem as a representative of certain structures in graphs. Maximum clique problem and related problems with this have been formulated as non linear functions which have been solved to research for new methods and good solution approximations for some reasonable time. It has been proposed several different extensions of Variable Neighborhood Search method. Related problems on graphs could be applied on information retrieval, scheduling, signal processing, theory of classi_cation, theory of coding, etc. Algorithms are implemented and successfully tested on various different tasks

Algorithms for vehicle routing problems with heterogeneous fleet, flexible time windows and stochastic travel times

Orientador: Vinícius Amaral ArmentanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Este trabalho aborda três variantes multiatributo do problema de roteamento de veículos. A primeira apresenta frota heterogênea, janelas de tempo invioláveis e tempos de viagem determinísticos. Para resolvê-la, são propostos algoritmos ótimos baseados na decomposição de Benders. Estes algoritmos exploram a estrutura do problema em uma formulação de programação inteira mista, e três diferentes técnicas são desenvolvidas para acelerá-los. A segunda variante contempla os atributos de frota heterogênea, janelas de tempo flexíveis e tempos de viagem determinísticos. As janelas de tempo flexíveis permitem o início do serviço nos clientes com antecipação ou atraso limitados em relação às janelas de tempo invioláveis, com custos de penalidade. Este problema é resolvido por extensões dos algoritmos de Benders, que incluem novos algoritmos de programação dinâmica para a resolução de subproblemas com a estrutura do problema do caixeiro viajante com janelas de tempo flexíveis. A terceira variante apresenta frota heterogênea, janelas de tempo flexíveis e tempos de viagem estocásticos, sendo representada por uma formulação de programação estocástica inteira mista de dois estágios com recurso. Os tempos de viagem estocásticos são aproximados por um conjunto finito de cenários, gerados por um algoritmo que os descreve por meio da distribuição de probabilidade Burr tipo XII, e uma matheurística de busca local granular é sugerida para a resolução do problema. Extensivos testes computacionais são realizados em instâncias da literatura, e as vantagens das janelas de tempo flexíveis e dos tempos de viagem estocásticos são enfatizadasAbstract: This work addresses three multi-attribute variants of the vehicle routing problem. The first one presents a heterogeneous fleet, hard time windows and deterministic travel times. To solve this problem, optimal algorithms based on the Benders decomposition are proposed. Such algorithms exploit the structure of the problem in a mixed-integer programming formulation, and three algorithmic enhancements are developed to accelerate them. The second variant comprises a heterogeneous fleet, flexible time windows and deterministic travel times. The flexible time windows allow limited early and late servicing at customers with respect to their hard time windows, at the expense of penalty costs. This problem is solved by extensions of the Benders algorithms, which include novel dynamic programming algorithms for the subproblems with the special structure of the traveling salesman problem with flexible time windows. The third variant presents a heterogeneous fleet, flexible time windows and stochastic travel times, and is represented by a two-stage stochastic mixed-integer programming formulation with recourse. The stochastic travel times are approximated by a finite set of scenarios generated by an algorithm which describes them using the Burr type XII distribution, and a granular local search matheuristic is suggested to solve the problem. Extensive computational tests are performed on instances from the literature, and the advantages of flexible windows and stochastic travel times are stressed.DoutoradoAutomaçãoDoutor em Engenharia Elétrica141064/2015-3CNP