A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems

Computational methods in codes and games

This dissertation discusses exhaustive search algorithms and heuristic search methods in combinatorial optimization, including combinatorial games. In this work unidirectional covering codes are introduced and some theoretical foundations for them are laid. Exhaustive search is used to construct asymmetric covering codes, unidirectional covering codes and multiple coverings with given parameters—or to show that no such codes exist. Integer programming formulations, bounds on maximal coverages of partial codes and code isomorphisms are used to prune the search space. Tabu search is used to construct asymmetric and unidirectional covering codes—with several record-breaking codes for the former. A new definition for neighborhood is derived. The traditional board game of go and computer go results are reviewed. The concept of entropy is introduced into the game context as a metric for complexity and for relevance (of features—like distance to the previous move). Experimental results and questionnaire studies are presented to support the use of entropy

A covering problem over finite rings

AbstractGiven a finite commutative ring with identity A, define c(A,n,R) as the minimum cardinality of a subset H of An which satisfies the following property: every element in An differs in at most R coordinates from a multiple of an element in H. In this work, we determine the numbers c(Zm,n,0) for all integers m≥2 and n≥1. We also prove the relation c(S×A,n,1)≤c(S,n−1,0)c(A,n,1), where S=Fq or Zq and q is a prime power. As an application, an upper bound is obtained for c(Zpm,n,1), where p is a prime

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Dynamic Optimization of Network Routing Problem through Ant Colony Optimization (ACO)

Search Based Software Engineering (SBSE) is a new paradigm of Software engineering, which considers software engineering problems as search problems and emphasizes to find out optimal solution for the given set of available solutions using metaheuristic techniques like hill climbing simulated annealing, evolutionary programming and tabu search. On the other hand AI techniques like Swarm particle optimization and Ant colony optimization (ACO) are used to find out solutions for dynamic problems. SBSE is yet not used for dynamic problems. In this study ACO techniques are applied on SBSE problem by considering Network routing problem as case study, in which the nature of problem is dynamic. Keywords: SBSE, ACO, Metaheuristic search techniques, dynamic optimizatio

Algoritmos e formulações matemáticas para problemas de roteamento em arcos

Orientador: Fábio Luiz UsbertiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de roteamento em arcos têm por objetivo determinar rotas de custo mínimo que visitam um subconjunto de arcos de um grafo, com uma ou mais restrições adicionais. Esta tese estuda três problemas NP-difíceis de roteamento em arcos: (1) o problema de roteamento em arcos capacitado (CARP); (2) o problema de roteamento em arcos capacitado e aberto (OCARP); e (3) o problema do carteiro chinês com cobertura (CCPP). Apresentamos formulações matemáticas e métodos exatos e heurísticos para tratar computacionalmente esses problemas: (i) uma heurística construtiva gulosa e randomizada é proposta para o CARP; (ii) uma metaheurística de algoritmos genéticos híbrido e dois métodos de limitantes inferiores por programação linear inteira, um branch-and-cut e um baseado em redes de fluxos, são propostos para o OCARP; e (iii) um método exato branch-and-cut com desigualdades válidas e uma heurística construtiva são propostos para o CCPP. Extensivos experimentos computacionais utilizando instâncias de benchmark foram executados para demonstrar o desempenho dos métodos propostos em relação aos métodos da literatura, considerando tanto a qualidade das soluções obtidas quanto o tempo de processamento. Nossos resultados mostram que os métodos propostos são estado da arte. Os problemas estudados apresentam aplicações práticas relevantes: o CARP tem aplicações em coleta de lixo urbano e remoção de neve de estradas; o OCARP tem aplicações em roteamento de leituristas e na definição de caminhos de corte em chapas metálicas; e o CCPP tem aplicações em roteamento de leituristas com o uso de tecnologia wireless. A solução desses problemas remete à diminuição de custos logísticos, melhorando a competitividade das empresasAbstract: Arc routing problems aim to find minimum cost routes that visit a subset of arcs of a graph, with one or more side constraints. This thesis studies three NP-hard arc routing problems: (1) the capacitated arc routing problem (CARP); (2) the open capacitated arc routing problem (OCARP); and (3) the covering Chinese postman problem (CCPP). We present mathematical formulations and heuristic and exact methods to computationally solve these problems: (i) a greedy and randomized constructive heuristic is proposed for the CARP; (ii) a hybrid genetic algorithm metaheuristic and two linear integer programming lower bound methods, one based on branch-and-cut and one based on flow networks, are proposed for the OCARP; and (iii) an exact branch-and-cut method with valid inequalities and a constructive heuristic are proposed for the CCPP. Extensive computational experiments using benchmark instances were performed to demonstrate the performance of the proposed methods in comparison to the previous methods, regarding both quality of solutions and processing time. Our results show that the proposed methods are state-of-the-art. The studied problems have many relevant practical applications: the CARP has applications on urban waste collection and snow removal; the OCARP has applications on the routing of meter readers and the cutting of metal sheets; and last, the CCPP has applications on automated meter readers routing. The solution of these problems leads to the reduction of logistics costs, improving businesses competitivenessDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2016/00315-0FAPES

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

Robustness - a challenge also for the 21st century: A review of robustness phenomena in technical, biological and social systems as well as robust approaches in engineering, computer science, operations research and decision aiding

Notions on robustness exist in many facets. They come from different disciplines and reflect different worldviews. Consequently, they contradict each other very often, which makes the term less applicable in a general context. Robustness approaches are often limited to specific problems for which they have been developed. This means, notions and definitions might reveal to be wrong if put into another domain of validity, i.e. context. A definition might be correct in a specific context but need not hold in another. Therefore, in order to be able to speak of robustness we need to specify the domain of validity, i.e. system, property and uncertainty of interest. As proofed by Ho et al. in an optimization context with finite and discrete domains, without prior knowledge about the problem there exists no solution what so ever which is more robust than any other. Similar to the results of the No Free Lunch Theorems of Optimization (NLFTs) we have to exploit the problem structure in order to make a solution more robust. This optimization problem is directly linked to a robustness/fragility tradeoff which has been observed in many contexts, e.g. 'robust, yet fragile' property of HOT (Highly Optimized Tolerance) systems. Another issue is that robustness is tightly bounded to other phenomena like complexity for which themselves exist no clear definition or theoretical framework. Consequently, this review rather tries to find common aspects within many different approaches and phenomena than to build a general theorem for robustness, which anyhow might not exist because complex phenomena often need to be described from a pluralistic view to address as many aspects of a phenomenon as possible. First, many different robustness problems have been reviewed from many different disciplines. Second, different common aspects will be discussed, in particular the relationship of functional and structural properties. This paper argues that robustness phenomena are also a challenge for the 21st century. It is a useful quality of a model or system in terms of the 'maintenance of some desired system characteristics despite fluctuations in the behaviour of its component parts or its environment' (s. [Carlson and Doyle, 2002], p. 2). We define robustness phenomena as solution with balanced tradeoffs and robust design principles and robustness measures as means to balance tradeoffs. --

Development Of Models And Solution Methods For Different Drayage Applications

In the last decades, intermodal freight transport is becoming more attractive in the global supply chains and freight transport policy makings. Intermodal freight transport provides a cost-effective, reliable, and efficient movement of freight by utilizing the strengths of different transport modes. The initial and final segment of intermodal freight transport, performed by truck, is known as “drayage.” The scheduling of truck movements in drayage operation within the service area of an intermodal terminal is an operational problem which leads to a truck scheduling problem that determines the efficient schedule of trucks while satisfying all transportation demands and constraints. Drayage accounts for a large percentage of the origin-destination expenses in the intermodal transport. Efficient planning of the drayage operations to improve the economic performance of this operation can increase the efficiency and attractiveness of intermodal transport. The primary objective of this research is to apply operation research techniques to optimize truck movements in drayage operation. The first study in this dissertation considers the drayage problem with time constraints at marine container terminals imposed by the truck appointment system and time-windows at customer locations. A mathematical model is proposed that solve the empty container allocation problem, vehicle routing problem, and appointment booking problem in an integrated manner. This model is an extension of a multiple traveling salesman problem with time windows (m-TSPTW) which is known to be NP-hard (i.e., non-deterministic polynomial-time hard). To solve this model, a reactive tabu search (RTS) algorithm is developed and its accuracy and computational efficiency are evaluated against an industry-established solver IBM ILOG CPLEX. In comparison with the CPLEX, RTS was able to find optimal or near-optimal solution in significantly shorter time. This integrated approach also allows for more accurate evaluation of the effects of the truck appointment system on the drayage operation. The second study extends the drayage literature by incorporating these features in drayage problem: (1) treating tractor, container, and chassis as separate resources which are provided in different locations, (2) ensuring that container and chassis are of the same size and type, (3) considering the possibility that drayage companies can sub-contract the work to owner-operators, and (4) a heterogeneous mix of drayage vehicles (from company fleet and owner-operators) with different start and end locations is considered; drayage company’s trucks start at company’s depot and should return to one of the company’s depots whereas owner-operators’ trucks should return to the same location from where they originated. A mixed-integer quadratic programming model is developed that solves scheduling of tractors, full containers, empty containers, and chassis jointly. A RTS algorithm combined with an insertion heuristic is developed to tackle the problem. The experimental results demonstrated the feasibility of the developed model and solution methodology. The results show that the developed integrated model is capable of finding the optimal solutions and is solvable within a reasonable time for operational problems. This new model allowed us to assess the effectiveness of different chassis supply models on drayage operation time, the percentage of empty movements and air emissions. The fourth work builds on our previous work and extends the integrated drayage scheduling model to consider uncertainty in the (un)packing operation. Recognizing the inherent difficulty in obtaining an accurate probability distribution, this paper develops two new stochastic drayage scheduling models without explicit assumption about the probability distributions of the (un)packing times. The first model assumes that only the mean and variance of the (un)packing times are available, and the second model assumes that the mean as well as the upper and lower bounds of the (un)packing times are available. To demonstrate the feasibility of the developed models, they are tested on problem instances with real-life characteristics. Future work would address the real-time scheduling of drayage problem. It would assume trucks’ locations, travel times, and customer requests are updated throughout the day. We would propose a solution approach for solving such a complex model. The solution approach would be based on re-optimization of the drayage problem and consist of two phases: (1) initial optimization at the beginning of the day, and (2) re-optimization during operation. The third study of this dissertation addresses the impact of a new trend in the North American intermodal terminals in using second-tier facilities on drayage operation. These facilities are located outside the terminals and are used to store loaded containers, empty containers, and chassis. This work builds on our previous work and extends the integrated drayage scheduling model to incorporate these features into drayage problem: (1) trucks do not have to wait at customers’ locations during the packing and unpacking operations, (2) drayage operations include a drop yard (i.e., second-tier facility) for picking up or/and dropping off loaded containers outside the marine container terminal, and (3) the job requests by customers is extended to include empty container pickup, loaded container pickup, empty container delivery, and loaded container delivery. As the mathematical model is an extension of the m-TSPTW, a RTS combined with an insertion heuristic developed by the authors is used to solve the problems