A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

Técnicas heurísticas para instâncias de grande porte do problema cabo-trincheira

Orientadores: Flávio Keidi Miyazawa, Eduardo Candido XavierDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O problema cabo trincheira foi apresentado em 2002 para modelar redes cabeadas. Esse problema pode ser visto como a união do problema de caminhos mínimos com o problema da árvore geradora mínima. Como entrada do problema temos um grafo $G=(V,E)$ com pesos nas arestas que indicam a distância entre os vértices incidentes na mesma. Há um vértice especial que representa uma instalação e demais vértices representam clientes. Uma solução para o problema é uma árvore geradora enraizada na instalação. O custo da solução é o custo da árvore geradora multiplicado por um fator de custo de trincheira mais os custos de cabos. Para cada cliente, o seu custo de cabo é dado pelo custo do caminho do cliente até a instalação multiplicado por um fator de custo de cabo. Esse problema modela cenários onde cada cliente deve ser conectado a uma instalação central através de um cabo dedicado. Cada cabo deve estar acomodado em uma trincheira e cada trincheira pode conter um número ilimitado de cabos. Sabendo que o custo dos cabos e trincheiras é proporcional a seu comprimento multiplicado por um fator de custo, o problema é encontrar uma rede com custo mínimo. Trabalhos anteriores  utilizaram o problema cabo trincheira para modelar problemas em telecomunicações, distribuição de energia, redes ferroviárias e até para reconstrução de vasos sanguíneos em exames de tomografia computadorizada. O trabalho foca na resolução do problema em instâncias de grande porte (superiores a 10 mil vértices). Foram desenvolvidas várias heurísticas para o problema. Na busca por simplificações de instâncias, foram demonstradas regras seguras, ou seja, que não comprometem nenhuma solução ótima, e heurísticas para a remoção de arestas eliminando aquelas que dificilmente estariam em ''boas soluções" de uma instância. Foi apresentado um algoritmo rápido para busca local capaz de ser executado mesmo em instâncias de grande porte. Foram desenvolvidos também algoritmos baseados em Greedy Randomized Adaptive Search Procedure (GRASP) e formulada uma heurística que contrai vértices. Com a contração de vértices, foram criadas instâncias do problema Cabo Trincheira com Demandas nos Vértices (CTDV). Essa versão com demandas tem um número menor de vértices que o problema original, o que viabiliza o uso de algoritmos baseados em programação linear para resolvê-lo. Foi demonstrado como é possível, ao resolver essa versão reduzida com demandas, remontar uma solução viável para o problema cabo trincheira original. Foram obtidos, com essas heurísticas, resultados melhores do que trabalhos anteriores encontrados na literatura do problema. Para além disso, foi demonstrado como essa técnica de contração de vértices tem o potencial para resolver instâncias de tamanhos ainda maior para o problema cabo trincheiraAbstract: The Cable Trench Problem (CTP) was presented in 2002 to model wired networks. This problem can be seen as the combination of the shortest path problem with the minimum spanning tree problem. An instance of the problem is composed by a graph $G=(V, E)$ with weigths, representing the distance between a pair of vertices. A special vertex represents a facility, and all others are clients. A solution to the problem is a spanning tree rooted in the facility. The solution's cost is given by the spanning tree cost multiplied by a trench cost factor, added by the cables cost reaching the root from each vertex in the graph. For each client, its cable cost is given by the path in the spanning tree, from the client to the root, multiplied by a cable cost factor. The CTP models a scenario where each client must be connected through a dedicated cable to a central facility. Each cable must be laying on a trench and a trench may hold an unlimited number of cables. Knowing that the cost of cables and trenches are proportional to its lengths multiplied by a cost factor, the problem is to find a network of minimum cost. Previous works in the literature used the CTP to model telecommunication problems, power distribution, rail networks, and even a blood vessel networks for computed tomography exams. In this research, we focused on large-scale instances of the problem (above 10 thousand vertices), achieving better results than previous works found in the literature. We developed a series of heuristics for the problem. Searching for a simplification for those instances, we present safe reductions, that do not affect any optimal solution, and heuristic reduction rules that are capable of removing edges unlikely to be part of ''good'' solutions in an instance. We present a fast local search algorithm, capable of improving even solutions for large-scale instances. We developed an algorithm based on a Greedy Randomized Adaptive Search Procedure (GRASP) and formulated a heuristic to cluster vertices. By clustering vertices, we represent a CTP instance as an instance of the Cable Trench Problem with Demands (CTPD). We represent the large-scale CTP instance into a vertex-wise smaller one adding demands to its vertices. Dealing with smaller instances, we enable a new range of techniques such as linear programming based algorithms to solve it. We demonstrate how this instances with demands can be used to build a viable solution for the original CTP instance. We also demonstrate how this vertex clustering technique has the potential to solve even larger scale instances for the CTPMestradoCiência da ComputaçãoMestre em Ciência da Computação133323/2018-8, 131175/2017-3CNP

Greedy randomized adaptive search procedure for traveling salesman problem

In this thesis we use greedy randomize adaptive search procedure (GRASP) to solve the traveling salesman problem (TSP). Starting with nearest neighbor method to construct the initial TSP tour, we apply the 2-opt and the path-relinking method for the initial tour improvement. To increase 2-opt search speed, fixed-radius near neighbor search and don0t − look bit techniques are introduced. For the same reason a new efficient data structure, the reverse array, is proposed to represent the TSP tour. Computational results show that GRASP gives fairly good solutions in a short time

Design of Heuristic Algorithms for Hard Optimization

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

The Shortest Path Tour Problem and its variants

Scope of this thesis is to provide a treatment of the Shortest Path Tour Problem, and its variants. It presents a deep investigation of two variants of the SPTP, the Constrained Shortest Path Tour Problem and Shortest Path Tour Problem with Time Windows, respectively. Moreover, a GRASP meta-heuristic is applied to solve further hard combinatorial optimization problems

Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

Meta-heuristic combining prior online and offline information for the quadratic assignment problem

The construction of promising solutions for NP-hard combinatorial optimization problems (COPs) in meta-heuristics is usually based on three types of information, namely a priori information, a posteriori information learned from visited solutions during the search procedure, and online information collected in the solution construction process. Prior information reflects our domain knowledge about the COPs. Extensive domain knowledge can surely make the search effective, yet it is not always available. Posterior information could guide the meta-heuristics to globally explore promising search areas, but it lacks local guidance capability. On the contrary, online information can capture local structures, and its application can help exploit the search space. In this paper, we studied the effects of using this information on metaheuristic's algorithmic performances for the COPs. The study was illustrated by a set of heuristic algorithms developed for the quadratic assignment problem. We first proposed an improved scheme to extract online local information, then developed a unified framework under which all types of information can be combined readily. Finally, we studied the benefits of the three types of information to meta-heuristics. Conclusions were drawn from the comprehensive study, which can be used as principles to guide the design of effective meta-heuristic in the future

A review of the Tabu Search Literature on Traveling Salesman Problems

The Traveling Salesman Problem (TSP) is one of the most widely studied problems inrncombinatorial optimization. It has long been known to be NP-hard and hence research onrndeveloping algorithms for the TSP has focused on approximate methods in addition to exactrnmethods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. Inrnthis paper, we review the tabu search literature on the TSP, point out trends in it, and bringrnout some interesting research gaps in this literature.

Synchronizing vans and cargo bikes in a city distribution network

One of the significant side-effects of growing urbanization is the constantly increasing amount of freight transportation in cities. This is mainly performed by conventional vans and trucks and causes a variety of problems such as road congestion, noise nuisance and pollution. Yet delivering goods to residents is a necessity. Sustainable concepts of city distribution networks are one way of mitigating difficulties of freight services. In this paper we develop a two-echelon city distribution scheme with temporal and spatial synchronization between cargo bikes and vans. The resulting heuristic is based on a greedy randomized adaptive search procedure with path relinking. In our computational experiments we use artificial data as well as real-world data of the city of Vienna. Furthermore we compare three distribution policies. The results show the costs caused by temporal synchronization and can give companies decision-support in planning a sustainable city distribution concept

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set