A computational study of parametric tabu search for 0-1 mixed integer programs

Orientador: Vinícius Amaral ArmentanoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Este trabalho apresenta um estudo computacional da busca tabu paramétrica para resolver problemas de programação inteira mista (PIM) com variáveis binárias. Trata-se de uma heurística genérica para problemas PIM gerais que resolve uma série de problemas de programação linear ao incorporar inequações de ramificação de variáveis inteiras como termos ponderados na função objetivo. O procedimento central do método é baseado em memória de curto prazo da busca tabu, enquanto fases de intensificação e diversificação são induzidas pela memória de longo prazo baseada em freqüência e idéias derivadas de scatter search. Novas estratégias são propostas para encontrar soluções de alta qualidade e extensivos testes computacionais são realizados em instâncias da literaturaAbstract: We present a computational study of parametric tabu search for solving 0-1 mixed integer programming (MIP) problems, a generic heuristic for general MIP problems that solves a series of linear programming problems by incorporating branching inequalities as weighted terms in the objective function. The core procedure is founded on short term memory, whereas both intensification and diversification phases are induced by long term memory based on frequency and ideas derived from scatter search. New strategies are proposed for uncovering feasible and high-quality solutions and extensive computational tests are performed on instances from the literatureDoutoradoAutomaçãoDoutor em Engenharia Elétric

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Hybrid enumeration strategies for mixed integer programming

In this paper we present several algorithms which combine a partial enumeration with meta-heuristics for the solution of general mixed-integer programming problems. The enumeration is based on the primal values assignable to the integer variables of the problem. We develop some algorithms for this integration, and test them using a set of well-known benchmark problems

Integrated Parametric Graph Closure and Branch-and-Cut Algorithm for Open Pit Mine Scheduling under Uncertainty

Open pit mine production scheduling is a computationally expensive large-scale mixed-integer linear programming problem. This research develops a computationally efficient algorithm to solve open pit production scheduling problems under uncertain geological parameters. The proposed solution approach for production scheduling is a two-stage process. The stochastic production scheduling problem is iteratively solved in the first stage after relaxing resource constraints using a parametric graph closure algorithm. Finally, the branch-and-cut algorithm is applied to respect the resource constraints, which might be violated during the first stage of the algorithm. Six small-scale production scheduling problems from iron and copper mines were used to validate the proposed stochastic production scheduling model. The results demonstrated that the proposed method could significantly improve the computational time with a reasonable optimality gap (the maximum gap is 4%). In addition, the proposed stochastic method is tested using industrial-scale copper data and compared with its deterministic model. The results show that the net present value for the stochastic model improved by 6% compared to the deterministic model

Tabu search-based method for bézier curve parameterization

A very important issue in many applied fields is to construct the fitting curve that approximates a given set of data points optimally in the sense of least-squares. This problem arises in a number of areas, such as computer-aided design & manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. This is also a hard problem, because it is highly nonlinear, over-determined and typically involves a large number of unknown variables. A critical step in this process is to obtain a suitable parameterization of the data points. In this context, this paper introduces a new method to obtain an optimal solution for the parameterization problem of the least-squares fitting Bézier curve. Our method is based on a local search metaheuristic approach for optimization problems called tabu search. The method is applied to some simple yet illustrative examples for the cases of 2D and 3D curves. The proposed method is simple to understand, easy to implement and can be applied to any kind of smooth data points. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy.This research has been financially supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University, the University of Cantabria, and the Instituto de Física de Cantabria, a mixed research center of the University of Cantabria and CSIC-Consejo Superior de Investigaciones Científicas.Peer Reviewe

Mixed Integer Programming Approaches to Novel Vehicle Routing Problems

This thesis explores two main topics. The first is how to incorporate data on meteorological forecasts, traffic patterns, and road network topology to utilize deicing resources more efficiently. Many municipalities throughout the United States find themselves unable to treat their road networks fully during winter snow events. Further, as the global climate continues to change, it is expected that both the number and severity of extreme winter weather events will increase for large portions of the US.We propose to use network flows, resource allocation, and vehicle routing mixed integer programming approaches to be able to incorporate all of these data in a winter road maintenance framework. We also show that solution approaches which have proved useful in network flows and vehicle routing problems can be adapted to construct high-quality solutions to this new problem quickly. These approaches are validated on both random and real-world instances using data from Knoxville, TN.In addition to showing that these approaches can be used to allocate resources effectively given a certain deicing budget, we also show that these same approaches can be used to help determine a resource budget given some allocation utility score. As before, we validate these approaches using random and real-world instances in Knoxville, TN.The second topic considered is formulating mixed integer programming models which can be used to route automated electric shuttles. We show that these models can also be used to determine fleet composition and optimal vehicle characteristics to accommodate various demand scenarios. We adapt popular vehicle routing solution techniques to these models, showing that these strategies continue to be relevant and robust. Lastly, we validate these techniques by looking at a case study in Greenville, SC, which recently received a grant from the Federal Highway Administration to deploy a fleet of automated electric shuttles in three neighborhoods

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