Dottorato di ricerca in:Ricerca Operativa, XXII Ciclo,2008-2009Combinatorial optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete... more
Dottorato di ricerca in:Ricerca Operativa, XXII Ciclo,2008-2009Combinatorial optimization is a branch of optimization. Its domain is optimization problems where the set of feasible solutions is discrete or can be reduced to a discrete one, the goal being that of nding the best possible solution. Two fundamental aims in optimization are nding algorithms characterized by both provably good run times and provably good or even optimal solution quality. When no method to nd an optimal solution, under the given constraints (of time, space etc.) is available, heuristic approaches are typically used. A metaheuristic is a heuristic method for solving a very general class of computational problems by combining user- given black-box procedures, usually heuristics themselves, in the hope of obtaining a more e cient or more robust procedure. The genetic algorithms are one of the best metaheuristic approaches to deal with optimization problems. They are a population- based search technique that uses an ever changing neighborhood structure, based on population evolution and genetic operators, to take into account di erent points in the search space. The core of the thesis is to introduce a variant of the classic GA approach, which is referred to as OMEGA (Multi Ethnic Genetic Algorithm). The main feature of this new metaheuristic is the presence of di erent populations that evolve simultaneously, and exchange genetic material with each other. We focus our attention on four di erent optimization problems de ned on graphs. Each one is iii iv proved to be NP-HARD. We analyze each problem from di erent points of view, and for each one we de ne and implement both a genetic algorithm and our OMEGA.Università della Calabri
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The Minimum Conflict Weighted Spanning Tree Problem is a variant of the Minimum Spanning Tree Problem in which, given a list of conflicting edges modelled as a conflict graph, we want to find a weighted spanning tree with the minimum... more
The Minimum Conflict Weighted Spanning Tree Problem is a variant of the Minimum Spanning Tree Problem in which, given a list of conflicting edges modelled as a conflict graph, we want to find a weighted spanning tree with the minimum number of conflicts as main objective function and minimize the total weight of spanning trees as secondary objective function. The problem is proved to be NP-Hard in its general form and finds applications in several real-case scenarios such as the modelling of road networks in which some movements are prohibited. We propose a genetic algorithm designed to minimize the number of conflict edge pairs and the total weight of the spanning tree. We tested our approach on benchmark instances, the results of our GA showed that we outperform the other approaches proposed in the literature.
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We consider a distribution problem in a supply chain consisting of multiple plants, multiple regional warehouses, and multiple customers. We focus on the problem of selecting a given number of warehouses among a set of candidate ones,... more
We consider a distribution problem in a supply chain consisting of multiple plants, multiple regional warehouses, and multiple customers. We focus on the problem of selecting a given number of warehouses among a set of candidate ones, assigning each customer to one or more of the selected warehouses while minimizing costs. We present a mixed integer formulation of the problem of minimizing the sum of the total transportation costs and of the fixed cost associated with the opening of the selected warehouses. We develop a heuristic and a metaheuristic algorithm to solve it. The problem was motivated by the request of a company in the US which was interested both in determining the optimal solution of the problem using available optimization solvers, and in the design and implementation of a simple heuristic able to find good solutions (not farther than 1% from the optimum) in a short time. A series of computational experiments on randomly generated test problems is carried out. Our re...
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Image analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques. Convolution is a technique used to enhance specific characteristics of an... more
Image analysis is a branch of signal analysis that focuses on the extraction of meaningful information from images through digital image processing techniques. Convolution is a technique used to enhance specific characteristics of an image, while deconvolution is its inverse process. In this work, we focus on the deconvolution process, defining a new approach to retrieve filters applied in the convolution phase. Given an image I and a filtered image $$I' = f(I)$$ I ′ = f ( I ) , we propose three mathematical formulations that, starting from I and $$I'$$ I ′ , are able to identify the filter $$f'$$ f ′ that minimizes the mean absolute error between $$I'$$ I ′ and $$f'(I)$$ f ′ ( I ) . Several tests were performed to investigate the applicability of our approaches in different scenarios. The results highlight that the proposed algorithms are able to identify the filter used in the convolution phase in several cases. Alternatively, the developed approaches can be us...
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There are several examples of dual propulsion vehicles: hybrid cars, bi-fuel vehicles, electric bikes. Compute a path from a starting point to a destination for these typologies of vehicles requires evaluation of many alternatives. In... more
There are several examples of dual propulsion vehicles: hybrid cars, bi-fuel vehicles, electric bikes. Compute a path from a starting point to a destination for these typologies of vehicles requires evaluation of many alternatives. In this paper we develop a mathematical model, able to compute paths for dual propulsion vehicles, that takes in account the power consumption of the two propulsors, the different types of charging, the exchange of energy and, last but not least, the total cost of the path. We focus our attention on electric bikes and we perform several experiments on real street network graph. In our tests we took into account the slope of roads, the recharge in downhill streets and the effort of the cyclist. To validate the model we performed computational tests on properly generated instances set. This set of instances is composed of graphs representing real cities of all around the world. The computational tests show the effectiveness of our approach and its applicability on a real street network.
This paper addresses the close-enough traveling salesman problem, a variant of the Euclidean traveling salesman problem, in which the traveler visits a node if it passes through the neighborhood set of that node. We apply an effective... more
This paper addresses the close-enough traveling salesman problem, a variant of the Euclidean traveling salesman problem, in which the traveler visits a node if it passes through the neighborhood set of that node. We apply an effective strategy to discretize the neighborhoods of the nodes and the carousel greedy algorithm to appropriately select the neighborhoods that, step by step, are added to the partial solution until a feasible solution is generated. Our heuristic, based on these ingredients, is able to compute tight upper and lower bounds on the optimal solution relatively quickly. The computational results, carried out on benchmark instances, show that our heuristic often finds the optimal solution, on the instances where it is known, and in general, the upper bounds are more accurate than those from other algorithms available in the literature. Summary of Contribution: In this paper, we focus on the close-enough traveling salesman problem. This is a problem that has attracted...
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Combinatorial Optimization, Modeling and Simulation, and 6 moreMetaheuristics, Numerical Analysis and Computational Mathematics, Greedy Algorithm, Vertex Cover, Disaster Recovery Using Operations Research and Management Science, and Independent set
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ABSTRACT In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the... more
ABSTRACT In this paper we take into account three different spanning tree problems with degree-dependent objective functions. The main application of these problems is in the field of optical network design. In particular, we propose the classical Minimum Leaves Spanning Tree problem as a relevant problem in this field and show its relations with the Minimum Branch Vertices and the Minimum Degree Sum problems. We present a unified memetic algorithm for the three problems and show its effectiveness on a wide range of test instances.
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ABSTRACT This paper concerns the problem to place N non overlapping circles in a circular container with minimum radius. This is a well known and widely studied problem with applications in manufacturing and logistics and, in particular,... more
ABSTRACT This paper concerns the problem to place N non overlapping circles in a circular container with minimum radius. This is a well known and widely studied problem with applications in manufacturing and logistics and, in particular, to problems related to cutting and packing. In this paper we propose an algorithm that by applying a strength along a selected direction on each circle, simulates the shifting of circles on the plane and tries to reduce the radius of the circular container during this movements. The algorithm is based on a multistart technique where the starting solutions are produced by a tabu search heuristic that uses also the current best solution. The algorithm takes part in a public international contest in order to find optimal solutions to a special case in circle packing. The contest saw the participation of 155 teams and our algorithm achieved the tenth position.
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ABSTRACT The problem of optimally locating sensors on a traffic network to monitor flows has been an object of growing interest in the past few years, due to its relevance in the field of traffic management and control. Sensors are often... more
ABSTRACT The problem of optimally locating sensors on a traffic network to monitor flows has been an object of growing interest in the past few years, due to its relevance in the field of traffic management and control. Sensors are often located in a network in order to observe and record traffic flows on arcs and/or nodes. Given traffic levels on arcs within the range or covered by the sensors, traffic levels on unobserved portions of a network can then be computed. In this paper, the problem of identifying a sensor configuration of minimal size that would permit traffic on any unobserved arcs to be exactly inferred is discussed. The problem being addressed, which is referred to in the literature as the Sensor Location Problem (SLP), is known to be NP-complete, and the existing studies about the problem analyze some polynomial cases and present local search heuristics to solve it. In this paper we further extend the study of the problem by providing a mathematical formulation that up to now has been still missing in the literature and present an exact branch and bound approach, based on a binary branching rule, that embeds the existing heuristics to obtain bounds on the solution value. Moreover, we apply a genetic approach to find good quality solutions. Extended computational results show the effectiveness of the proposed approaches in solving medium-large instances.