Image convolution: a linear programming approach for filters design

AbstractImage 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 used to verify whether a specific input image I can be transformed into a sample image $$I'$$ I ′ through a convolution filter while returning the desired filter as output

The Cost-Balanced Path Problem: A Mathematical Formulation and Complexity Analysis

This paper introduces a new variant of the Shortest Path Problem (SPP) called the Cost-Balanced Path Problem (CBPP). Various real problems can either be modeled as BCPP or include BCPP as a sub-problem. We prove several properties related to the complexity of the CBPP problem. In particular, we demonstrate that the problem is NP-hard in its general version, but it becomes solvable in polynomial time in a specific family of instances. Moreover, a mathematical formulation of the CBPP, as a mixed-integer programming model, is proposed, and some additional constraints for modeling real requirements are given. This paper validates the proposed model and its extensions with experimental tests based on random instances. The analysis of the results of the computational experiments shows that the proposed model and its extension can be used to model many real applications. Obviously, due to the problem complexity, the main limitation of the proposed approach is related to the size of the instances. A heuristic solution approach should be required for larger-sized and more complex instances

A Rich Vehicle Routing Problem for a City Logistics Problem

In this work, a Rich Vehicle Routing Problem (RVRP) is faced for solving city logistic problems. In particular, we deal with the problem of a logistic company that has to define the best distribution strategy for obtaining an efficient usage of vehicles and for reducing transportation costs while serving customers with different priority demands during a given planning horizon. Thus, we deal with a multi-period vehicle routing problem with a heterogeneous fleet of vehicles, with customers’ requirements and company restrictions to satisfy, in which the fleet composition has to be daily defined. In fact, the company has a fleet of owned vehicles and the possibility to select, day by day, a certain number of vehicles from the fleet of a third-party company. Routing costs must be minimized together with the number of vehicles used. A mixed integer programming model is proposed, and an experimental campaign is presented for validating it. Tests have been used for evaluating the quality of the solutions in terms of both model behavior and service level to grant to the customers. Moreover, the benefits that can be obtained by postponing deliveries are evaluated. Results are discussed, and some conclusions are highlighted, including the possibility of formulating this problem in such a way as to use the general solver proposed in the recent literature. This seems to be the most interesting challenge to permit companies to improve the distribution activities

Omega our multi ethnic genetic algorithm

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

OMEGA one multi ethnic genetic approach

The genetic algorithm (GA) is a quite efficient paradigm to solve several optimization problems. It is substantially a search technique that uses an ever-changing neighborhood structure related to a population which evolves according to a number of genetic operators. In the GA framework many techniques have been devised to escape from a local optimum when the algorithm fails in locating the global one. To this aim we present a variant of the GA which we call OMEGA (One Multi Ethnic Genetic Approach). The main difference is that, starting from an initial population, k different sub-populations are produced at each iteration and they independently evolve in k different environments. The resulting sub–populations are then recombined and the process is iterated. Our basic algorithmic scheme is tested on a recent and well-studied variant of the classic problem of the minimum spanning tree: the Minimum Labeling Spanning Tree problem. We compare our algorithm with several approaches drawn from the literature. The results are encouraging in view of future application of OMEGA to other classes of problems

The monochromatic set partitioning problem.Presentato al convegno Airo 2010, 07-10 Settembre 2010, Villa San Giovanni (RC).

On the last few years several problems have been studied on a particular class of graphs, where each edge has a label (color) assigned to it. Real applications for this class of problems arise in fields such as telecommunication or multimodal transport networks (edges of the same color can model transportation lines of the same type, or connections belonging to the same company). Moreover, the edge-labeled graphs can be of interest whenever we need some measure of homogeneity (or heterogeneity) regarding the edges in the solution we are looking for. In this context we focalize our attention on the "monochromatic set partitioning problem" (MSP). Let G=(V,E) be an edge-colored graph. A sub-graph H of G is said to be monochromatic if all the edges of H have the same color and multicolored if no two edges of H have the same color. A feasible solution for the MSP is a partitioning of G in monochromatic sub-graph. We look for a feasible solution containing the minimum number of such monochromatic sub-graph. In our work we first prove the complexity of this problem. Then we propose a mathematical formulation and a polynomial case. Finally we present a meta-heuristic approach to solve the problem and show some preliminary computational results

Carousel Greedy Algorithms for Feature Selection in Linear Regression

The carousel greedy algorithm (CG) was proposed several years ago as a generalized greedy algorithm. In this paper, we implement CG to solve linear regression problems with a cardinality constraint on the number of features. More specifically, we introduce a default version of CG that has several novel features. We compare its performance against stepwise regression and more sophisticated approaches using integer programming, and the results are encouraging. For example, CG consistently outperforms stepwise regression (from our preliminary experiments, we see that CG improves upon stepwise regression in 10 of 12 cases), but it is still computationally inexpensive. Furthermore, we show that the approach is applicable to several more general feature selection problems