Puzzle Game about Connectivity and Biological Corridors

Biodiversity puzzle gameLandscape fragmentation prevents some species from moving as they should. This fragmentation, mainly due to urbanization, agriculture and forest exploitation, is a major cause of biodiversity loss. One of the options commonly envisaged to remedy this fragmentation - restore some connectivity - is the development of biological corridors. These corridors are natural spaces, usually linear. They allow species to move between different areas that are natural habitats for them.The aim of this game is to raise awareness among different audiences about issues related to biodiversity conservation, and more specifically the notion of landscape connectivity. The question is approached in a playful way: to determine, in a hypothetical landscape, the network of biological corridors, at the lowest cost, that would connect a fragmented set of natural habitats. The costs associated with sites that could be protected to form a corridor include monetary costs, ecological costs and social costs. This game also makes it possible to evoke human activities likely to develop in unprotected sites and have a negative impact on the preservation of biodiversity. It is a very simple game that cannot, of course, take into account all the complexity inherent in connectivity problems

Using a conic bundle method to accelerate both phases of a quadratic convex reformulation

We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem $(SDP)$, and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving $(SDP)$ that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm

Designing Protected Area Networks

There is a broad consensus in considering that the loss of biodiversity is accelerating which is due, for example, to the destruction of habitats, overexploitation of wild species and climate change. Many countries have pledged at various international conferences to take swift measures to halt this loss of biodiversity. Among these measures, the creation of protected areas – which also contribute to food and water security, the fight against climate change and people’ health and well-being – plays a decisive role, although it is not sufficient on its own. In this book, we review classic and original problems associated with the optimal design of a network of protected areas, focusing on the modelling and practical solution of these problems. We show how to approach these optimisation problems within a unified framework, that of mathematical programming, a branch of mathematics that focuses on finding good solutions to a problem from a huge number of possible solutions. We describe efficient and often innovative modellings of these problems. Several strategies are also proposed to take into account the inevitable uncertainty concerning the ecological benefits that can be expected from protected areas. These strategies are based on the classical notions of probability and robustness. This book aims to help all those, from students to decision-makers, who are confronted with the establishment of a network of protected areas to identify the most effective solutions, taking into account ecological objectives, various constraints and limited resources. In order to facilitate the reading of this book, most of the problems addressed and the approaches proposed to solve them are illustrated by fully processed examples, and an appendix presents in some detail the basic mathematical concepts related to its content

Solving a general mixed-integer quadratic problem through convex reformulation : a computational study

International audienceLet (QP) be a mixed integer quadratic program that consists of minimizing a qua-dratic function subject to linear constraints. In this paper, we present a convex reformulation of (QP), i.e. we reformulate (QP) into an equivalent program, with a convex objective function. Such a reformulation can be solved by a standard solver that uses a branch and bound algorithm. This reformulation, that we call MIQCR (Mixed Integer Quadratic Convex Reformulation), is the best one within a convex reformulation scheme, from the continuous relaxation point of view. It is based on the solution of an SDP relaxation of (QP). Computational experiences were carried out with instances of (QP) with one equality constraint. The results show that most of the considered instances, with up to 60 variables, can be solved within 1 hour of CPU time by a standard solver

Programmation mathématique en tomographie discrète

La tomographie est un ensemble de techniques visant à reconstruirel intérieur d un objet sans toucher l objet lui même comme dans le casd un scanner. Les principes théoriques de la tomographie ont été énoncéspar Radon en 1917. On peut assimiler l objet à reconstruire à une image,matrice, etc.Le problème de reconstruction tomographique consiste à estimer l objet àpartir d un ensemble de projections obtenues par mesures expérimentalesautour de l objet à reconstruire. La tomographie discrète étudie le cas où lenombre de projections est limité et l objet est défini de façon discrète. Leschamps d applications de la tomographie discrète sont nombreux et variés.Citons par exemple les applications de type non destructif comme l imageriemédicale. Il existe d autres applications de la tomographie discrète, commeles problèmes d emplois du temps.La tomographie discrète peut être considérée comme un problème d optimisationcombinatoire car le domaine de reconstruction est discret et le nombrede projections est fini. La programmation mathématique en nombres entiersconstitue un outil pour traiter les problèmes d optimisation combinatoire.L objectif de cette thèse est d étudier et d utiliser les techniques d optimisationcombinatoire pour résoudre les problèmes de tomographie.The tomographic imaging problem deals with reconstructing an objectfrom a data called a projections and collected by illuminating the objectfrom many different directions. A projection means the information derivedfrom the transmitted energies, when an object is illuminated from a particularangle. The solution to the problem of how to reconstruct an object fromits projections dates to 1917 by Radon. The tomographic reconstructingis applicable in many interesting contexts such as nondestructive testing,image processing, electron microscopy, data security, industrial tomographyand material sciences.Discete tomography (DT) deals with the reconstruction of discret objectfrom limited number of projections. The projections are the sums along fewangles of the object to be reconstruct. One of the main problems in DTis the reconstruction of binary matrices from two projections. In general,the reconstruction of binary matrices from a small number of projections isundetermined and the number of solutions can be very large. Moreover, theprojections data and the prior knowledge about the object to reconstructare not sufficient to determine a unique solution. So DT is usually reducedto an optimization problem to select the best solution in a certain sense.In this thesis, we deal with the tomographic reconstruction of binaryand colored images. In particular, research objectives are to derive thecombinatorial optimization techniques in discrete tomography problems.PARIS-CNAM (751032301) / SudocSudocFranceF

Approximate and exact solution methods for the hyperbolic 0-1 knapsack problem

The hyperbolic 0-1 knapsack problem (HKP) to obtain a 0-1 solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. First it is shown how to find approximate solutions of this problem with a given accuracy by solving successively two mixed integer linear programs. Then, six mixed integer programming-based strategies are compared for finding exact solutions of HKP. Some of these strategies exploit the knowledge of an approximate solution. The computational results that are reported give a comparison of the different strategies and show the efficiency of one of them since it allows instances comprising up to 10,000 variables to be solved. Keywords: Fractional 0-1 programming, Hyperbolic 0-1 knapsack problem, Mixed integer programming, Approximate solutions, Exact solutions, Computational experiments

Redundancy Allocation for Series-Parallel Systems Using Integer Linear Programming

We consider the problem of maximizing the reliability of a series-parallel system given cost and weight constraints on the system. The number of components in each subsystem and the choice of components are the decision variables. In this paper, we propose an integer linear programming approach that gives an approximate feasible solution, close to the optimal solution, together with an upper bound on the optimal reliability. We show that integer linear programming is an interesting approach for solving this reliability problem: the mathematical programming model is relatively simple; its implementation is immediate by using a mathematical programming language and an integer linear programming software, and the computational experiments show that the performance of this approach is excellent based on comparison with previous results

Minimising Total Average Cycle Stock Subject to Practical Constraints

Silver and Moon [E.A. Silver and I. Moon, JORS 50(8)(1999) 789-796] address the problem of minimising total average cycle stock subject to two practical constraints. They provide a dynamic programming formulation for obtaining an optimal solution and propose a simple and efficient heuristic algorithm. Hsieh [Y.-C. Hsieh, JORS 52(4)(2001) 463-470] proposes a 0-1 linear programming approach to the problem and a simple heuristic based upon the relaxed 0-1 programming formulation. We show in this paper that the formulation of Hsieh can be improved for solving very large size instances of this inventory problem. So the mathematical approach is interesting for several reasons: the definition of the model is simple, its implementation is immediate by using a mathematical programming language together with a mixed integer programming software and the performance of the approach is excellent. Computational experiments carried out on the set of realistic examples considered in the above references are reported. We also show that the general framework for modelling given by mixed integer programming allows the initial model to be extended in several interesting directions.Keywords: inventory; cycle stock; mixed integer programming; computational experiment