Papers by Xavier Gandibleux
Journal of Heuristics, Sep 20, 2019
At a high level, data centres are large IT facilities hosting physical machines (servers) that of... more At a high level, data centres are large IT facilities hosting physical machines (servers) that often run a large number of virtual machines (VMs)but at a lower level, data centres are an intricate collection of interconnected and virtualised computers, connected services, complex service-level agreements. While data centre managers know that reassigning VMs to the servers that would best serve them and also minimise some cost for the company can potentially save a lot of money-the search space is large and constrained, and the decision complicated as they involve different dimensions. This paper consists of a comparative study of heuristics and exact algorithms for the Multi-objective Machine Reassignment problem. Given the common intuition that the problem is too complicated for exact resolutions, all previous works have focused on various (meta)heuristics such as First-Fit, GRASP, NSGA-II or PLS. In this paper, we show that the state-of-art solution to the single objective formulation of the problem (CBLNS) and the classical multi-objective solutions fail to bridge the gap between the number, quality and variety of
HAL (Le Centre pour la Communication Scientifique Directe), Jun 1, 2013
International audienc
Multi-objective multi-dimensional knapsack problems (pOmDKP) are widely used to represent practic... more Multi-objective multi-dimensional knapsack problems (pOmDKP) are widely used to represent practical problems as capital budgeting or allocating processors. It aims to select a subset of n items such that the sum of weight of the selected items does not exceed the capacity on any of the m dimensions, while maximizing p objective functions. Each item has a weight on each dimension and a profit for each objective function. This problem is known for being particularly difficult as soon as the number of dimensions exceeds one, even in its single-objective version. There are many published papers focusing on the exact solution of multi-objective single-dimensional knapsack. The solutions methods are often two-phases methods. The second phase is either a branch-and-bound method (as in [1] for the bi-objective case or in [2] for the three-objective case), either a dynamic programming method [3], or a dedicated ranking method [2]. Only a few works have studied exactly the multi-objective mul...
Railway infrastructure managers must deal with new operators' requests for capacity. Planning... more Railway infrastructure managers must deal with new operators' requests for capacity. Planning the construction of new infrastructure or rehabilitation of existing infrastructure must be carried out very carefully due to the huge investment needed. This paper examines a Constraint Programming (CP) model of the railway infrastructure saturation problem. The CP model is applied to assess the capacity of a junction or a station. Two resolution algorithms have been developed and combined to be applied to an actual case study.
This paper presents an algorithm aiming to compute an upper bound set for a multi-objective linea... more This paper presents an algorithm aiming to compute an upper bound set for a multi-objective linear optimisation problem with binary variables (p-01LP). Inspired by the well known « Feasibility Pump » algorithm in single objective optimisation, it belongs to the class of primal heuristics. The proposed algorithm, named « Gravity Machine », aims to deal with generic p-01LP. In that sense, it does not exploit any information coming from the combinatorial structure of the problem. Sober in memory and computational resources, and given a time limit, the algorithm explores a p-01LP problem in order to discover a tight upper bound set, without guarantee of returning such a set. The paper describes the current version of the proposed algorithm. It reports numerical results obtained on instances of set partitioning problem available on the OR-library, extended to two objectives.
Lecture Notes in Computer Science, 2017
Multiple Criteria Decision Analysis, 2016
The EU has set targets for reducing its greenhouse gas emissions progressively up to 2050. Recogn... more The EU has set targets for reducing its greenhouse gas emissions progressively up to 2050. Recognizing that the sectors of heat & electricity generation and transport are the world’s largest contributors to climate change, the deployment of clean energy and transportation technologies is widely stimulated. Unfortunately, better environmental performances often imply higher economic costs. This trade-off between two conflicting objectives calls for a multi-objective optimization (MOO) assessment, aiming to find the “best” possible solutions, i.e. the Pareto optimal solutions. Whereas the economic and ecological optimization of energy systems is extensively studied in literature, little research has been done on transportation systems. Furthermore, we argue that it is valuable to simultaneously optimize energy and transportation systems for two reasons. First, most entities (e.g. firms, areas, individuals) have needs regarding both energy and transportation. Second, when considered simultaneously, synergies between the energy and transportation systems can be exploited. This paper aims at filling this gap by performing a MOO on a Belgian case study, i.e. a SME having a certain need for electricity and traveling. The considered energy technologies are solar photovoltaics and grid electricity; for transport internal combustion engine vehicles, grid powered battery electric vehicles (BEVs), and solar powered BEVs are available. Aiming to obtain realistic results, the possible existence of scale economies is taken into account. The latter implies a mixed integer programming problem. Accordingly, this paper applies the exact algorithm described in: T. Vincent, et al.; Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case. Computers & Operations Research, 40(1)498-509, 2013. Additionally, the impact of policy measures on the Pareto front is visualized.
This book deals with homotopy theory, which is one of the main branches of algebraic topology. Th... more This book deals with homotopy theory, which is one of the main branches of algebraic topology. The ideas and methods of homotopy theory have pervaded many parts of topology as well as many parts of mathematics. A general approach in these areas has been to reduce a geometric, analytic, or topological problem to a homotopy problem, and to then attempt to solve the homotopy problem, usually by algebraic methods. Thus, in addition to being interesting and important in its own right, homotopy theory has been successfully applied to geometry, analysis, and other parts of topology. There are several treatments of homotopy theory in general categories. However we confine ourselves to a study of classical homotopy theory, that is, homotopy theory of topological spaces and continuous functions. There are a number of books devoted to classical homotopy theory as well as extensive expositions of it in books on algebraic topology. This book differs from those in that the unifying theme by which the subject is developed is the Eckmann–Hilton duality theory. The Eckmann–Hilton theory has been around for about fifty years but there appears to be no book-length exposition of it, apart from the early lecture notes of Hilton [40]. There are advantages, both expository and pedagogical, to presenting homotopy theory in this way. Dual concepts occur in pairs, such as H-space and co-H-space, fibration and cofibration, loop space and suspension, and so on, and so do many theorems. We often give complete details in describing one of these and only sketch its dual. This is done when the latter can essentially be derived by dualization. In this way we shorten the exposition by reducing the amount of repetitious material. This also allows the reader to test his or her understanding of the subject by supplying the missing details. There is another advantage to studying Eckmann–Hilton duality theory. Frequently the dual of a result is known or trivial. But from time to time the dual result is neither of these and is in fact an interesting problem. This could give the reader material to work on.
INFORMS Journal on Computing, 2010
In this paper, we present two versions of an algorithm for the computation of all nondominated ex... more In this paper, we present two versions of an algorithm for the computation of all nondominated extreme points in the outcome set of a multiobjective integer programme. We define adjacency of these points based on weight space decomposition. Thus, our algorithms generalise the well-known dichotomic scheme to compute the set of nondominated extreme points in the outcome set of a biobjective programme. Both algorithms are illustrated with and numerically tested on instances of the assignment and knapsack problems with three objectives.
European Journal of Operational Research, 2010
The bi-objective set packing problem is a multi-objective combinatorial optimization problem simi... more The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge, this problem has surprisingly not yet been studied. In order to resolve a practical problems encountered in railway infrastructure capacity planning, procedures for computing a solution to this bi-objective combinatorial problem were investigated. Unfortunately, solving the problem exactly in a reasonable time using a generic solver (Cplex) is only possible for small instances. We designed three alternative procedures approximating solutions to this problem. The first is based on version 1 of the 'Strength Pareto Evolutionary Algorithm', which is a population based-metaheuristic. The second is an adaptation of the 'Greedy Randomized Adaptative Search Procedure', which is a constructive metaheuristic. As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics. Thus, the third alternative, which is the primary subject of this paper, is an original hybridization of the previous two metaheuristics. The algorithmic aspects, which differ from the original definition of these metaheuristics, are described, so that our results can be reproduced. The performance of our procedures is reported and the computational results for 120 numerical instances are discussed.
Discrete Optimization, 2010
In this paper, we present a generalization of the two phase method to solve multi-objective integ... more In this paper, we present a generalization of the two phase method to solve multi-objective integer programmes with p > 2 objectives. We apply the method to the assignment problem with three objectives. We have recently proposed an algorithm for the first phase, computing all supported efficient solutions. The second phase consists in the definition and the exploration of the search area inside of which nonsupported nondominated points may exist. This search area is not defined by trivial geometric constructions in the multi-objective case, and is therefore difficult to describe and to explore. The lower and upper bound sets introduced by Ehrgott and Gandibleux in 2001 are used as a basis for this description. Experimental results on the three-objective assignment problem where we use a ranking algorithm to explore the search area show the efficiency of the method.
Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems, 2014
The vehicle routing problem with route balancing is a bi-objective routing problem, in which the ... more The vehicle routing problem with route balancing is a bi-objective routing problem, in which the total route length and the balance of routes (i.e. the difference between the maximal and minimal route length) have to be minimized. In this paper, we propose an approach based on two solution representations: a giant tour representing a sequence of customers (indirect representation) and a complete solution with a decomposition of the giant tour, combined with a split algorithm to alternate between them. This approach offers a mainly efficient way to explore the solution space. Our motivation is based on the possibility to generate efficiently several solutions a time using an indirect representation which has been already proved to be efficient in numerous routing problems resolution. The originality here is to tune the split algorithm considering two objectives. An evolutionary path relinking algorithm is embedded to improve the obtained solutions. The proposed approach is evaluated on classical vehicle routing problem instances and the results push us into accepting that the method is competitive with the best published mono-objective methods (on criteria one : the total route length). On a bi-objective point of view, our method is competitive with the lexicographic solutions reported in the literature in the sense that it provides similar or better results in comparable computational time.
Lecture Notes in Computer Science, 2014
The Set Packing Problem (SPP) is a well-known NP-hard combinatorial optimization problem. This pa... more The Set Packing Problem (SPP) is a well-known NP-hard combinatorial optimization problem. This paper addresses the SPP through a practical case study, namely the Railway Infrastructure Capacity (RIC) problem. SPP instance sizes yielded by this problem contain up to 20,000 variables and 350,000 constraints and consequently appear intractable in reasonable computational time by pure exact algorithms. As an operational response, approximate methods based on Ant Colony Optimization (ACO) and Greedy Randomized Adaptive Search Procedure (GRASP) have been developed. However, even though ACO has given the best results so far, it still requires a significant computational time on some instances. This paper presents a hybridization coupling an ACO metaheuristic with a Column Generation (CG) procedure. CG is used as a preprocessing to provide a reduced SPP instance to ACO as well as a valuable upper bound on the solution quality. Experiments show that the cumulated computational time of ACO wi...
Computers & Operations Research, 2017
International Series in Operations Research & Management Science, 2000
This chapter provides an annotated bibliography of multiple objective combinatorial optimization,... more This chapter provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe their main characteristics, and review the main properties and theoretical results. One section is devoted to a brief description of the available solution methodology, both exact and heuristic. The main part of the chapter consists of an annotation of
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Papers by Xavier Gandibleux