Research Interests:
Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After... more
Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g. , payment of royalties). Copies may be requested from IBM T. J.
Research Interests:
Several variants of generalized minimum spanning tree problems (GMSTPs) have been introduced in the literature in different papers by a number of authors. Roughly speaking, all these variants are generalizations of the classical minimum... more
Several variants of generalized minimum spanning tree problems (GMSTPs) have been introduced in the literature in different papers by a number of authors. Roughly speaking, all these variants are generalizations of the classical minimum spanning tree on an undirected graph G=(V,E) in which the node set V is partitioned into a given set of clusters, and the minimum tree has to ‘span’ those clusters instead of simple nodes. In particular, in this paper we are concerned with two specific variants, the most classical one in which exactly one node in each cluster has to be visited (E-GMSTP), and the less studied problem in which at least one node in each cluster has to be reached (L-GMSTP). This paper presents several effective techniques to improve on the branch-and-cut approaches for E-GMSTP and L-GMSTP proposed by C. Feremans, M. Labbé and G. Laporte [Networks 43, No. 2, 71–86 (2004; Zbl 1069.68114)] and by C. Feremans [“Generalized spanning trees and extensions”, Ph.D. thesis, Univ. ...
Research Interests:
— Surrogate Branching (SB) methods provide a staged parametric relaxation of customary branching methods used in branch-and-bound and branch-and-cut algorithms. SB methods operate by forming surrogate constraints composed of nonnegative... more
— Surrogate Branching (SB) methods provide a staged parametric relaxation of customary branching methods used in branch-and-bound and branch-and-cut algorithms. SB methods operate by forming surrogate constraints composed of nonnegative linear combinations of component inequalities of three types: (1) ordinary branching inequalities, (2) redundant inequalities involving bounds on variables, and (3) the strictly redundant inequality 0 ≤ 1. The usefulness of surrogate constraint relaxations in mixed integer programming acquires a new scope through these surrogate branching inequalities, by allowing branching decisions to be progressively compounded, and We write the mixed integer programming (MIP) problem in the form MIP: Maximize xo = cx subject to Ax ≤ b
Research Interests:
We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the... more
We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.
Research Interests:
method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the... more
method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generating a valid inequality violated by a given real vector, usually arising as the solution to a relaxation of the original problem. We show that the prob- lem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program. In some cases, this bilevel program can be easily reformulated as a single-level mathematical program, yielding a stan- dard mathematical programming formulation for the separation problem. In other cases, no reformulation exists. We illustrate the principle by considering the separation problem for two well-known classes of valid inequalities. Formally, we consider a MIP of the form
IntroductionMany Constraint Satisfaction Problems (CSPs) can be modelled using so called constraint of difference.In fact, many real life problems contain, as a subpart, a weighted matching problem. For this purpose,modern industrial CP... more
IntroductionMany Constraint Satisfaction Problems (CSPs) can be modelled using so called constraint of difference.In fact, many real life problems contain, as a subpart, a weighted matching problem. For this purpose,modern industrial CP tools define a global constraint which enforces that all variables involved assumedifferent values. We refer to the ILOG Solver global constraint IlcAllDiff. If a cost is associated toeach
Research Interests:
We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to... more
We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width,
Research Interests:
ABSTRACT We analyze the computational complexity of three fundamental variants of the bilevel knapsack problem. All three variants are shown to be complete for the second level of the polynomial hierarchy. We also discuss the somewhat... more
ABSTRACT We analyze the computational complexity of three fundamental variants of the bilevel knapsack problem. All three variants are shown to be complete for the second level of the polynomial hierarchy. We also discuss the somewhat easier situation where the weight and profit coefficients in the knapsack problem are encoded in unary: two of the considered bilevel variants become solvable in polynomial time, whereas the third becomes NP-complete. Furthermore, we design a polynomial time approximation scheme for this third variant, whereas the other two variants cannot be approximated in polynomial time within any constant factor (assuming P\;$\ne$\;NP).
Research Interests:
ABSTRACT We analyze three fundamental variants of the bilevel knapsack problem, which all are complete for the second level of the polynomial hierarchy. If the weight and profit coefficients in the knapsack problem are encoded in unary,... more
ABSTRACT We analyze three fundamental variants of the bilevel knapsack problem, which all are complete for the second level of the polynomial hierarchy. If the weight and profit coefficients in the knapsack problem are encoded in unary, then two of the bilevel variants are solvable in polynomial time, whereas the third is NP-complete. Furthermore we design a polynomial time approximation scheme for this third variant, whereas the other two variants cannot be approximated in polynomial time within any constant factor (assuming P≠NP).
The paper deals with the solution of the optimal short-term unit commitment (UC) problem in an electric power system. The optimization model takes into account the main operating constraints and physical characteristics of the power... more
The paper deals with the solution of the optimal short-term unit commitment (UC) problem in an electric power system. The optimization model takes into account the main operating constraints and physical characteristics of the power generation system. A comparison between Lagrangian heuristics and Tabu Search techniques on different classes of realistic instances is presented. Such a comparison is aimed at
Research Interests:
The 2-dimensional bin packing problem (2BP) is a generalization of the classical Bin Packing problem and is defined as follows: Given a collection of rectangles specified by their width and height, pack these into the minimum number of... more
The 2-dimensional bin packing problem (2BP) is a generalization of the classical Bin Packing problem and is defined as follows: Given a collection of rectangles specified by their width and height, pack these into the minimum number of square bins of unit size. We study the case of 'orthogonal packing without rotations', where rectangles cannot be rotated and must be
Research Interests:
Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an unlimited number of identical rectangular large stock pieces. We consider the problem of determining the guillotine-cuttable patterns that... more
Résumé/Abstract We are given a set of rectangular small pieces which may be rotated by 90, and an unlimited number of identical rectangular large stock pieces. We consider the problem of determining the guillotine-cuttable patterns that provide all the pieces, such that the total number of required stock pieces is minimized. We show how some classical greedy algorithms given in the literature for the case where no rotation is allowed can be adapted to our problem; in addition, an original heuristic algorithm is presented. We then introduce a ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
The paper investigates the relationship between counting the lattice points belonging to an hyperplane and the separation of Chvátal-Gomory cutting planes. In particular, we show that counting can be exploited in two ways: (i) to... more
The paper investigates the relationship between counting the lattice points belonging to an hyperplane and the separation of Chvátal-Gomory cutting planes. In particular, we show that counting can be exploited in two ways: (i) to strengthen the cuts separated, e.g., by Gomory classical procedure, and (ii) to heuristically evaluate the effectiveness of those cuts and possibly select only a subset of them. Empirical results on a small set of 0-1 Integer Programming instances are presented.
Research Interests:
Research Interests:
Let G=(V,E) be a complete graph. Then the semimetric polytope M(G){\cal M}(G) associated with G is defined by the following system of inequalities called the triangle inequalities.
Research Interests:
In this paper we show how to exploit in Constraint Programming (CP) a well-known integer programming technique, the additive bounding procedure, when using Limited Discrepancy Search (LDS). LDS is an effective search strategy based on the... more
In this paper we show how to exploit in Constraint Programming (CP) a well-known integer programming technique, the additive bounding procedure, when using Limited Discrepancy Search (LDS). LDS is an effective search strategy based on the concept of discrepancy, ie, a branching decision which does not follow the suggestion of a given heuristic. The property of a node to have an associated discrepancy k can be modeled (and enforced) through a constraint, called k-discrepancy constraint. Our key result is the exploitation of the k- ...
Research Interests:
Research Interests:
Abstract Two-dimensional bin packing problems consist of allocating, without overlapping, a given set of small rectangles (items) to a minimum number of large identical rectangles (bins), with the edges of the items parallel to those of... more
Abstract Two-dimensional bin packing problems consist of allocating, without overlapping, a given set of small rectangles (items) to a minimum number of large identical rectangles (bins), with the edges of the items parallel to those of the bins. According to the specific application, the items may either have a fixed orientation or they can be rotated by 90. In addition, it may or not be imposed that the items are obtained through a sequence of edge-to-edge cuts parallel to the edges of the bin. In this article, we consider the class of problems ...
Research Interests:
... 1210 West Dayton Street, Madison, WI 53706, USA, e-mail: ferris@cs .wisc.edu ChristianK anz ow: University of Hamburg, Institute of Applied Mathematics,B undesstrasse 55, D-20146 Hamburg,Germany, e-mail: anzow@math.uni-hamburg.de Todd... more
... 1210 West Dayton Street, Madison, WI 53706, USA, e-mail: ferris@cs .wisc.edu ChristianK anz ow: University of Hamburg, Institute of Applied Mathematics,B undesstrasse 55, D-20146 Hamburg,Germany, e-mail: anzow@math.uni-hamburg.de Todd Munson: University of ...
Research Interests:
Research Interests:
Research Interests:
... An introduction to Constraint Programming. Titolo Rivista: RICERCA OPERATIVA. Autori/Curatori: Filippo Focacci, Andrea Lodi, Michela Milano, Daniele Vigo. Anno di pubblicazione: 1999 Fascicolo: 91 Lingua: IT Numero ...