Dominique Quadri

Exact solution method to solve large scale integer quadratic multidimensional knapsack problems

Abstract In this paper we develop a branch-and-bound algorithm for solving a particular integer quadratic multi-knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre-procedure techniques in order to reduce the problem size before starting the branch-and-bound process. We lead a numerical comparison between our method and three other existing algorithms. The approach we propose outperforms other procedures for large-scaled instances (up to 2000 variables and constraints).

Decentralized optimization of last-mile delivery services with non-cooperative bounded rational customers

The goal of this paper is to introduce bounded rational behaviors in a competitive queuing system. Furthermore, we propose a realistic queuing model for two last-mile delivery services in which consumers are in competition. This work is derived from a real-world e-commerce application. We study the problem using a game theoretical point of view: the e-consumers are interacting through the last-mile delivery service system creating congestion for each other. Specifically, we focus our analysis on several equilibrium concepts from congestion/routing games: Wardrop and Logit equilibria. The difference in these equilibrium concepts is on the rationality level of players in the game. We are able to prove the existence and uniqueness of both equilibria. We compare them through a new metric called the Price of Rationality and we also compare each one to the social optimum solution through the Price of Anarchy. Some numerical results are presented in order to illustrate the theoretical results obtained.

0-1 Quadratic Knapsack Problems: An Exact Approach Based on a

This paper presents an exact solution method based on a new linearization scheme for the 0-1 quadratic knapsack problem, which consists of maximizing a quadratic pseudo-Boolean function with nonnegative coefficients subject to a linear capacity constraint. Contrasting with traditional linearization schemes, our approach adds only one extra variable. The suggested linearization framework provides a tight upper bound, which is used in a branch-and-bound scheme. This upper bound is numerically compared with that of [A. Billionnet, A. Faye, and E. Soutif, European J. Oper. Res., 112 (1999), pp. 664--672], and our branch-and-bound scheme with the exact algorithm of [W. D. Pisinger, A. B. Rasmussen, and R. Sandvik, INFORMS J. Comput., 19 (2007), pp. 280--290]. The experiments show that our upper bound is quite competitive (less than

t

1\%

-Linearization

from the optimum). In addition, the proposed branch-and-bound clearly outperforms the algorithm developed by Pisinger et al. for low density instances (

On a class of periodic scheduling problems: Models, lower bounds and heuristics

25\%

Mathematical Programming with Stochastic Equilibrium Constraints applied to Optimal Last-mile Delivery Services☆

) for all instanc...

A roof linearization algorithm to obtain a tight upper bound for integer nonseparable quadratic programming

We study in this paper a generalization of the basic strictly periodic scheduling problem where two positive integer constants, associated to each task, are introduced such that to replace the usual strict period. This problem is motivated by the combat of the dengue which is one of the major tropical disease. We discuss general properties and propose two integer mathematical models of the problem considered which are compared theoretically. We also suggest a lower bound which is derived from the structure of the problem. It appears to be quickly obtained and of good quality. Three greedy algorithms are proposed to provide feasible solutions which are compared with the optimum (when it can be obtained by the use of ILOG-Cplex10.0). It is shown that for special instances greedy algorithms are optimal.

Two phase solution for an intelligent moving target search problem based on a 0–1 linear model

In e-commerce business, the delivery of products is a crucial part for the success of an e-shop. An efficient delivery system should offer various services and predict customers behaviour. The latter are influenced by the price of a delivery service, but also by its quality (perceived through congestion effect induced by customers’ choices). In this study, we introduce a bi-level model to optimize a delivery system. At the upper level, the provider control services’ tariffs. At the lower level, users react by choosing their delivery service according to a disutility function which icorporates the provider tariff and the congestion effects. We model the customers’ reaction using stochastic user equilibrium (SUE). We also present a sensitivity analysis for the SUE that gives explicit expression of the derivatives of customers distribution with respect to services’ tariffs. Based on a local search that exploits the derivatives information, a new heuristic algorithm for a delivery services pricing problem is developed and compared to others existing methods.

Concept Discovery and Automatic Semantic Annotation for Language Understanding in an Information-Query Dialogue System Using Latent Dirichlet Allocation and Segmental Methods

Abstract We study in this paper a general case of integer quadratic multi-knapsack problem (QMKP) where the objective function is non separable. An upper bound is proposed for (QMKP) which is computed via two steps. We first rewrite (QMKP) into an equivalent separable mixed integer quadratic program (QPx,y), using Gauss decomposition of the quadratic terms matrix. We then suggest an original technique, we call roof linearization, to linearize (QPx,y) so as to obtain a mixed integer linear program which optimal value provides an upper bound for both (QPx,y) and (QMKP). Preliminary computational experiments are conducted so as to assess that the proposed algorithm provides a tight upper bound in fast CPU times.