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Paris Sud University - Paris 11, France

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14 Papers

On a Traveling Salesman based Bilevel Programming Problem

Topics: Simulation; Optimization; Linear Programming; Network Optimization; Routing; Resource Allocation; OR in Telecommunications

Authors: Pablo Adasme ¹ , Rafael Andrade ² , Janny Leung ³ and Abdel Lisser ⁴

Affiliations: ¹ Universidad de Santiago de Chile, Chile , ² Universidade Federal do Ceará, Brazil , ³ Chinese University of Hong Kong, Hong Kong , ⁴ Université de Paris-Sud 11, France

Digital Object Identifier: 10.5220/0006190503290336

Proceedings of ICORES 2017, ISBN: 978-989-758-218-9

Quick Abstract

In this paper, we consider a linear bilevel programming problem where both the leader and the follower maximize their profits subject to budget constraints. Additionally, we impose a Hamiltonian cycle topology constraint in the leader problem. In particular, models of this type can be motivated by telecommunication companies when dealing with traffic network flows from one server to another one within a ring topology framework. We transform the bilevel programming problem into an equivalent single level optimization problem that we further linearize in order to derive mixed integer linear programming (MILP) formulations. This is achieved by replacing the follower problem with the equivalent Karush Kuhn Tucker conditions and with a linearization approach to deal with the complementarity constraints. The topology constraint is handled by the means of two compact formulations and an exponential one from the classic traveling salesman problem. Thus, we compute optimal solutions and upper bounds with linear programs. One of the compact models allows to solve instances with up to 250 nodes to optimality. Finally, we propose an iterative procedure that allows to compute optimal solutions in remarkably less computational effort when compared to the compact models.

Related Ontology Subjects/Areas/Topics (21)

Agents	Knowledge Discovery and Information Retrieval	OR in Telecommunications
Applications	Knowledge-Based Systems	Pattern Recognition
Artificial Intelligence	Linear Programming	Resource Allocation
Bioinformatics	Methodologies and Technologies	Routing
Biomedical Engineering	Network Optimization	Simulation
Enterprise Information Systems	Operational Research	Software Engineering
Information Systems Analysis and Specification	Optimization	Symbolic Systems

A Complementarity Problem Formulation for Chance-constraine Games

Topics: Optimization; Game Theory; Stochastic Optimization

Authors: Vikas Vikram Singh ¹ , Oualid Jouini ² and Abdel Lisser ¹

Affiliations: ¹ Universite Paris Sud XI, France , ² Ecole Centrale Paris, France

Digital Object Identifier: 10.5220/0005754800580067

Proceedings of ICORES 2016, ISBN: 978-989-758-171-7

Quick Abstract

We consider a two player bimatrix game where the entries of each player’s payoff matrix are independent random variables following a certain distribution. We formulate this as a chance-constrained game by considering that the payoff of each player is defined by using a chance-constraint. We consider the case of normal and Cauchy distributions. We show that a Nash equilibrium of the chance-constrained game corresponding to normal distribution can be obtained by solving an equivalent nonlinear complementarity problem. Further if the entries of the payoff matrices are also identically distributed with non-negative mean, we show that a strategy pair, where each player’s strategy is the uniform distribution on his action set, is a Nash equilibrium of the chance-constrained game. We show that a Nash equilibrium of the chance-constrained game corresponding to Cauchy distribution can be obtained by solving an equivalent linear complementarity problem.

Related Ontology Subjects/Areas/Topics (9)

Artificial Intelligence	Knowledge-Based Systems	Optimization
Game Theory	Methodologies and Technologies	Stochastic Optimization
Knowledge Discovery and Information Retrieval	Operational Research	Symbolic Systems

A Two-stage Stochastic Programming Approach for the Traveling Salesman Problem

Topics: Simulation; Optimization; Linear Programming; Mathematical Modeling; Stochastic Optimization

Authors: Pablo Adasme ¹ , Rafael Andrade ² , Janny Leung ³ and Abdel Lisser ⁴

Affiliations: ¹ Universidad de Santiago de Chile, Chile , ² Universidade Federal do Ceará, Brazil , ³ Chinese University of Hong Kong, Hong Kong , ⁴ Université de Paris-Sud 11, France

Digital Object Identifier: 10.5220/0005738801630169

Proceedings of ICORES 2016, ISBN: 978-989-758-171-7

Quick Abstract

In the context of combinatorial optimization, recently some efforts have been made by extending classical optimization problems under the two-stage stochastic programming framework. In this paper, we introduce the two-stage stochastic traveling salesman problem (STSP). Let G = (V,ED ∪ES) be a non directed complete graph with set of nodes V and set of weighted edges ED ∪ES where ED ∩ES = 0/. The edges in ED and ES have deterministic and uncertain weights, respectively. Let K = {1,2,··· ,|K|} be a given set of scenarios referred to the uncertain weights of the edges in ES. The STSP consists in determining Hamiltonian cycles of G, one for each scenario s ∈ K, sharing the same deterministic edges while minimizing the sum of the deterministic weights plus the expected weight over all scenarios associated with the uncertain edges. We propose two compact models and a formulation with an exponential number of constraints which are adapted from the classic TSP. One of the compact models allows to solve instances with up to 40 nodes and 5 scenarios to optimality. Finally, we propose an iterative procedure that allows to compute optimal solutions and tight lower bounds within very small CPU time.

Related Ontology Subjects/Areas/Topics (16)

Agents	Knowledge Discovery and Information Retrieval	Operational Research
Artificial Intelligence	Knowledge-Based Systems	Optimization
Bioinformatics	Linear Programming	Simulation
Biomedical Engineering	Mathematical Modeling	Stochastic Optimization
Enterprise Information Systems	Methodologies and Technologies	Symbolic Systems
Information Systems Analysis and Specification

A Comparative Study of Network-based Approaches for Routing in Healthcare Wireless Body Area Networks

Topics: Optimization; Mathematical Modeling

Authors: Pablo Adasme ¹ , Rafael Andrade ² , Janny Leung ³ and Abdel Lisser ⁴

Affiliations: ¹ Universidad de Santiago de Chile, Chile , ² Universidade Federal do Ceará, Brazil , ³ Chinese University of Hong Kong, Hong Kong , ⁴ Université Paris-Sud XI, France

Digital Object Identifier: 10.5220/0005218001250132

Proceedings of ICORES 2015, ISBN: 978-989-758-075-8

Quick Abstract

In this paper, we propose a minmax robust formulation for routing in healthcare wireless body area networks (WBAN). The proposed model minimizes the highest power consumption of each bio-sensor node placed in the body of a patient subject to flow rate and network topology constraints. We consider three topologies in the problem: a spanning tree, a star, and a ring topology as well. In particular, we use an equivalent polynomial formulation of the spanning tree polytope (Yannakakis, 1991) to avoid having an exponential number of cycle elimination constraints in the model. For the ring topology approach, we use constraints from the well known mixed integer linear programming (MILP) formulation of the traveling salesman problem (Pataki, 2003). Thus, we compute optimal solutions and lower bounds directly using the MILP and linear programming (LP) relaxations. Finally, we propose a Kruskal-based (Cormen et al., 2001) variable neighborhood search metaheuristic to improve the solutions obtained with the star topology approach. Our preliminary numerical results indicate that the tree approach is more convenient as it allows saving significantly more power while the ring approach is the most expensive one. They also indicate that the difference between the optimal objective function values for the tree and star formulations is not very large and that VNS can improve significantly the solutions obtained with the star configuration, although, at a higher computational cost.

Related Ontology Subjects/Areas/Topics (8)

Artificial Intelligence	Mathematical Modeling	Optimization
Knowledge Discovery and Information Retrieval	Methodologies and Technologies	Symbolic Systems
Knowledge-Based Systems	Operational Research

A Sampling Method to Chance-constrained Semidefinite Optimization

Topic: Stochastic Optimization

Authors: Chuan Xu , Jianqiang Cheng and Abdel Lisser

Affiliation: Université Paris-Sud 11, France

Digital Object Identifier: 10.5220/0005276400750081

Proceedings of ICORES 2015, ISBN: 978-989-758-075-8

Quick Abstract

Semidefinite programming has been widely studied for the last two decades. Semidefinite programs are linear programs with semidefinite constraint generally studied with deterministic data. In this paper, we deal with a stochastic semidefinte programs with chance constraints, which is a generalization of chance-constrained linear programs. Based on existing theoretical results, we develop a new sampling method to solve these chance constraints semidefinite problems. Numerical experiments are conducted to compare our results with the state-of-the-art and to show the strength of the sampling method.

Related Ontology Subjects/Areas/Topics (3)

Methodologies and Technologies

Operational Research

Stochastic Optimization

A Multicommodity Formulation for Routing in Healthcare Wireless Body Area Networks

Topics: Network Optimization; Routing; OR in Telecommunications; OR in Health

Authors: Pablo Adasme ¹ , Abdel Lisser ² and Chuan Xu ²

Affiliations: ¹ Universidad de Santiago de Chile, Chile , ² Université Paris-Sud XI, France

Digital Object Identifier: 10.5220/0004831704090416

Proceedings of ICORES 2014, ISBN: 978-989-758-017-8

Quick Abstract

In this paper, we propose a minmax multicommodity netflow model for routing in healthcare wireless body area networks (WBAN). The model is aimed at minimizing the worst power consumption of each bio-sensor node placed in the body of a patient plus the total heating costs subject to flow conservation and maximum capacity energy constraints. The model is formulated as a mixed integer linear program (MILP). Thus, we propose a variable neighborhood search (VNS) metaheuristic procedure to come up with tight near optimal solutions. Our preliminary numerical results indicate the VNS approach obtains near optimal solutions with integrality gaps no larger than 3.5 %. Finally, since the proposed model has two conflicting objectives, i.e, heating costs and worst power consumption, we adopt a weighted sum criteria for each objective in order to analyze the behavior of the model.

Related Ontology Subjects/Areas/Topics (8)

Applications	OR in Health	Routing
Network Optimization	OR in Telecommunications	Software Engineering
Operational Research	Pattern Recognition

A Stochastic Programming Approach for Staffing and Scheduling Call Centers with Uncertain Demand Forecasts

Topics: Optimization; Queuing Theory; Resource Allocation; Mathematical Programming

Authors: Mathilde Excoffier ¹ , Céline Gicquel ¹ , Oualid Jouini ² and Abdel Lisser ¹

Affiliations: ¹ Laboratoire de Recherche en Informatique - LRI, France , ² Ecole Centrale Paris - ECP, France

Digital Object Identifier: 10.5220/0004832100800088

Proceedings of ICORES 2014, ISBN: 978-989-758-017-8

Quick Abstract

We consider a workforce management problem arising in call centers, namely a staffing and shift-scheduling problem. It consists in determining the minimum-cost number of agents to be assigned to each shift of the scheduling horizon so as to reach the required customer quality of service. We assume that the mean call arrival rate in each period of the horizon is a random variable following a continuous distribution. We model the resulting optimization problem as a stochastic program involving joint probabilistic constraints. This allows to manage the risk of not reaching the required quality of service at the horizon level rather than on a period by period basis. We propose a solution approach based on linear approximations to provide approximate solutions of the problem. We finally give numerical results carried out on a real-life instance. These results show that the proposed approach compares well with previously published approaches both in terms of risk management and cost minimization.

Related Ontology Subjects/Areas/Topics (10)

Artificial Intelligence	Methodologies and Technologies	Queuing Theory
Knowledge Discovery and Information Retrieval	Operational Research	Resource Allocation
Knowledge-Based Systems	Optimization	Symbolic Systems
Mathematical Programming

On the Use of Copulas in Joint Chance-constrained Programming

Topics: Optimization; Mathematical Programming

Authors: Michal Houda and Abdel Lisser

Affiliation: Université Paris Sud, France

Digital Object Identifier: 10.5220/0004831500720079

Proceedings of ICORES 2014, ISBN: 978-989-758-017-8

Quick Abstract

In this paper, we investigate the problem of linear joint probabilistic constraints with normally distributed constraints. We assume that the rows of the constraint matrix are dependent, the dependence is driven by a convenient Archimedean copula. We describe main properties of the problem and show how dependence modeled through copulas translates to the model formulation. We also develop an approximation scheme for this class of stochastic programming problems based on second-order cone programming.

Related Ontology Subjects/Areas/Topics (8)

Artificial Intelligence	Mathematical Programming	Optimization
Knowledge Discovery and Information Retrieval	Methodologies and Technologies	Symbolic Systems
Knowledge-Based Systems	Operational Research

The p-Median Problem with Concave Costs

Topics: Optimization; Linear Programming; Mathematical Modeling

Authors: Chuan Xu ¹ , Abdel Lisser ¹ , Janny Leung ² and Marc Letournel ¹

Affiliations: ¹ Laboratoire de Recherche en Informatique(LRI) and Bât 650, France , ² The Chinese University of Hong Kong, Hong Kong

Digital Object Identifier: 10.5220/0004832502050212

Proceedings of ICORES 2014, ISBN: 978-989-758-017-8

Quick Abstract

In this paper, we propose a capacitated p-median problem with concave costs, in which the global cost incurred for each established facility is a concave function of the quantity q delivered by this facility. We use DICOPT to solve this concave model. And then we transform this model into a linear programming problem and solve it using the commercial solver CPLEX. We also use the metaheuristic Variable Neighbourhood Search (VNS) to solve this problem. Computational results show that our linearization method helps to improve the calculations of the concave model. With VNS, we solve large size instances with up to 1500 facilities within a reasonable CPU time.

Related Ontology Subjects/Areas/Topics (9)

Artificial Intelligence	Linear Programming	Operational Research
Knowledge Discovery and Information Retrieval	Mathematical Modeling	Optimization
Knowledge-Based Systems	Methodologies and Technologies	Symbolic Systems

A Distributionally Robust Formulation for Stochastic Quadratic Bi-level Programming

Topics: Stochastic Processes; Optimization; Mathematical Modeling

Authors: Pablo Adasme ¹ , Abdel Lisser ² and Chen Wang ²

Affiliations: ¹ Universidad de Santiago de Chile, Chile , ² Universite Paris-Sud XI, France

Digital Object Identifier: 10.5220/0004207100240031

Proceedings of ICORES 2013, ISBN: 978-989-8565-40-2

Quick Abstract

In this paper, we propose a distributionally robust model for a (0-1) stochastic quadratic bi-level programming problem. To this purpose, we first transform the stochastic bi-level problem into an equivalent deterministic formulation. Then, we use this formulation to derive a bi-level distributionally robust model (Liao, 2011). The latter is accomplished while taking into account the set of all possible distributions for the input random parameters. Finally, we transform both, the deterministic and the distributionally robust models into single level optimization problems (Audet et al., 1997). This allows comparing the optimal solutions of the proposed models. Our preliminary numerical results indicate that slight conservative solutions can be obtained when the number of binary variables in the upper level problem is larger than the number of variables in the follower.

Related Ontology Subjects/Areas/Topics (9)

Artificial Intelligence	Mathematical Modeling	Optimization
Knowledge Discovery and Information Retrieval	Methodologies and Technologies	Stochastic Processes
Knowledge-Based Systems	Operational Research	Symbolic Systems