Laurent Houssin

Just in Time Control of Constrained (max,+)-Linear Systems

This paper deals with just in time control of (max,+)-linear systems. The output tracking problem, considered in previous studies, is generalized by considering additional constraints in the control objective. The problem is formulated as an extremal fixed point computation. This control is applied to timetables computation for urban bus networks.

Control of (max,+)-linear systems minimizing delays

In this paper, we develop a new control technique for discrete event dynamic systems subject to synchronization phenomena. We propose a feedback controller for (max, + )-linear systems which delays input events as little as possible while constraints on internal or output events are satisfied. The synthesis is mainly based on new results about fixed points of antitone (i.e., order reversing) mappings.

TIMETABLE SYNTHESIS USING (MAX,+) ALGEBRA

Abstract This paper deals with control of transportation systems. We propose an approach based on dioid theory to compute timetables of a transportation network. We generalize the problem by considering additional constraints for the control objective.

CONTROL OF CONSTRAINED (MAX,+)-LINEAR SYSTEMS MINIMIZING DELAYS

Abstract This paper deals with feedback controller synthesis for (max,+) -linear systems. We attempt to compute a feedback which ensures some given constraints while delaying as less as possible the system. The controller synthesis presented here is based on fixed points results of antitone mappings.

Modelling and control of urban bus networks in dioids algebra

Abstract We aim at applying dioids algebraic tools to the study of urban bus networks. In particular, we show how they can be used for timetables synthesis.

On scheduling models for the frequency interval assignment problem with cumulative interferences

In this article, models and methods for solving a real-life frequency assignment problem based on scheduling theory are investigated. A realistic frequency assignment problem involving cumulative interference constraints in which the aim is to maximize the number of assigned users is considered. If interferences are assumed to be binary, a multiple carrier frequency assignment problem can be treated as a disjunctive scheduling problem since a user requesting a number of contiguous frequencies can be considered as a non-preemptive task with a processing time, and two interfering users can be modelled through a disjunctive constraint on the corresponding tasks. A binary interference version of the problem is constructed and a disjunctive scheduling model is derived. Based on the binary representation, two models are proposed. The first one relies on an interference matrix and the second one considers maximal cliques. A third, cumulative, model that yields a new class of scheduling problems is also proposed. Computational experiments show that the case-study frequency assignment problem can be solved efficiently with disjunctive scheduling techniques.

A robust basic cyclic scheduling problem

This paper addresses the Basic Cyclic Scheduling Problem where the processing times are affected by uncertainties. We formulate the problem as a two-stage robust optimization problem with a budgeted uncertainty set. More precisely, we consider the uncertainty set introduced by Bertsimas and Sim (Oper Res 52(1):35–53, 2004) where the activity durations are subject to interval uncertainty and the level of robustness is controlled by a parameter. We propose three exact algorithms for solving the problem. Two of them use a negative circuit detection algorithm as a subroutine, and the last one is a Howard’s algorithm adaptation. Results of numerical experiments on randomly generated instances show that the Howard’s algorithm adaptation yields efficient results and opens perspectives on more difficult robust cyclic scheduling problems.

Frequency allocation in a SDMA satellite communication system with beam moving

Spatial Division Multiple Access (SDMA) is a principle of radio resource sharing that separates communication channels in space. It relies on adaptive and dynamic beam-forming technology and well-designed algorithms for resource allocation. As satellite communication systems move towards greater capacity in both the number of users and throughput, SDMA becomes one of the most promising techniques that can achieve these two goals. This paper studies static Frequency Assignment Problem (FAP) in a satellite communication system involving a satellite and a number of users located in a service area. The objective is to maximize the number of users that the system can serve while maintaining the signal to interference plus noise ratio of each user under a predefined threshold. Traditionally, interference is binary and fixed. In this paper, the interference is cumulative and variable depending on how the frequency is assigned. To solve the problem, we work on both discrete and continuous optimizations. Integer linear programming formulations and greedy algorithms are proposed for solving the discrete frequency allocation problem. The solution is further improved by beam moving algorithm which involves continuous adjustment of satellite beams and deals with non-linear change of interference.

Hybrid Discrete-Continuous Optimization for the Frequency Assignment Problem in Satellite Communication System

Abstract This paper studies static Frequency Assignment Problem (FAP) in a satellite communication system involving a satellite and a number of users located in a service area. The objective is to maximise the number of users that the system can serve while maintaining the signal to interference plus noise ratio of each user under a predefined threshold. Traditionally, interference is binary and fixed. In this paper, the interference is cumulative and variable depending on how the frequency is assigned. To solve the problem, we work on both discrete and continuous optimizations. Integer linear programming formulations and greedy algorithms are proposed for solving the discrete frequency allocation problem. The solution is further improved by beam moving algorithm which involves continuous adjustment of satellite beams and deals with non-linear change of interference.

A New Procedure for the Cyclic Job Shop Problem

Abstract The topic of this paper is the cyclic job shop problem which aims at minimizing the cycle time under precedence and resource constraints. Based on graph theory, we propose a new branch and bound enumeration procedure to solve this problem. We compare the new procedure with other exact methods and present numerical test results.