Gérard Fleury

Improving robustness of solutions to arc routing problems

This paper considers the stochastic capacitated arc routing problem (SCARP), obtained by taking random demands in the CARP. For real-world problems, it is important to create solutions that are insensitive to changes in demand, because these quantities are not deterministic but randomly distributed. This paper provides the basic concept of a new technique to compute such solutions, based upon the best method published for CARP: a hybrid genetic algorithm (HGA). The simulation analysis was achieved with the well-known DeArmons, Egleses and Belenguers instances. This intensive evaluation process was carried out with 1000 replications providing high-quality statistical data. The results obtained prove that there is a great interest to optimize not only the solution cost but also the robustness of solutions. This work is a step forward to treat more realistic problems including industrial goals and constraints linked to demand variations.

Evolutionary Algorithms for Stochastic Arc Routing Problems

The Capacitated Arc Routing Problem (CARP) is a combinatorial optimization problem in which vehicles with limited capacity must treat a set of arcs in a network, to minimize the total cost of the trips. The SCARP is a stochastic version with random demands on the arcs. The management rules used for instance in waste collection enable to derive mathematical expressions for objectives like the expected total cost. A memetic algorithm (MA) for the SCARP is proposed and compared with two deterministic versions based on average demands. All solutions are evaluated by simulation, to see how they are affected by random fluctuations of demands. This evaluation confirms the expected cost computed by the MA and shows its ability to provide robust solutions, without significant enlargement of the cost of planned trips.

Genetic algorithms applied to workshop problems

We evaluate in this paper the qualities of stochastic algorithms, mainly genetic and simulated annealing-type algorithms, against heuristic methods, in the scheduling of workshops. We are particularly interested in flow-shops (minimizing makespan) and one machine schedules (minimizing total tardiness, or minimizing total flow time). Many numerical results for various samples are given, and our conclusions are supported by statistical tests. When the initial population is randomly generated, genetic algorithms are shown to be statistically less efficient than annealing-type algorithms, and better than heuristic methods. But, as soon as at least one good item (e.g.,heuristicallyfound) belongs to the initial population, genetic algorithms become as good, or better than annealing-type algorithms. The resolution methods we propose are evaluated and can be used for when scheduling more complicated real workshops.

Convergence of Numerical Schemes for Stochastic Differential Equations

In this paper, the approximation of contimious processes defined by a Stochastic Differential Equation by processes defined by discrete time schemes is studied. Under minimal hypotheses, for many implicit or explicit usual schemes, the convergence in probability of the approximating process to the exact one is proved. The hypotheses are in particular satisfied when the coefficients of the Stochastic Differential Equation are only locally Lipschitz and the solution does not explode. Degenerated Stochastic differential equations are allowed.

Stochastic Newmark scheme

In this paper, we are concerned with numerical resolution of the dynamical equation of linear oscillators. An answer is given to the following question: can one use widely implemented Newmarks algorithm when the acceleration is a white noise instead of a regular deterministic one? After showing drawbacks of such a practice, a modification of the usual Newmark schemes is introduced, to be used for the numerical resolution of such a stochastic dynamical equation. The modification is only in the stochastic part, so that already implemented softwares can be used, the input only having to be carefully adapted. After that, mathematical analysis of this new scheme is fulfilled. First and second moments, as well as the power spectral density resulting from the use of this scheme are compared with the corresponding quantities resulting from the theoretical process, and also from usual Newmark scheme and Euler schemes. Almost sure convergence of this new scheme is proved.

Multi-agent approach and stochastic optimization: random events in manufacturing systems

We propose a method to solve industrial problems and to take into account random events. It is called the triple coupling. It is based on stochastic algorithms, a simulation model and the multi-agents model of artificial intelligence. The method we propose is easy to use and allows us to take into account most of the constraints found in manufacturing systems. Experts look for solutions to increasing the capacity of production. But the production can be disturbed by random events experienced by the system. Industrial experts need schedules which prevent the consequences of random events. Minimizing such consequences is very important to increasing system delivery. Capital investment is often very high in factories and the cost of the investment goes on regardless of whether the resources are running or not. The multi-agent approach is used to determine schedules for which the consequences of random events are low, and a stochastic algorithm is proposed which permits us to optimize a random variable. We prove that this algorithm finds, with probability one, the schedule of the production for which the consequences of random events are the lowest. We propose to measure the consequences of random events using an influence ratio. Our approach has been used to study the consequences of random events in Peugeot sand foundries of Sept-Fons (France). A benchmark test is presented to prove the efficiency of our solution. For the Peugeot sand foundry of Sept-Fond, random events increase the production time by about 20% compared with the production time without any random events occurring. We have determined schedules of production for which the consequences of random events are about 0.5%.

Crew scheduling for an Urban transit company

After a presentation of the problem: crew scheduling for drivers in an urban transit company, we exhibit the difficulties of this kind of optimization problem.

Simulated Annealing and Scheduling in Manufacturing Systems

For scheduling in manufacturing systems, the make-span, or total flow time, is the difference between the output date of the last job on the last machine, and the input date of the first job on the first machine. The problem is to find a schedule which minimises the make-span.