Jacques A. Ferland

Genetic and hybrid algorithms for graph coloring

Some genetic algorithms are considered for the graph coloring problem. As is the case for other combinatorial optimization problems, pure genetic algorithms are outperformed by neighborhood search heuristic procedures such as tabu search. Nevertheless, we examine the performance of several hybrid schemes that can obtain solutions of excellent quality. For some graphs, we illustrate that genetic operators can fulfill long-term strategic functions for a tabu search implementation that is chiefly founded on short-term memory strategies.

An Algorithm for Generalized Fractional Programs

An algorithm is suggested that finds the constrained minimum of the maximum of finitely many ratios. The method involves a sequence of linear (convex) subproblems if the ratios are linear (convex-concave). Convergence results as well as rate of convergence results are derived. Special consideration is given to the case of (a) compact feasible regions and (b) linear ratios.

A Tactical Planning Model for Rail Freight Transportation

This paper examines the problems of routing freight traffic, scheduling train services and allocating classification work between yards on a rail network. It describes a general optimization model which takes into account the interactions between these activities and develops global strategies for their management over a medium term planning horizon. A heuristic algorithm developed to solve this nonlinear, mixed-integer multicommodity flow problem is also presented with some computational results based on an example at the Canadian National Railroads.

Optimization of electrical distribution feeders using simulated annealing

The planning of electrical power distribution systems strongly influences the supply of electrical power to consumers. The problem is to minimize both the investment cost for feeder and substations, and the power-loss cost. When the substations can already provide enough power flow, then the problem reduces to minimize the total cost related to the feeders and their power-loss. The difficulty of dealing with this problem increases rapidly with its size (i.e., the number of customers). It seems appropriate to use heuristic methods to obtain suboptimal solutions, since exact methods are too much time consuming. In this paper, a simulated annealing algorithm is used. A set of numerical results are provided.

Algorithms for generalized fractional programming

A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ℝn. The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includes results and comments on the numerical efficiency of these algorithms.

A mathematical programming approach for scheduling physicians in the emergency room

Preparing a schedule for physicians in the emergency room is a complex task, which requires taking into account a large number of (often conflicting) rules, related to various aspects: limits on the number of consecutive shifts or weekly hours, special rules for night shifts and weekends, seniority rules, vacation periods, individual preferences, ... In this paper, we present a mathematical programming approach to facilitate this task. The approach models the situation in a major hospital of the Montréal region (approximately 20 physicians are members of the working staff). We show that the approach can significantly reduce the time and the effort required to construct a six-month schedule. A human expert, member of the working staff, typically requires a whole dedicated week to perform this task, with the help of a spreadsheet. With our approach, a schedule can be completed in less than one day. Our approach also generates better schedules than those produced by the expert, because it can take into account simultaneously more rules than any human expert can do.

Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons

A first order criterion for pseudo-convexity and second order criteria for quasi-convexity and pseudo-convexity are given for twice differentiable functions on open convex sets. The relationships between these second order criteria and other known criteria are also analysed. Finally, the numbers of operations required to verify these criteria are calculated and compared.

A large scale timetabling problem

Abstract This problem has two main components. In the timetabling subproblem a master timetable is derived taking into account student registrations and lecturer and classroom availabilities. The grouping subproblem specifies groups of students for large courses that have to be repeated several times during the week. In this paper we propose an approach to handle both subproblems and to deal with their strong relationship. The solution approach includes several heuristic procedures to handle the subproblems which are formulated as assignment type problems in which entities are assigned to resources by using penalty terms for conflicts and excessive use of classrooms. Finally numerical results are also reported.

Duality in generalized linear fractional programming

We consider a generalization of a linear fractional program where the maximum of finitely many linear ratios is to be minimized subject to linear constraints. For this Min-Max problem, a dual in the form of a Max-Min problem is introduced and duality relations are established.

Decision Support System for the School Districting Problem

For a school board with several schools in its territory, the School Districting Problem is to specify the groups of children attending each school. A decision support system used to help administrators is described in this paper. It includes several heuristic procedures to assign edges of the network to the schools. The color graphics display is extensively used to assess the quality of the solution and to provide interactive functions for modifying the solution.