Massimiliano Caramia

GENETIC ALGORITHMS IN BUS NETWORK OPTIMIZATION

This paper focuses on a new method to compute fitness function (ff) values in genetic algorithms for bus network optimization. In the proposed methodology, a genetic algorithm is used to generate iteratively new populations (sets of bus networks). Each member of the population is evaluated by computing a number of performance indicators obtained by the analysis of the assignment of the O/D demand associated to the considered networks. Thus, ff values are computed by means of a multicriteria analysis executed on the performance indicators so found. The goal is to design a heuristic that allows to achieve the best bus network satisfying both the demand and the offer of transport.

New Algorithms for Examination Timetabling

In examination timetabling a given set of examinations must be assigned to as few time slots as possible so as to satisfy certain side constraints and so as to reduce penalties deriving from proximity constraints. In this paper, we present new algorithms for this problem and report the results of an extensive experimental study. All our algorithms are based on local search and are compared with other existing implementations in the literature.

Multi-objective management in freight logistics: Increasing capacity, service level and safety with optimization algorithms

In this chapter, we introduce freight distribution logistic, discussing some statistics about future trends in this area. Basically, it appears that, even though there has been a slight increase in the use of rail and water transportation modes, there is room to obtain a more efficient use of the road mode, mainly not to increase air pollution (fossil-fuel combustion represents about 80% of the factors that jeopardize air quality). In order to be able to reach an equilibrium among different transportation modes, the entire supply chain has to be studied to install the appropriate service capacity and to define effective operational procedures to optimize the system performance. 1.1 Freight Distribution Logistic The way the governments and the economic world are now looking at transportation problems in general and at distribution logistic in particular has changed from past years. Europe, in particular, has adopted the so-called European Sustainable Development Strategy (SDS) in the European Council held in Gothenburg in June 2001. That was the opportunity to set out a coherent approach to sustainable development renewed in June 2006 to reaffirm the aim of continuous improvement of quality of life and economic growth through the efficient use of resources, and promoting the ecological and the social innovation potentials of the economy. Recently, in December 2007, the European Council insisted on the need to give priority to implementation measures. Paragraph 56 of Commission Progress Report of 22 October 2007 reads “. . . The EU must continue to work to move towards more sustainable trans-

Novel Local-Search-Based Approaches to University Examination Timetabling

Examination timetabling assigns examinations to a given number of time slots so that there are no conflicts. A conflict occurs if a student has to take more than one examination at the same time, or when the number of students that must take an exam exceeds the capacity of the classroom assigned. The objective is to minimize penalties from proximity constraints. We present new algorithms based on local search and report on an extensive experimental study. We consider also a variant where the concern is to produce conflict-free timetables minimizing the number of time slots, regardless of how close exams appear in the schedule. The algorithms proposed also manage the trade-off between the two objective functions and produce the best results on several standard benchmark instances, compared to the best existing algorithms.

A Milk Collection Problem with Incompatibility Constraints

The milk collection problem is well known in rural areas of the world. This paper considers this real-life problem for an Italian dairy company that collects raw milk from farmers. In our milk collection problem, we address the constraint that some farms are small and inaccessible by large vehicles; moreover, these farmers produce different milk types, and the tank trucks used for transporting the milk have multiple compartments. This generates the additional constraint that at most one milk type can be assigned to a tank compartment. The goal of this paper is to show how operations research techniques helped the company to improve its daily performance. In particular, we present a solution approach based on two mathematical formulations and local search, all embedded within a multiple-restart mechanism. The first mathematical formulation minimizes the number of vehicles to be routed in the network; the second minimizes the tour length. We also discuss experiments we conducted as part of our case study and compare our solution with the process that the company used previously.

A heuristic approach for the truck and trailer routing problem

AbstractIn this paper, we propose an approach based on mathematical programming and local search to cope with the truck and trailer vehicle routing problem. The mathematical programming framework models two subproblems that are solved sequentially, that is, the customer-route assignment problem (CAP), with the objective of minimizing the fleet size used to service clients, and the route definition problem, with the objective of minimizing the total tour length given the set of clients assigned to each vehicle. Since the route assignment model can return infeasible solutions, the local search plays the role of possibly retrieving a feasible solution. The mathematical formulations and the local search work iteratively, embedded in a multiple restarting mechanism able to diversify solutions by (i) identifying additional constraints for the CAP formulation to be taken into account during the algorithm progress, (ii) using a tabu like customer-route matrix to avoid assignments already analysed in the previous iterations of the algorithm. Also a lower bound to assess the solution quality is given. Experiments and comparison with competing approaches suggest that the results of the proposed machinery are promising, producing, on average, a smaller total tour lengths on benchmarks.

Coloring graphs by iterated local search traversing feasible and infeasible solutions

Graph coloring is one of the hardest combinatorial optimization problems for which a wide variety of algorithms has been proposed over the last 30 years. The problem is as follows: given a graph one has to assign a label to each vertex such that no monochromatic edge appears and the number of different labels used is minimized. In this paper we present a new heuristic for this problem which works with two different functionalities. One is defined by two greedy subroutines, the former being a greedy constructive one and the other a greedy modification one. The other functionality is a perturbation subroutine, which can produce also infeasible colorings, and the ability is then to retrieve feasible solutions. In our experimentation the proper tuning of this optimization scheme produced good results on known graph coloring benchmarks.

An exact algorithm to minimize the makespan in project scheduling with scarce resources and generalized precedence relations

In this paper we propose an exact algorithm for the Resource Constrained Project Scheduling Problem (RCPSP) with generalized precedence relationships (GPRs) and minimum makespan objective. For the RCPSP with GPRs we give a new mathematical formulation and a branch and bound algorithm exploiting such a formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same mathematical formulation. We provide an extensive experimentation and a comparison with known lower bounds and competing exact algorithms drawn from the state of the art.

A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations

In this paper we propose a new lower bound for the resource-constrained project scheduling problem with generalized precedence relationships. The lower bound is based on a relaxation of the resource constraints among independent activities and on a solution of the relaxed problem suitably represented by means of an AON acyclic network. Computational results are presented and confirmed a better practical performance of the proposed method with respect to those present in the literature.

Constraint Propagation in Graph Coloring

In this paper we propose a method for integrating constraint propagation algorithms into an optimization procedure for vertex coloring with the goal of finding improved lower bounds. The key point we address is how to get instances of Constraint Satisfaction Problems (CSPs) from a graph coloring problem in order to give rise to new lower bounds outperforming the maximum clique bound. More precisely, the algorithms presented have the common goal of finding CSPs in the graph for which infeasibility can be proven. This is achieved by means of constraint propagation techniques which allow the algorithms to eliminate inconsistencies in the CSPs by updating domains dynamically and rendering such infeasibilities explicit. At the end of this process we use the largest CSP for which it has not been possible to prove infeasibility as an input for an algorithm which enlarges such CSP to get a feasible coloring. We experimented with a set of middle-high density graphs with quite a large difference between the maximum clique and the chromatic number.