A Genetic Algorithm with Fuzzy Comprehensive Evaluation for Driver Scheduling

Abstract: Based on fuzzy set theory, this paper presents a new algorithm for public transport driver schedulingproblems, which involves solving a set covering model. A greedy heuristic is used to construct a schedule bysequentially selecting shifts to cover the remaining work. Assessment of the potential shifts in the selectionprocess employs a new approach which applies fuzzy comprehensive evaluation to consider the structuralefficiency of driver shifts. A Genetic Algorithm (GA) is employed to produce a near-optimal weight distributionamongst fuzzified criteria expressed as membership functions. Comparative results on real-world problems arepresented.Keywords: Fuzzy sets, Genetic Algorithms, Driver scheduling 1 Introduction Bus and rail driver scheduling is a process of partitioning blocks of work, each of which is serviced by onevehicle, into a set of legal driver shifts. The main objective is to minimise the total number of shifts and the totalshift costs. This problem has attracted much research interest since the 1960’s. Wren and Rousseau [1] gave anoverview of the approaches, many of which have been reported in a series of international workshopconferences ([2], [3], [4]).The driver scheduling problem can be formulated as a set covering Integer Linear Programme (ILP). All thelegal potential shifts are first constructed. Then, a least cost subset covering all the work is selected to form asolution schedule. A typical problem may have a solution schedule requiring over 100 shifts chosen from apotential set of about 50,000.Set covering is one of the oldest and most studied NP-hard problems ([5], [6], [7], [8]). Given a ground set U ofm elements, and a weight for each set, the goal is to cover U with the smallest possible number of sets. In thecase of driver scheduling, there is the additional objective of minimising the total weight.Since the set covering problem is unlikely to be solved optimally in polynomial time, there has been a lot ofwork in exploring the possibility of obtaining efficiently near-optimal solutions. One of the best polynomialtime algorithms is the greedy algorithm: at each step choose the unused set which covers the largest number ofremaining elements. Johnson and Lovasz ([6], [7]) proved in the mid 70’s that the performance ratio of the