Street-Based Routing Using an Evolutionary Algorithm

Much research has been carried out into solving routing problems using both Evolutionary Techniques and other methods. In this paper the authors investigate the usage of an Evolutionary Algorithms to solve the StreetBased Routing Problem (SBRP). The SBRP is a subset of the Travelling Salesman Problem that deals specifically with a street-based environment. The paper also compares two possible strategies for evolving networks of routes. This paper may be considered introduction to the particular problem, and opens the way for future research into this area. 1. A Description of the Problem Much previous research into routing has concentrated on solving the Travelling Salesman Problem (TSP) [11][12]. The objective of the TSP is to produce the optimum (shortest) route around a set of delivery points, visiting each point only once and returning to the start. Most previous attempts at solving this problem using evolutionary algorithms have used a permutation-based representation. If the pattern of deliveries to households within an urban area is examined, it will become immediately apparent that significant adjacent clusters of delivery points occur as they are grouped into streets. It follows that all delivery points within a street will normally be serviced in sequence, before moving on to the next street. Some considerable advantage may be drawn from grouping delivery points into street sections and solving the problem by ordering street sections rather than individual delivery points. For practical purposes a street section is defined as all the delivery points on one side of a street between two junctions. Thus most named streets within a town are divided into several street sections. The authors have named this technique Street Based Routing (SBR). The street based routing problem (SBRP) may be considered to be a sub-problem of the Travelling Salesman Problem. It is the authors’ belief that when the proposed representation is applied to street-based routing problems the majority of excluded solutions will be inefficient solutions. For example, given a problem that involves delivery to 471 delivery points a permutation-based approach would yield 471! = 1.499x10^1056 potential solutions. By grouping the houses into short sections, and then using a permutation of sections, the reduction in search space is significant. For instance if the delivery points are grouped into 113 sections the search space is now 113!=2.23x10^184. Within each street section, one of three pre-defined delivery patterns may be applied to obtain the order in which the delivery points within the section are to be serviced. Within each street section the possible patterns of delivery have been identified, as: 1. Deliver to all the households on one side of the street, then cross over and deliver to the opposite side, ending up at the start point (see fig1). 2. Traverse the street from end to end, delivering to both sides, crossing over as required, finishing at the opposite end of the street from the starting point (see fig 2). 3. Deliver to all of the households on one side, then deliver to the opposite side at a later stage in the route (see fig 3). Fig. 1. Deliveries pattern 1; deliver to both sides of the street, crossing at the last house. Fig. 2. Deliveries pattern 2; deliver to both sides of the street, crossing as required. Fig. 3. Deliveries pattern 3; the two sides of the road receive deliveries at separate points within the round. 2 An Evolutionary Algorithm for solving the SBRP.