A Grouping Genetic Algorithm for the Multiple Traveling Salesperson Problem

Abstract

The multiple traveling salesperson problem (MTSP) involves scheduling m > 1 salespersons to visit a set of n > m locations. Thus, the n locations must be divided into m groups and arranged so that each salesperson has an ordered set of cities to visit. The grouping genetic algorithm (GGA) is a type of genetic algorithm (GA) designed particularly for grouping problems. It has been successfully applied to a variety of grouping problems. This paper focuses on the application of a GGA to solve the MTSP. Our GGA introduces a new chromosome representation to indicate which salesperson is assigned to each tour and the ordering of the cities within each tour. We compare our method to standard GAs that employ either the one-chromosome or two-chromosome representation for MTSP. This research demonstrates that our GGA with its new chromosome representation is capable of solving a variety of MTSP problems from the literature and can outperform the traditional encodings of previously published GA methods.

Minimization of the Total Traveling Distance and Maximum Distance by Using a Transformed-Based Encoding EDA to Solve the Multiple Traveling Salesmen Problem

“…There are five major direct encodings of EAs: one-chromosome [17], two-chromosome [13,24,[46][47][48] Print scheduling Print press scheduling [49] Preprint advertisement scheduling [50] Workforce planning Bank crew scheduling [51] Technical crew scheduling [52] Photographer team scheduling [53] Interview scheduling [54] Workload balancing [55] Security service scheduling [56] Transportation planning School bus routing [57] Crane scheduling [58] Local truckload pickup and delivery [59] Vehicle routing problem [60,61] Mission planning Planning of autonomous mobile robots [62][63][64][65] Planning of unmanned air vehicles [66] Production planning Hot rolling scheduling [17] Parallel machine scheduling with setup [29] Satellite systems Designing satellite surveying systems [67] Cities Cities per [ 18,19], two-part chromosome [13], grouping genetic algorithms (GGAs) [20][21][22], and matrix representation [23]. Two-part chromosome encoding, which is superior to oneand two-chromosome encoding [13] because of its smaller solution space, is depicted in Figure 1.…”

A new grouping genetic algorithm approach to the multiple traveling salesperson problem

“…The MTSP seeks a partition of n cities into m groups as well as an ordering among the cities in each group, so that each group of cities is visited by exactly one salesperson in their specified order in such a way that each city is visited once and only once and the total distance traveled by all the salespersons is minimized. Like two recent works on MTSP (Carter and Ragsdale 2006;Brown et al 2007), we have also considered an alternate objective of minimizing the maximum distance traveled by any single salesperson. This objective is related with balancing the workload among salespersons.…”

“…Carter and Ragsdale (2006) proposed a genetic algorithm (GA) for the MTSP that uses a new two-part chromosome representation and related genetic operators. Brown et al (2007) proposed a grouping genetic algorithm (Falkenauer 1998) that uses a chromosome representation and genetic operators derived directly from those proposed in Falkenauer (1998). Among the earlier works, Tang et al (2000) proposed the one-chromosome representation for the MTSP problem and applied it to solve the hot rolling production scheduling problem.…”

“…The two-chromosome representation used in Malmborg (1996) and Park (2001) for the VSP can also be used for the MTSP. In fact, both Carter and Ragsdale (2006) and Brown et al (2007) have compared the performance of their genetic algorithms against the genetic algorithms using one-chromosome and two chromosome representations. All the aforementioned chromosome representations are discussed in detail in Sect.…”

“…However, our GGA uses different chromosome representation and genetic operators than those used in GGA of Brown et al (2007). Moreover, our GGA uses steady-state population replacement model (Davis 1991), whereas GGA of Brown et al (2007) uses generational model. We have compared the results of our approach with those reported in Carter and Ragsdale (2006) and Brown et al (2007).…”