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

Abstract

The multiple traveling salesperson problem (MTSP) is an extension of the well known traveling salesperson problem (TSP). Given m > 1 salespersons and n > m cities to visit, the MTSP seeks a partition of cities into m groups as well as an ordering among 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 exactly once and sum of total distance traveled by all the salespersons is minimized. Apart from the objective of minimizing the total distance traveled by all the salespersons, we have also considered an alternate objective of minimizing the maximum distance traveled by any one salesperson, which is related with balancing the workload among salespersons. In this paper, we have proposed a new grouping genetic algorithm based approach for the MTSP and compared our results with other approaches available in the literature. Our approach outperformed the other approaches on both the objectives.

Double evolutsional artificial bee colony algorithm for multiple traveling salesman problem

“…The genetic algorithm with one chromosome representation and the genetic algorithm with two chromosomes used in [8]; the two-part chromosome representation based on genetic algorithm proposed in [8] is referred to as GA2PC, the steady state grouping genetic algorithm proposed in [9] is referred to as GGA-SS; the ant colony algorithm proposed in [10] is referred to as ACO. The values of parameters are shown in the table 2, which are chosen empirically.…”

“…Table 4 and 5 compare the performance of DEABC with GA1C, GA2C, GA2PC, GGA-SS, ACO and TCX of average solution quality for objective 1 and objective2 on test problems used in [8]. The results of GA1C, GA2C, GA2PC are taken from [8], the results of GGA-SS, ACO and TCX are taken from [9], [10]. The S.D.…”

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.…”

Grouping genetic operators for the delineation of functional areas based on spatial interaction

“…In most of these applications only one mutation operator is used: In [26] and [31] random groups are removed and a reconstruction subroutine (repair) is applied to reassign their elements to the remaining groups and to create new groups if necessary, as it is done by Falkenauer in [10] solving a bin packing problem. In [36] random elements are removed from their groups and reassigned to the remaining groups, or to new groups if necessary. Similarly, in [29] a group-based differential mutation is used to remove the elements of an individual that have the same encoding as other given individual from its groups, and then reassign the free elements through a repair heuristic.…”