A Genetic Algorithm with New Local Operators for Multiple Traveling Salesman Problems

Abstract

Multiple Traveling Salesman Problem (MTSP) is able to model and solve various real-life applications such as multiple scheduling, multiple vehicle routing and multiple path planning problems, etc. While Traveling Salesman Problem (TSP) focuses on searching a path of minimum traveling distance to visit all cities exactly once by one salesman, the objective of the MTSP is to find m paths for m salesmen with a minimized total cost -the sum of traveling distances of all salesmen through all of the respective cities covered. They have to start from a designated depot which is the departing and returning location of all salesmen. Since the MTSP is a NP-hard problem, a new effective Genetic Algorithm with Local operators (GAL) is proposed in this paper to solve the MTSP and generate high quality solution within a reasonable amount of time for real-life applications. Two new local operators, Branch and Bound (BaB) and Cross Elimination (CE), are designed to speed up the convergence of the search process and improve the solution quality. Results demonstrate that GAL finds a better set of paths with a 9.62% saving on average in cost comparing to two existing MTSP algorithms.

Experimental Study of a Hybrid Genetic Algorithm for the Multiple Travelling Salesman Problem

“…en a hybrid GA (HGA) is developed using a heuristic method for creating initial population, SCX, swap mutation, local search approach, and an immigration approach for finding highquality solution to the reduced problem. e usefulness of our proposed HGA is observed against some ACO-based algorithms [21][22][23], GAs [24,25], and a gravitational emulation approach [26] on some symmetric instances from TSPLIB [27]. e computational experiences demonstrate the usefulness of the proposed HGA.…”

“…We compare our proposed HGA with some state-of-theart algorithms on the abovementioned six instances using m � 5. e state-of-the-art algorithms are a hybrid approach that combines ACO, 2-opt, and GA algorithms (AC2OptGA) [21], GA with local operators (GAL) [25], modified sweep and ant colony algorithm (SW + AS elite ) [22], modified gravitational emulation local search (M-GELS) [26], modified GA (MGA) [24], and novel modified ACO (NMACO) [23]. We used the same parameters for our HGA which are used for all of these algorithms.…”

New Ant Colony Optimization Algorithm for the Traveling Salesman Problem

“…Because the TSP is a well-known NP-hard combinatorial optimization problem that is computationally difficult, in addition to ACO, many other new metaheuristic optimization algorithms have been applied to solve it, such as the quantum heuristic algorithm (QHA) [19], the discrete artificial bee colony algorithm with a neighborhood operator (DABC-NO) [20], the shrinking blob algorithm (SBA) [21], the discrete cuckoo search algorithm (DCSA) [22], the random-key cuckoo search (RKCS) [23], the African buffalo optimization (ABO) [24], the discrete bat algorithm (DBA) [25], the fruit fly optimization algorithm (FFOA) [26], a hybrid algorithm using a GA and a multiagent reinforcement learning heuristic (GA-MRLH) [27], the artificial atom algorithm (AAA) [28], the greedy flower pollination algorithm (GFPA) [29], the imperial competitive algorithm (ICA) [30], the black hole algorithm (BHA) [31], the simulated annealing-based symbiotic organisms search optimization algorithm (SA-SOSOA) [32], the discrete symbiotic organisms search algorithm (DSOSA) [33], the hybrid discrete artificial bee colony algorithm with a threshold acceptance criterion (DABC-TAC) [34], a minimum spanning tree-based heuristic (MSTH) [35], a genetic algorithm with local operators (GAL) [36], a new hybrid optimization algorithm based on wolf pack search and local search (WPS-LS) [37], discrete spider monkey optimization (DSMP) [38], discrete pigeon-inspired optimization (DPIO) [39], and the parthenogenetic algorithm (PGA) [40], and so on. For those algorithms, many are newly proposed metaheuristic algorithms, such as QHA, SBA, DCSA, RKCS, ABO, DBA, FFOA, AAA, GFPA, ICA, BHA, DSOSA, MSTH, DSMP, DPIO, and PGA.…”

“…However, this algorithm is very complex and more parameters are needed. GAL [36] is a hybrid algorithm of genetic algorithm with local operators and its results for solving TSPs are good in terms of the solution quality and speed too. However, the algorithm is also very complex and more parameters are needed.…”

Region Division in Logistics Distribution With a Two-Stage Optimization Algorithm

“…Genetic algorithm is widely used and researched in MTSP. For example, Yuan et al adopted the two-part chromosome crossover for solving the MTSP using a genetic algorithm [25]; Zhou et al proposed a partheno genetic algorithm with a new selection operator and a more comprehensive mutation operator to solve the MTSP [26]; Lo et al designed a new Genetic Algorithm with two local operators, branch and bound and cross elimination, to solve the MTSP [27]. Then, swarm-intelligence-based approaches have also been applied to the MTSP successfully.…”