Imperial competitive algorithm with policy learning for the traveling salesman problem

Abstract

The traveling salesman problem (TSP) is one of the most studied combinatorial optimization problems. In this paper, we present the new idea of combining the imperial competitive algorithm with a policy-learning function for solving the TSP problems. All offspring of each country are defined as representing feasible solutions for the TSP. All countries can grow increasingly strong by learning the effective policies of strong countries. Weak countries will generate increasingly excellent offspring by learning the policies of strong countries while retaining the characteristics of their own country. Imitating these policies will enable the weak countries to produce improved offspring; the solutions generated will, therefore, acquire a favorable scheme while maintaining diversity. Finally, experimental results for TSP instances from the TSP library have shown that our proposed algorithm can determine the salesman's tour with more effective performance levels than other known methods.

Modified ant colony optimization with improved tour construction and pheromone updating strategies for traveling salesman problem

“…Moreover, the deep analysis on its applicability for different scales of TSPs has not been conducted too, and it is also our future work. To verify the MACO more deeply, the computing results of MACO are compared with some state-of-the-art metaheuristic algorithms from the literature, including list-based simulated annealing algorithm (LBSA) proposed in 2016 (Zhan et al 2016), discrete cuckoo search algorithm (DCSA) proposed in 2014 (Ouaarab et al 2014) proposed in 2017 (Huang et al 2017), artificial atom algorithm (AAA) proposed in 2018 (Yildirim and Karci 2018), hybrid algorithm using a genetic algorithm and multiagent reinforcement learning heuristic (GA-MRLH) proposed in 2018 (Alipour et al 2018), imperial competitive algorithm with policy learning (ICA-PL) proposed in 2017 (Chen et al 2017), simulated annealing-based symbiotic organisms search optimization algorithm (SA-SOSO) proposed in 2017 , and hybrid discrete artificial bee colony algorithm with threshold acceptance criterion (DABC-TAC) proposed in 2017 (Zhong et al 2017). Most of these algorithms have been proposed in nearly three years.…”

New Ant Colony Optimization Algorithm for the Traveling Salesman Problem

“…It should be noted that, in Table 2, algorithms 1 to 17 represent the new algorithm in this paper, HMMAS [13], HEAS [16], ACO-3Opt [17], DABC-NO [20], DCSA [22], RKCS [23], ABO [24], DBA [25], FFOA [26], GA-MRLH [27], AAA [28], ICA [30], BHA [31], SA-SOSOA [32], DSOSA [33], and DABC-TAC [34], respectively.…”

“…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.…”

A hybrid two-stage sweep algorithm for capacitated vehicle routing problem

“…Therefore, the solution may not be an optimal solution. The procedure of greedy search [18] is given as follows:…”