Solving Competitive Traveling Salesman Problem Using Gray Wolf Optimization Algorithm

In this paper a Gray Wolf Optimization (GWO) algorithm is presented to solve the Competitive Traveling Salesman Problem (CTSP). In CTSP, there are numbers of non-cooperative salesmen their goal is visiting a larger possible number of cities with lowest cost and most gained benefit. Each salesman will get a benefit when he visits unvisited city before all other salesmen. Two approaches have been used in this paper, the first one called static approach, it is mean evenly divides the cities among salesmen. The second approach is called parallel at which all cities are available to all salesmen and each salesman tries to visit as much as possible of the unvisited cities. The algorithms are executed for 1000 times and the results prove that the GWO is very efficient giving an indication of the superiority of GWO in solving CTSP

The design and applications of the african buffalo algorithm for general optimization problems

Optimization, basically, is the economics of science. It is concerned with the need to maximize profit and minimize cost in terms of time and resources needed to execute a given project in any field of human endeavor. There have been several scientific investigations in the past several decades on discovering effective and efficient algorithms to providing solutions to the optimization needs of mankind leading to the development of deterministic algorithms that provide exact solutions to optimization problems. In the past five decades, however, the attention of scientists has shifted from the deterministic algorithms to the stochastic ones since the latter have proven to be more robust and efficient, even though they do not guarantee exact solutions. Some of the successfully designed stochastic algorithms include Simulated Annealing, Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, Artificial Bee Colony Optimization, Firefly Optimization etc. A critical look at these ‘efficient’ stochastic algorithms reveals the need for improvements in the areas of effectiveness, the number of several parameters used, premature convergence, ability to search diverse landscapes and complex implementation strategies. The African Buffalo Optimization (ABO), which is inspired by the herd management, communication and successful grazing cultures of the African buffalos, is designed to attempt solutions to the observed shortcomings of the existing stochastic optimization algorithms. Through several experimental procedures, the ABO was used to successfully solve benchmark optimization problems in mono-modal and multimodal, constrained and unconstrained, separable and non-separable search landscapes with competitive outcomes. Moreover, the ABO algorithm was applied to solve over 100 out of the 118 benchmark symmetric and all the asymmetric travelling salesman’s problems available in TSPLIB95. Based on the successful experimentation with the novel algorithm, it is safe to conclude that the ABO is a worthy contribution to the scientific literature

The AddACO: A bio-inspired modified version of the ant colony optimization algorithm to solve travel salesman problems

The Travel Salesman Problem (TSP) consists in finding the minimal-length closed tour that connects the entire group of nodes of a given graph. We propose to solve such a combinatorial optimization problem with the AddACO algorithm: it is a version of the Ant Colony Optimization method that is characterized by a modified probabilistic law at the basis of the exploratory movement of the artificial insects. In particular, the ant decisional rule is here set to amount in a linear convex combination of competing behavioral stimuli and has therefore an additive form (hence the name of our algorithm), rather than the canonical multiplicative one. The AddACO intends to address two conceptual shortcomings that characterize classical ACO methods: (i) the population of artificial insects is in principle allowed to simultaneously minimize/maximize all migratory guidance cues (which is in implausible from a biological/ecological point of view) and (ii) a given edge of the graph has a null probability to be explored if at least one of the movement trait is therein equal to zero, i.e., regardless the intensity of the others (this in principle reduces the exploratory potential of the ant colony). Three possible variants of our method are then specified: the AddACO-V1, which includes pheromone trail and visibility as insect decisional variables, and the AddACO-V2 and the AddACO-V3, which in turn add random effects and inertia, respectively, to the two classical migratory stimuli. The three versions of our algorithm are tested on benchmark middle-scale TPS instances, in order to assess their performance and to find their optimal parameter setting. The best performing variant is finally applied to large-scale TSPs, compared to the naive Ant-Cycle Ant System, proposed by Dorigo and colleagues, and evaluated in terms of quality of the solutions, computational time, and convergence speed. The aim is in fact to show that the proposed transition probability, as long as its conceptual advantages, is competitive from a performance perspective, i.e., if it does not reduce the exploratory capacity of the ant population w.r.t. the canonical one (at least in the case of selected TSPs). A theoretical study of the asymptotic behavior of the AddACO is given in the appendix of the work, whose conclusive section contains some hints for further improvements of our algorithm, also in the perspective of its application to other optimization problems

Hybrid iterated local search algorithm for optimization route of airplane travel plans

The traveling salesman problem (TSP) is a very popular combinatorics problem. This problem has been widely applied to various real problems. The TSP problem has been classified as a Non-deterministic Polynomial Hard (NP-Hard), so a non-deterministic algorithm is needed to solve this problem. However, a non-deterministic algorithm can only produce a fairly good solution but does not guarantee an optimal solution. Therefore, there are still opportunities to develop new algorithms with better optimization results. This research develops a new algorithm by hybridizing three local search algorithms, namely, iterated local search (ILS) with simulated annealing (SA) and hill climbing (HC), to get a better optimization result. This algorithm aimed to solve TSP problems in the transportation sector, using a case study from the Traveling Salesman Challenge 2.0 (TSC 2.0). The test results show that the developed algorithm can optimize better by 15.7% on average and 11.4% based on the best results compared to previous studies using the Tabu-SA algorithm

WoLF Ant

Ant colony optimization (ACO) algorithms can generate quality solutions to combinatorial optimization problems. However, like many stochastic algorithms, the quality of solutions worsen as problem sizes grow. In an effort to increase performance, we added the variable step size off-policy hill-climbing algorithm called PDWoLF (Policy Dynamics Win or Learn Fast) to several ant colony algorithms: Ant System, Ant Colony System, Elitist-Ant System, Rank-based Ant System, and Max-Min Ant System. Easily integrated into each ACO algorithm, the PDWoLF component maintains a set of policies separate from the ant colony\u27s pheromone. Similar to pheromone but with different update rules, the PDWoLF policies provide a second estimation of solution quality and guide the construction of solutions. Experiments on large traveling salesman problems (TSPs) show that incorporating PDWoLF with the aforementioned ACO algorithms that do not make use of local optimizations produces shorter tours than the ACO algorithms alone