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

Ant colony optimization with direct communication for the traveling salesman problem

This article is posted here with permission from IEEE - Copyright @ 2010 IEEEAnts in conventional ant colony optimization (ACO) algorithms use pheromone to communicate. Usually, this indirect communication leads the algorithm to a stagnation behaviour, where the ants follow the same path from early stages. This occurs because high levels of pheromone are developed, which force the ants to follow the same corresponding trails. As a result, the population gets trapped into a local optimum solution which is difficult to escape from it. In this paper, a direct communication (DC) scheme is proposed where ants are able to exchange cities with other ants that belong to their communication range. Experiments show that the DC scheme delays convergence and improves the solution quality of conventional ACO algorithms regarding the traveling salesman problem, since it guides the population towards the global optimum solution. The ACO algorithm with the proposed DC scheme has better performance, especially on large problem instances, even though it increases the computational time in comparison with a conventional ACO algorithm

A Hybrid Lehmer Code Genetic Algorithm and Its Application on Traveling Salesman Problems

Traveling Salesman Problems (TSP) is a widely studied combinatorial optimization problem. The goal of the TSP is to find a tour which begins in a specific city, visits each of the remaining cities once and returns to the initial cities such that the objective functions are optimized, typically involving minimizing functions like total distance traveled, total time used or total cost. Genetic algorithms were first proposed by John Holland (1975). It uses an iterative procedure to find the optimal solutions to optimization problems. This research proposed a hybrid Lehmer code Genetic Algorithm. To compensate for the weaknesses of traditional genetic algorithms in exploitation while not hampering its ability in exploration, this new genetic algorithm will combine genetic algorithm with 2-opt and non-sequential 3-opt heuristics. By using Lehmer code representation, the solutions created by crossover parent solutions are always feasible. The new algorithm was used to solve single objective and multi-objectives Traveling Salesman Problems. A non Pareto-based technique will be used to solve multi-objective TSPs. Specifically we will use the Target Vector Approach. In this research, we used the weighted Tchebycheff function with the ideal points as the reference points as the objective function to evaluate solutions, while the local search heuristics, the 2-opt and non-sequential 3-opt heuristics, were guided by a weighted sum function

An Evolutionary Strategy based on Partial Imitation for Solving Optimization Problems

In this work we introduce an evolutionary strategy to solve combinatorial optimization tasks, i.e. problems characterized by a discrete search space. In particular, we focus on the Traveling Salesman Problem (TSP), i.e. a famous problem whose search space grows exponentially, increasing the number of cities, up to becoming NP-hard. The solutions of the TSP can be codified by arrays of cities, and can be evaluated by fitness, computed according to a cost function (e.g. the length of a path). Our method is based on the evolution of an agent population by means of an imitative mechanism, we define `partial imitation'. In particular, agents receive a random solution and then, interacting among themselves, may imitate the solutions of agents with a higher fitness. Since the imitation mechanism is only partial, agents copy only one entry (randomly chosen) of another array (i.e. solution). In doing so, the population converges towards a shared solution, behaving like a spin system undergoing a cooling process, i.e. driven towards an ordered phase. We highlight that the adopted `partial imitation' mechanism allows the population to generate solutions over time, before reaching the final equilibrium. Results of numerical simulations show that our method is able to find, in a finite time, both optimal and suboptimal solutions, depending on the size of the considered search space.Comment: 18 pages, 6 figure

A grid-based ant colony algorithm for automatic 3D hose routing

Ant Colony Algorithms applied to difficult combinatorial optimization problems such as the traveling salesman problem (TSP) and the quadratic assignment problem. In this paper we propose a grid-based ant colony algorithm for automatic 3D hose routing. Algorithm uses the tessellated format of the obstacles and the generated hoses in order to detect collisions. The representation of obstacles and hoses in the tessellated format greatly helps the algorithm towards handling free-form objects and speed up the computations. The performance of the algorithm has been tested on a number of 3D models