Akshay Joshi #1, C.G.Nitash #2, Anish Sawkar #3 Prof. Nilesh B Fal Dessai #4 and Prof Vijay Borges #5 # Information Technology Department, Goa College of Engineering, Goa firstname.lastname@example.org, email@example.com, firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
The Ant Colony Optimization (ACO) technique uses the foraging behaviour of biological ants, which rely on less on memory and depends more on collective intelligence. These same principles are used to create artificial ants which iteratively develop partial solutions to the problem and hence obtain optimal solutions. The objective of this paper is to develop a novel approach to the ACO meta-heuristic called P-Evolution. P-Evolution is a modification to the ACO meta-heuristic which can be applied to a range of problem models, and problem instances. The working of PEvolution is demonstrated on the Travelling Salesman Problem (TSP) problem. This approach could also be used to solve dynamically changing models, which are representative of a number of real life systems.
from the foraging behavior of biological ants. In the real world, ants when searching for food initially starting from nest move randomly in the search space to search for food. As soon as ant finds the food it analyses its quantity and quality and carries some of it back to the nest depositing a chemical pheromone trail on the ground. These pheromone trails are directly proportional to the quality and quantity of the food source and guides other ant to the food source. This indirect communication between the ants through the pheromone trail leads them to find the shortest path between the source and the nest. This property of real ant colony is exploited to artificial ant colony to solve NP-Problems. 
Key Words: Travelling Salesperson
Problem (TSP), Ant Colony Optimization (ACO), Stochastic, Meta-heuristic, P-Evolution.
Ant Colony Optimization is a paradigm for designing meta-heuristic algorithm for combinatorial optimization problems . ACO’s belong to the class of meta-heuristics which are approximate algorithms to obtain near optimal solutions which are inspired
The Traveling Salesman Problem or TSP is a best known Combinatorial Optimization Problem (COP) .Generally speaking in TSP we have a set of cities along with the traveling distance between each pair of cities and one wishes to find a tour of cities visiting each city exactly once by minimizing the cost of travel. TSP is notoriously hard to solve, being one of the hardest NP-complete problem. In this paper we will consider all cities are in single plane and co-ordinates of each city are known in 2D. 
2. ACO-Algorithm for TSP
Procedure ACO algorithm for TSPs Set parameters, initialize pheromone trails While(termination conditions not met) do Construct Solutions Apply local Search Update trail End End ACO algorithm for TSPs
quality for future runs of the ACO algorithm. This method essentially uses a pool of solutions obtained from a collection of independent ACO algorithms, each running their own set of parameter values. Then using optimality criteria, such as rate of convergence, distance from optimum, etc, the P-Evolution method selects the parameter sets that show the best results in terms of solution quality. These parameter sets are then given preference in the future runs of the independent ACO algorithms. It is important that the problem model and the problem space upon which each ACO algorithm works must be the same; only the parameter settings should vary. This ensures the evolution of better parameter settings relevant to the problem model in question.
The workings of all ACO meta-heuristics rely upon the initial parameter settings, i.e upon the pheromone evaporation rate, pheromone updation quantities, etc. The parameter settings associated with any given problem model will vary and will...