Ant Colony Optimization Revisited from a Randomized Shortest Path Perspective

نویسندگان

  • Caroline Herssens
  • Amin Mantrach
  • Marco Saerens
چکیده

In this letter, it is shown that the randomized shortest-path framework (RSP, [15]) provides a theoretical interpretation of a class of ant colony optimization (ACO) algorithms, enjoying some nice properties. According to RSP, ants are sent from some initial node until they either eventually reach the goal node, or abandon and come back unsuccessfully along the same path. During their return travel (backward pass), each node on the trajectory is rewarded if the goal was reached – successful walk. The policy, which takes the form of the probabilities of following arc k → k′ in each node k, is updated periodically at each epoch t, and is set to the previous policy times (1) the proportion of successful walks starting from node k′ (probability of success, the pheromone), and (2) exp[−θckk′ ] (the heuristic function), where ckk′ is the cost associated to arc k → k′. The RSP framework shows that (i) this policy is optimal at any epoch t in that it minimizes the expected cost for reaching the goal node (exploitation) while maintaining a constant relative entropy spread in the graph (exploration), and (ii) the procedure converges to the minimal cost policy when t → ∞, provided the probability of success is well-estimated, that is, enough ants are sent at each epoch (asymptotic convergence). In other words, it provides an optimal trade-off between exploration and exploitation. We therefore decided to bring the RSP framework to the attention of the evolutionary computation community, hoping that it will stimulate the design as well as the empirical evaluation of new ACO algorithms having interesting theoretical properties.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finding the Shortest Hamiltonian Path for Iranian Cities Using Hybrid Simulated Annealing and Ant Colony Optimization Algorithms

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

متن کامل

Modified Fast Bandwidth-Constrained Shortest Path Algorithm for MACO

Ant Colony Optimization is a probabilistic technique for finding the optimal path for reaching a destination using graphs. This algorithm was further developed to introduce the concept of Multiple Ant Colony Optimization technique in which ants were classified into various families that worked to provide optimal path solutions to the destination for their own family. This paper aims at proposin...

متن کامل

Performance Comparison of Prim’s and Ant Colony Optimization Algorithm to Select Shortest Path in Case of Link Failure

Abstract—Ant Colony Optimization (ACO) is a promising modern approach to the unused combinatorial optimization. Here ACO is applied to finding the shortest during communication link failure. In this paper, the performances of the prim’s and ACO algorithm are made. By comparing the time complexity and program execution time as set of parameters, we demonstrate the pleasant performance of ACO in ...

متن کامل

Convergence results for continuous - time dynamics arising in ant colony optimization ⋆

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is ...

متن کامل

Solving the Shortest Path Problem in Vehicle Navigation System by Ant Colony Algorithm

A shortest path search method based on ant colony algorithm is proposed. The method contracts the search space appropriately, obtaining, in a short time, a path that is as close as possible to the path obtained by the Dijkstra method (the optimum path). To improve the performance, we modify the pheromone update rule and introduce a learning strategy into the ant colony algorithm. The method obt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009