Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology A self-organizing neural network using ideas from the immune system to solve the traveling salesman problem Thiago A.S. Masutti, Leandro N. de Castro InS, Vol.179, 2009, pp. 1454–1468. Presenter : Wei-Shen Tai 2009/11/17

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 2 Outline Introduction Self-organized networks applied to the TSP: a brief review Modified RABNET-TSP Performance evaluation Discussion and future investigations Comments

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 3 Motivation SOM for TSP  The number N of neurons in the network is usually greater than or equal to the number n of cities.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 4 Objective Modified Real-Valued Antibody Network designed to solve the Traveling Salesman Problem (RABNET-TSP)  Improves its efficacy (quality of the solutions found) and reducing the computational time of the algorithm.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 5 Main feature (1) Feedforward neural network with no hidden layer. (2) Competitive and unsupervised learning based on some immune principles. (3) constructive network architecture with growing and pruning phases based on some immune principles. (4) pre-defined circular neighborhood.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 6 Modified RABNET Adaption based on immune principle  Nine phases: (1) network initialization; (2) presentation of input patterns; (3) competition; (4) cooperation; (5) adaptation; (6) growing; (7) stabilization of the winners; (8) network convergence; and (9) pruning. Adaption constraint and stabilization of the winners  Improve the computational efficiency.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 7 Initialization and competition Network initialization  It is initialized with only one antibody (neuron). Presentation of antigens  Each city corresponds to one antigen (input) Competition  Finds the network antibody that is most similar to the antigen presented.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 8 Cooperation and adaption Cooperation(neighborhood function) Adaptation  Constrains update to only those cases in which updating will be significant (achieved by setting k )

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 9 Network growing  The most stimulated antibody in the immune system is selected for cloning (splitting).  Conditions The highest concentration of antigens.(hit probability) The greatest Euclidean distance between antibody and antigen in this antibody.(error) Error is greater than a pre-defined threshold ε.  Newly created antibody It is the same as the one from its parent antibody.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 10 Stabilization and pruning Stabilization of the winners  Suppresses cooperation as soon as no variation, Δv, in the winners is detected. (projected result is stable) Network pruning  All antibodies with concentration level γ j = 0 (empty neuron), are removed from the network.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 11 Experimental evaluation

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 12 Conclusions Improve the efficacy and the efficiency of an immune-inspired network  (1) a threshold to the use of antibodies updating.  (2) the use of a winners’ stabilization mechanism. Sample size and performance  For almost all instance with less than 500 cities, finding solutions that are less than 1% worse than the best results.  For larger instances, a percentage deviation of up to 14% was found in relation to the best known solutions.

N.Y.U.S.T. I. M. Intelligent Database Systems Lab 13 Comments Advantage  This paper improve the computational efficiency and result effectiveness of RABNET in TSP. Drawback  Epoch and iteration are the same meaning in this paper. However, they should keep consistence throughout the context. Application  Problems resemble TSP.