Thiago A.S. Masutti , Leandro N. de Castro InS , Vol.179, 2009, pp. 1454–1468.

A self-organizing neural network using ideas from the immune systemto 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

Outline • Introduction • Self-organized networks applied to the TSP: a brief review • Modified RABNET-TSP • Performance evaluation • Discussion and future investigations • Comments

Motivation • SOM for TSP • The number N of neurons in the network is usually greater than or equal to the number n of cities.

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.

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.

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.

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.

Cooperation and adaption • Cooperation(neighborhood function) • Adaptation • Constrains update to only those cases in which updating will be significant (achieved by setting k)

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.

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 γj= 0 (empty neuron), are removed from the network.

Experimental evaluation

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.

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.

Thiago A.S. Masutti , Leandro N. de Castro InS , Vol.179, 2009, pp. 1454–1468.