# Parameters of energy function for TSP

[This question was initially asked here. It went unanswered so I thought I should ask it in a different community.]

I am reading this paper by Hopfield et al. On page six, the authors defined the energy function of the Traveling-Salesman-Problem (TSP) mapped onto an artificial neural network as follows:

$$E = \frac{A}{2} \sum_X \sum_i \sum_{j \ne i} V_{Xi} V_{Xj} + \frac{B}{2} \sum_i \sum_X \sum_{X\ne Y} V_{Xi} V_{Yi} + \frac{C}{2} (\sum_X \sum_i V_{Xi} - n)^2 + \frac{1}{2D} \sum_X \sum_{Y\ne X} \sum_i d_{XY} V_{Xi} (V_{Y, i+1} + V_{Y, i-1})$$

Here the first three terms maintain correctness of the function while the final term calculate actual distance of the tour. Later on page seven, the authors picked the values of A, B, C and D for simulation.

I don't understand on what basis they choose those values. Any help?

• Pretty much arbitrarily. Jul 12 '13 at 14:32
• @MCH If arbitrarily how can we use it for practical purposes? Jul 12 '13 at 14:37
• When it comes to heuristics, we care more about whether things work rather than why. Jul 12 '13 at 21:44
• @MCH, I am afraid I don't get it yet. Why didn't Hopfield just defined A, B and C to be 2's so that we could get rid of the fractions? Jul 13 '13 at 5:53
• @Kaveh, when we implement this expression, do we take derivatives at any point? Jul 14 '13 at 13:37