Adapting the Energy Landscape for MFA

Combinatorial optimization problems such as the Traveling Salesman Problem TSP Graph Bi partitioning and Graph Colouring have been used extensively for bench marking new optimization algorithms The challenge is to develop a general purpose algorithm that converges rapidly and yet still produces a high quality solution When an optimization problem is mapped onto a neural network as states of nodes connected by edges we assign the problem a Cost or Energy function This energy is a function of the global state of the network at any one instant and the energy function itself models the problem at hand High energy represents a state that is far from the desired solution As we iterate through a node updating procedure we change the states of nodes and attempt to reduce the overall energy eventually nding a near optimal solution The solution space for the problem can be thought of as a multi dimensional energy landscape containing deep valleys or local minima Local minima can trap a gradient descent technique resulting in a high energy solution being found Simulated Annealing SA appears to provide us with the best compromise between rate of convergence and solution quality Transitions to states that increase