Optimization on Rugged Landscapes: A New General Purpose Monte Carlo Approach

A new strategy for finding optimal solutions to complex problems with many competing requirements is proposed. It consists in an alternating optimization of the energy, cost, or fitness function of the system itself, and of subsystems of all sizes with an appropriate weight function. For various spin glasses (the $N-k$ model, the low autocorrelation binary sequence model, and the Coulomb glass), and for traveling salesman problems, the corresponding Monte Carlo algorithm is shown to yield results superior to those obtained by previous optimization techniques.