A multi-dimensional Gauss distribution generating portion obtains one vector from a multi-dimensional Gauss probability distribution and outputs it as an initial momentum. An approximated energy function differential generating portion generates a gradient of an approximated energy function. A Hamilton equation integral portion integrates a Hamilton equation using a gradient of an approximated energy function for a predetermined integral period with initial conditions of an initial state and an initial momentum. The result of the integration as the state of the next alternative is output from a next alternative generating apparatus. The state is used with a high probability corresponding to the difference of approximated energy calculated by an approximated energy difference calculating portion and the difference between a value of an original energy in the present state and that in the next state.