In addition, a method of generating MINLP solutions that feature integer stage-numbers is also presented.
As N = 2 x × 3 y, (x ≠ 1), if x is even (integer stages from radix-4) the butterfly performs radix-4 computations till the end then switches to perform radix-3 stages.
We formulate the problem as two stage integer recourse problem to find a set of optimal network configuration and assignment of transportation modes and the respective flows in order to minimize total cost and total service time, simultaneously.
The resulting SAA problem is a two-stage integer programming model, in which the analytical expression of second-stage value function is unavailable, we cannot solve it by conventional optimization algorithms.
As the result, the original large-scale two-stage integer programming problem can be approximately solved by solving a series of small-scale mixed-integer programming, which can be implemented on a workstation or a PC.
The scheduling problem is represented as a two-stage stochastic integer program and solved by a stage-decomposition based hybrid algorithm with an evolutionary algorithm for the first-stage and mathematical programming for the second-stage.
We first prescribe a two-stage cutting plane approach with integer variables in both stages, and examine computational difficulties associated with the proposed cutting planes.
Following this study, Maqsood et al. ([2004]) proposed an inexact two-stage mixed integer linear programming (ITMILP) model through integrating mixed integer, two-stage stochastic and interval-parameter programming approaches within a general optimization framework and applied ITMILP to the planning of regional solid waste management systems under uncertainty.
The problem is formulated as a two stage stochastic integer program with discrete scenarios.
They proposed a two stage binary integer programming and two efficient heuristics, best fit butterfly (BBF) and best fit decreasing (DBF), for solving large scale problems.
In this paper, the processing times of the first and third stages are integer values that are randomly generated from the uniform distribution (1,100) on all m first stage machines and single third stage machine, second stage processing times are integers that are randomly generated from the uniform distribution (1, 10) on single second stage machine [3].
