solver followed by local solver finds a solution less often than expected which is the case for problems in region 3 near p s at 1060 p s is increased if multiple runs of the global solver followed by a local solver finds a solution more often than expected as for problems in region 4 near p s the embodiments described herein can also be applied to constrained optimization problems with the introduction of the objective function there is a tradeoff between the objective and constraint satisfaction if constraint satisfaction is treated as the first priority and objective minimization as secondary then when the time expires the goal is to obtain a feasible solution in a cooperative solver the local solving part will focus on constraint satisfaction while the global solving part may give more attention to objective minimization and solve the problem in a different space than the local solving part this is the case in the cooperative solver consisting of an unconstrained and a constrained optimizer the former typically minimizes a penalty function amount of constraint violation that combines the objective and constraint violation its solutions likely have higher constraint violations than those found by the constrained optimizer thus when the time bound is tight the constrained optimizer is selected to obtain a feasible solution first and then improve the objective selecting the cooperative solver consisting of the two solvers in this case incurs the danger that the first solver itself may consume the available time and return an infeasible solution on the other hand when the time bound is sufficient for the cooperative.