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Most of real world problems contain complex and various constraints, and the penalty depending on the degree of violation is often used to handle them. However, two objectives, to reduce the violation and to optimize the primary value, are inherently oppositive. Therefore, using additive penalty method (APM) often leads the fatal compromise to a solution with bad primary objective value in return for no violation. In this paper, we employ separated constraint satisfaction (SCS), to deal these two objectives independently like as a multi-objective optimization. The efficiency of SCS is shown on a simple benchmark and the sewerage system control problem.

Optimization Using Separated Constraint Satisfaction and its Application to the Sewerage System Control Problem