Optimal cost design of branched sewer systems

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Abstract
Techniques using dynamic programing (DP) and discrete differential dynamic programing (DDDP) to achieve optimal cost design of pipe sizes and elevations of branched sewer systems have been developed and demonstrated by an example. The branched system is decomposed into equivalent serial subsystems, which are then solved in sequence. DDDP requires less computer time than DP, although it cannot guarantee global optimization. Major factors affecting the efficiency in using DDDP are the location and width of the initial trial trajectory corridor, the number of states (lattice points) used, and the reduction rate of the state increment during iterations.