Dynamic optimal control of groundwater remediation with heuristic pumping constraints and optimized treatment capacity

Inefficient handling of constraints has reduced the performance of optimal control algorithms and limited their application in groundwater remediation design. In this research, two new constraint approaches, termed heuristic approach and proportional approach, were developed and incorporated into two variations of the differential dynamic programming (DDP) algorithms: a successive approximation linear quadratic regular (SALQR) algorithm and a Quasi-Newton DDP (QNDDP) algorithm, in order to improve the efficiency of the constraint handling, reduce the CPU time, and facilitate a technically efficient and cost effective design for groundwater reclamation.;The optimization algorithms with two new constraint approaches, which are based on practical engineering judgement, were applied to optimal groundwater remediation test problems with the consideration of (1) the operating cost alone, and (2) both the operating cost and the capital cost of the treatment facility capacity. To test the performance of the six optimal control algorithms (SALQR, QNDDP, SALQR+Heuristic, SALQR+Proportional, QNDDP+Heuristic and QNDDP+Proportional), eight hypothetical groundwater reclamation test problems have been formulated. The performances of the new constraint approaches are evaluated on a set of forty-eight groundwater remediation test cases (eight test example problems, each with six different lengths of management periods). Results from the forty-eight test cases conclude that the heuristic approach, which does not increase either the computational time per iteration or the memory requirements, significantly improves the performance of the optimal control algorithms when applied to the groundwater remediation test problems. In most dynamic cases, SALQR+Heuristic algorithm is found to be better than SALQR, SALQR+Proportional, QNDDP, and QNDDP+Proportional algorithms. As compared to the traditional penalty function approach, the combination of the SALQR algorithm with a simple heuristic constraint approach increased the likelihood of finding a minimum cost solution. Without the heuristic pumping constraint, optimal control algorithms require many more iterations to optimality, and the failure rate to optimality is much higher than that with heuristic. Typically, when considering the operating cost alone, SALQR+Heuristic algorithm saves 63% of CPU time compared to SALQR algorithm. With the consideration of both the operating cost and the capital cost of the treatment facility capacity, the SALQR+Heuristic algorithm saves even more CPU time (65%) compared to the SALQR algorithm.;The heuristic approach shows great promise on handling of constraints. It minimizes the constraint violations, speeds up the performance of the line search and reduces the computational time required to facilitate the selection of an improved operating policy and the optimal solution. In addition, the heuristic approach has the average lowest cost, and the highest reliability. Therefore, the heuristic approach is considered to be very effective. (Abstract shortened by UMI.).