7 results found
Pecci F, Abraham E, Stoianov I, 2018, Global optimality bounds for the placement of control valves in water supply networks, Optimization and Engineering, Pages: 1-39, ISSN: 1389-4420
This manuscript investigates the problem of optimal placement of control valves in water supply networks, where the objective is to minimize average zone pressure. The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP). Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of the computed valve configurations. In our approach, we implement a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The algorithm relies on the solution of mixed integer linear programs, whose formulations include linear relaxations of the nonconvex hydraulic constraints. We investigate the implementation and performance of different linear relaxation schemes. In addition, a tailored domain reduction procedure is implemented to tighten the relaxations. The developed methods are evaluated using two benchmark water supply networks and an operational water supply network from the UK. The proposed approaches are shown to outperform state-of-the-art global optimization solvers for the considered benchmark water supply networks. The branch and bound algorithm converges to good quality feasible solutions in most instances, with bounds on the optimality gap that are comparable to the level of parameter uncertainty usually experienced in water supply network models.
Pecci F, Abraham E, Stoianov I, Model reduction and outer approximation for optimising the placement of control valves in complex water networks, Journal of Water Resources Planning and Management, ISSN: 0733-9496
The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimisation frame work, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimisation framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimisation problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models.
Pecci F, Abraham E, Stoianov I, 2017, Outer approximation methods for the solution of co-design optimisation problems in water distribution networks, 20th IFAC World Congress, Publisher: Elsevier, Pages: 5373-5379, ISSN: 1474-6670
In the present manuscript, we investigate and demonstrate the use of outer approximation methods for simultaneously optimising the placement and operation of control valves in water distribution networks. The problem definition results in a mixed-integer nonlinear program with nonconvex constraints. We simplify the formulation, compared to previous literature, in order to reduce the degree of nonlinearity in the constraints and decrease the total problem size. We then formulate the application of outer approximation based methods for the generation of good quality local optimal solutions for the considered co-design problem. Finally, we present the results of applying the developed techniques to two case studies, and also comparing the performances of the outer approximation approaches with those of other local mixed integer nonlinear programming solution methods.
Pecci F, Abraham E, Stoianov I, 2017, Quadratic head loss approximations for optimisation problems in water supply networks, JOURNAL OF HYDROINFORMATICS, Vol: 19, Pages: 493-506, ISSN: 1464-7141
Pecci F, Abraham E, Stoianov I, 2017, Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks, COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, Vol: 67, Pages: 201-223, ISSN: 0926-6003
Pecci F, Abraham E, Stoianov I, 2017, Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach, STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION, Vol: 55, Pages: 857-869, ISSN: 1615-147X
Pecci F, Abraham E, Stoianov I, 2015, Mathematical programming methods for pressure management in water distribution systems, Computing and Control for the Water Industry (CCWI2015)- Sharing the Best Practice in Water Management, Publisher: ELSEVIER SCIENCE BV, Pages: 937-946, ISSN: 1877-7058
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