Imperial College London


Faculty of EngineeringDepartment of Civil and Environmental Engineering

Senior Lecturer



+44 (0)20 7594 6035ivan.stoianov Website




Miss Judith Barritt +44 (0)20 7594 5967




408Skempton BuildingSouth Kensington Campus






BibTex format

author = {Pecci, F and Abraham, E and Stoianov, I},
doi = {10.1007/s00158-016-1537-8},
journal = {Structural and Multidisciplinary Optimization},
pages = {857--869},
title = {Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach},
url = {},
volume = {55},
year = {2016}

RIS format (EndNote, RefMan)

AB - In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.
AU - Pecci,F
AU - Abraham,E
AU - Stoianov,I
DO - 10.1007/s00158-016-1537-8
EP - 869
PY - 2016///
SN - 1615-1488
SP - 857
TI - Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach
T2 - Structural and Multidisciplinary Optimization
UR -
UR -
VL - 55
ER -