The exercise of solving engineering problems that require optimisation procedures can be seriously affected by uncertain variables, resulting in potential underperforming solutions. Although this is a well-known problem, important knowledge gaps are still to be addressed. For example, concepts of robustness largely differ from study to study, robust solutions are generally provided with limited information about their uncertainty, and robust optimisation is difficult to apply as it is a computationally demanding task. The proposed research aims to address the mentioned challenges and focuses on robust optimisation of multiple objectives and multiple sources of probabilistically described uncertainty. This is done by the development of the Robust Optimisation and Probabilistic Analysis of Robustness algorithm (ROPAR), which integrates widely accepted robustness metrics into a single flexible framework. In this thesis, ROPAR is not only tested in benchmark functions, but also in engineering problems related to the water sector, in particular the design of urban drainage and water distribution systems. ROPAR allows for employing practically any existing multi-objective optimisation algorithm as its internal optimisation engine, which enables its applicability to other problems as well. Additionally, ROPAR can be straightforwardly parallelized, allowing for fast availability of results.@en

This paper considers the problem of robust optimization, and presents the technique called Robust Optimization and Probabilistic Analysis of Robustness (ROPAR). It has been developed for finding robust optimum solutions of a particular class in model-based multi-objective optimization (MOO) problems (i.e. when the objective function is not known analytically), where some of the parameters or inputs to this model are assumed to be uncertain. A Monte Carlo simulation framework is used. It can be straightforwardly implemented in a distributed computing environment which allows the results to be obtained relatively fast. The technique is exemplified in the two case studies: (a) a benchmark problem commonly used to test MOO algorithms (a version of the ZDT1 function); and (b) a design problem of a simple storm drainage system, where the uncertainty is associated with design rainfall events. It is shown that the design found by ROPAR can adequately cope with these uncertainties. The approach can be useful for assisting in a wide range of risk-based decisions.@en

Water distribution networks (WDNs) need to guarantee that water is delivered with adequate quality. This paper compares the performance of 12 multiobjective procedures to limit water quality deterioration in a WDN through the optimal operation of valves. The first objective (ObF1) is to minimize the water age, chosen as a surrogate parameter of quality deterioration, and the second objective (ObF2) is to minimize the number of valve closures. The 12 procedures are derived from the combination of 4 different optimization algorithms and 3 formulations of ObF1, namely, to minimize the maximum, the arithmetic mean, and the demand-weighted mean water age. The optimization algorithms considered are random search (RS), Loop for Optimal Valve Status Configuration (LOC), and a combination of each of these two with the Archive-based Micro Genetic Algorithm. The procedures are tested on two networks of different complexity. Results show how LOC is able to find near-optimal solutions using a fraction of the computational time required by a brute force search. Furthermore, among the ObF1 formulations, the use of the averages (either arithmetic or demand-weighted) gives better results in terms of impact on the population served by a WDN.

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Water quality deterioration in water distribution networks can be associated with high water residence time in the network. To this end, some previous studies have proposed optimization procedures for valve management. However, these studies generally come up with operational configurations assuming deterministic user demand patterns that may never occur in reality. In consequence, the proposed solutions may not be effective for improving water quality or do not comply with pressure constraints if different demand patterns are observed. This study proposes a methodology to determine robust configurations of the valves to keep water residence time at acceptable levels regardless of the variability in demand patterns. The methodology is tested on four different distribution systems of varying topology and size. Results show the importance of executing robust – instead of deterministic, optimization to find valve configurations that guarantee the performance of the networks in terms of hydraulics and water quality. @en