Risk- and robustness-based solutions to a multi-objective water distribution system rehabilitation problem under uncertainty .

The water distribution system (WDS) rehabilitation problem is defined here as a multi-objective optimisation problem under uncertainty. Two alternative problem formulations are considered. The first objective in both approaches is to minimise the total rehabilitation cost. The second objective is to either maximise the overall WDS robustness or to minimise the total WDS risk. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Total risk is defined as the sum of nodal risks, where nodal risk is defined as the product of the probability of pressure failure at that node and consequence of such failure. Decision variables are the alternative rehabilitation options for each pipe in the network. The only source of uncertainty is the future water consumption. Uncertain demands are modelled using any probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analysed nodal heads are calculated using the Latin Hypercube sampling technique. The optimal rehabilitation problem is solved using the newly developed rNSGAII method which is a modification of the well-known NSGAII optimisation algorithm. In rNSGAII a small number of demand samples are used for each fitness evaluation leading to significant computational savings when compared to the full sampling approach. The two alternative approaches are tested, verified and their performance compared on the New York tunnels case study. The results obtained demonstrate that both new methodologies are capable of identifying the robust (near) Pareto optimal fronts while making significant computational savings.

Automatic calibration of urban drainage model using a novel multi-objective genetic algorithm.

In order to successfully calibrate an urban drainage model, multiple calibration criteria should be considered. This raises the issue of adopting a method for comparing different solutions (parameter sets) according to a set of objectives. Amongst the global optimization techniques that have blossomed in recent years, Multi Objective Genetic Algorithms (MOGA) have proved effective in numerous engineering applications, including sewer network modelling. Most of the techniques rely on the condition of Pareto efficiency to compare different solutions. However, as the number of criteria increases, the ratio of Pareto optimal to feasible solutions increases as well. The pitfalls are twofold: the efficiency of the genetic algorithm search worsens and decision makers are presented with an overwhelming number of equally optimal solutions. This paper proposes a new MOGA, the Preference Ordering Genetic Algorithm, which alleviates the drawbacks of conventional Pareto-based methods. The efficacy of the algorithm is demonstrated on the calibration of a physically-based, distributed sewer network model and the results are compared with those obtained by NSGA-II, a widely used MOGA.

Scheduling of water distribution system rehabilitation using structured messy genetic algorithms.

A methodology is presented for the optimal design and scheduling of investment for the rehabilitation of water distribution networks. Based on the evolutionary programming technique known as Structured Messy Genetic Algorithms, the methodology utilizes a multi-objective formulation which improves the evolutionary process and provides nondominated optimal solutions over a range of costs and benefits. The model is applied to an example-a small artificial network of fifteen pipes. The effects on the optimal solutions of varying parameters such as interest rate and inflation rate are also investigated.

Posttraumatic cutaneous meningioma of the face.

We present the CT and MR features of a posttraumatic cutaneous meningioma of the face. We postulate that the patient's trauma and associated skull fracture resulted in a trapping of extracranial meningeal tissue, which many years later gave rise to a secondary facial meningioma.