Abstract
A new multi-directional search approach that aims at maximizing the flow entropy of water distribution systems is investigated. The aim is to develop an efficient and practical maximum entropy based approach. The resulting optimization problem has four objectives, and the merits of objective reduction in the computational solution of the problem are investigated also. The relationship between statistical flow entropy and hydraulic reliability/failure tolerance is not monotonic. Consequently, a large number of maximum flow entropy solutions must be investigated to strike a balance between cost and hydraulic reliability. A multi-objective evolutionary optimization model is developed that generates simultaneously a wide range of maximum entropy values along with clusters of maximum and near-maximum entropy solutions. Results for a benchmark network and a real network in the literature are included that demonstrate the effectiveness of the procedure.
Highlights
In the context of the design of water distribution systems, the least cost feasible solution is marginally able to satisfy the hydraulic requirements
The absence of an agreed definition of reliability for water distribution systems along with the computational complexity associated with its evaluation (Wagner et al 1988) led researchers to suggest various alternative surrogate reliability measures that are easy to evaluate within an optimization framework
The minimum nodal residual pressure constraints were combined with the two goals of flow entropy maximization, i.e. simultaneously maximizing the entropy of each design based on its flow distribution and seeking the design that has the global maximum entropy value
Summary
In the context of the design of water distribution systems, the least cost feasible solution is marginally able to satisfy the hydraulic requirements. The absence of an agreed definition of reliability for water distribution systems along with the computational complexity associated with its evaluation (Wagner et al 1988) led researchers to suggest various alternative surrogate reliability measures that are easy to evaluate within an optimization framework. These measures include statistical entropy (Tanyimboh and Templeman 1993a, b, c, d), resilience index (Todini 2000), network resilience (Prasad and Park 2004), modified resilience index (Jayaram and Srinivasan 2008) and surplus power factor (Vaabel et al 2006). All solutions both feasible and infeasible are rated strictly in accordance with Pareto-dominance, without recourse to constraint-violation penalties or tournaments
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