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|عنوان فارسی مقاله||مقایسه تکنیک های بهینه سازی مبتنی بر جمعیت برای گسترش و عملیات سیستم توزیع آب|
|عنوان انگلیسی مقاله||A Comparison of Population-based Optimization Techniques for Water Distribution System Expansion and Operation|
|رشته های مرتبط||مهندسی عمران، مدیریت منابع آب|
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|نشریه||الزویر – Elsevier|
|مجله||شانزدهمین کنفرانس تجزیه و تحلیل سیستم توزیع آب – ۱۶th Conference on Water Distribution System Analysis|
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Population-based optimization techniques have gained currency in recent years in their application to Water Distribution Systems (WDS) design and operation, with the emergence of genetic algorithms  and memetic algorithms such as the Shuffled Frog Leaping Algorithm  and Ant Colony Optimization . This paper seeks to apply and compare a number of these algorithms to the Battle of Background Leakage Assessment for Water Networks (BBLAWN) challenge – part of the Water Distribution Systems Analysis (WDSA) conference, 2014.
The optimization software developed closely couples a number of population-based optimization techniques implemented in C++ with the EPANET2 hydraulic solver  to model the effect on the performance of the hydraulic network when considering pipe replacement and duplication and the modification of pump and pressure reduction valve (PRV) operations.
The BBLAWN optimization has been formulated as a single or twin-objective optimization problem according to the needs of the optimization algorithms applied. In the case of the twin-objective formulation, the objectives are: 1. Total Cost – the sum of annualized infrastructure upgrade costs (pipe replacement and duplications, tank, pump and valve installation) and annual operational (pumping) costs. 2. Leakage – the absolute annual volume of water lost as leakage. The single objective formulation combines the above objectives by assigning a cost to the annual leakage volume at a rate of €۲/m3 .
۲٫۳ Decision Variables
Table 2 enumerates the decision variable configuration employed for the optimization. In order to maximize the freedom afforded the optimization, no attempt has been made to simplify the problem by, and for example, grouping pipes. The potential sites for the 39 possible PRV installations were determined manually and, naturally, this will have biased the range of potential solutions accordingly.
The optimization employs five “hard” constraints – violation of which result in a solution being marked as infeasible and, therefore, unlikely to play a significant role in the progress of the optimization. Firstly, the network produced must be hydraulically valid – that is to say that the EPANET solver solves the network without raising any errors. In addition, the solution of the network should not provoke any warnings to be emitted from EPANET. Of particular concern for the BBLAWN optimization are the warnings related to negative pressures, disconnected nodes and pumps operating beyond their normal flow regime. A minimum pressure constraint applies such that demand nodes must demand must satisfy a given pressure level (20m) for nodes with demand in order for a solution to be considered valid. In any event, there must be no negative pressures in the network at any point. Tanks are not permitted to empty, thus a constraint is also included to reflect this. To produce a solution that is repeatable over successive weeks, a further constraint is implemented such that the levels of any tanks in the system should be at least as high as they were at the beginning of the weekly extended period simulation. Differential constraint weightings are used to signify the relative importance of meeting the optimization constraints. The EPANET Error and EPANET Warning constraints are given the highest priority in order to prioritise the generation of feasible solutions by the optimization.
۲٫۵ Optimization techniques
The Acquamark environment decouples the implementation of the objective function for a problem from the operation of the algorithm. This makes it straightforward to implement and test the various algorithms without recourse to significant programming changes to accommodate the differing techniques. For example, the implementation of the objective function is able to adapt to being used with single and multiple-objective algorithms as well as discrete, continuous or mixed decision variable approaches. A number of population-based optimization algorithms were evaluated for their suitability for application to the BBLAWN problem. Owing to the extended runtimes that were anticipated for the problem, it was decided to perform short tests on each algorithm to gauge its performance on the full problem. The procedures examined include a number of genetic and memetic algorithms as well as Parallel Differential Evolution  which differ markedly in their mechanisms for inheriting and sharing knowledge about the search space between members of their populations. The genetic algorithms employed were NSGA-II  and its closely related derivative, OmniOptimizer (OO) . The memetic algorithms used were a Discrete Shuffled Frog optimizer  based on the Shuffled Frog Leaping algorithm  and a Discrete Particle Swarm Optimizer (DPSO) incorporating heterogeneous traits for individual particles . The initial results for the memetic algorithms and Parallel Differential Evolution were disappointing. Whilst all of the techniques were able to resolve feasible solutions – and, indeed, more efficiently than the two genetic algorithm variants – none of the algorithms were able to significantly improve upon their early feasible solutions. It is unclear whether this is an issue relating to the scale of the problem encountered here or a short-coming in the authors’ implementation of these algorithms. Certainly the DPSO has demonstrated itself on lower-dimensioned water distribution system problems without encountering such issues. Owing to time-constraints it was decided to postpone further evaluation of these techniques and to rely on the tested NSGA-II/OO algorithms at least until such time as a representative set of solutions had been derived in order to provide as baseline for further comparisons. The application of OO to this problem did, however, highlight significant drawbacks to the technique which have not previously been encountered by the Authors. One of the principal differences between OO and NSGA-II is the former’s incorporation of a crowding metric in decision space in addition to the metric in objective space common to the two algorithms. When applied to high numbers of decision variables, the statistics required by this additional metric entail considerable computational effort, particularly when calculating the Euclidean distance between each solution for each of the decision variables. A consequence of this was that over 50% of the runtime was spent in the computation of this metric. To minimize the effect of this problem, the statistical analysis was parallelized to run on all the available processor cores on the host machine executing the OO algorithm.