Representations and Evolutionary Operators for the Scheduling of Pump Operations in Water Distribution Networks

Abstract

Reducing the energy consumption of water distribution networks has never had more significance. The greatest energy savings can be obtained by carefully scheduling the operations of pumps. Schedules can be defined either implicitly, in terms of other elements of the network such as tank levels; or explicitly, by specifying the time during which each pump is on/off. The traditional representation of explicit schedules is a string of binary values with each bit representing pump on/off status during a particular time interval. In this paper, we formally define and analyze two new explicit representations based on time-controlled triggers, where the maximum number of pump switches is established beforehand and the schedule may contain fewer than the maximum number of switches. In these representations, a pump schedule is divided into a series of integers with each integer representing the number of hours for which a pump is active/inactive. This reduces the number of potential schedules compared to the binary representation, and allows the algorithm to operate on the feasible region of the search space. We propose evolutionary operators for these two new representations. The new representations and their corresponding operations are compared with the two most-used representations in pump scheduling, namely, binary representation and level-controlled triggers. A detailed statistical analysis of the results indicates which parameters have the greatest effect on the performance of evolutionary algorithms. The empirical results show that an evolutionary algorithm using the proposed representations is an improvement over the results obtained by a recent state of the art hybrid genetic algorithm for pump scheduling using level-controlled triggers.

Lost in optimisation of water distribution systems? A literature review of system operation

“… To reduce the search space, decision variables are combined applying relative time control triggers (Lopez-Ibanez et al 2011).  Time horizon is 24 hours divided into 1-hour intervals.…”

Exploration of Ontological Representations for Evolutionary Computation

“…It has been shown that integration of domain knowledge as an element of the evolutionary process is beneficial [19], [20]. For example, [21] demonstrated the benefits of incorporating semantic attributes of the problem domain into the representation framework when designing networks for water distribution. Similarly, in [22], an N -dimensional pixel was used as the key element to represent solutions in a shapeoptimisation problem; demonstrating that a representation that emulates the real-world morphology obtains better results than a more generic "traditional" representation.…”

A systematic mixed-integer differential evolution approach for water network operational optimization

“…To define pump schedules, binary encoding is most commonly adopted, where only fixed-speed pumps are involved in the network and their on/off states across different time intervals can thus be represented by several binary bits. Alternatively, time-controlled triggers [ 14 , 15 ] can also be used, where the active and inactive periods of time intervals resulting from every pump switch are successively coded in an individual solution. On the other hand, real-value encoding is used to directly define the actuator's continuous states for water networks where only variable-speed pumps are involved, though this has attracted significantly less research.…”