T. Devi Prasad

Multi-objective optimisation of the pump scheduling problem using SPEA2

Significant operational cost and energy savings can be achieved by optimising the schedules of pumps, which pump water from source reservoirs to storage tanks, in water distribution networks. Despite the fact that pump scheduling problem involves several conflictive objectives, few studies have considered multi-objective optimisation in terms of Pareto optimality. Our approach links a well-known multi-objective optimiser, SPEA2, with a hydraulic simulator, EPANET, in order to provide a Pareto set of explicit schedules. Since only fixed speed pumps and fixed time intervals are considered, we use a natural binary representation and simple and straightforward initialisation and recombination operators. Unlike earlier studies, feasibility constraints are handled by a methodology based on the dominance relation rather than using penalty functions or reparation mechanisms. We test the proposed approach using a network instance and an assessment of the results is carried out by means of empirical attainment surfaces. The results show that the proposed approach is able to obtain better schedules than the state-of-the-art single-objective algorithm for this network instance and within the same number of function evaluations

Representations and evolutionary operators for the scheduling of pump operations in water distribution networks

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.

ANT-COLONY OPTIMIZATION FOR OPTIMAL PUMP SCHEDULING

This paper presents a method to solve the pump scheduling problem using Ant-colony optimisation. In the past, many researchers have attempted to solve the problem of optimal pump scheduling for complex water distribution systems. Despite the practical importance of the problem, many of the methods published have shortcomings range from lack of generality in the representation of state variables to excessively high computational effort. The present work considers the minimization of cost of pumping as the objective and incorporates the constraint on number of pump switches into the representation. The main emphasis of this work is on restricting the search space and reducing the number of function evaluations. Solutions to pump scheduling problem are, usually, encoded using a binary string showing the state (on/off) of each pump during each time interval. Using binary pump schedules and Ant-colony optimisation, a new method for optimal pump scheduling is developed. The representation of a solution is modified to restrict the number of pump switches to a specified value and to suit the application of Antcolony optimisation. A comparison of the results obtained using the proposed method was compared with those obtained using Evolutionary algorithms.

A CLONAL SELECTION ALGORITHM FOR THE C-TOWN NETWORK CALIBRATION

This paper presents the calibration results of the C-Town network obtained using an artificial immune algorithm called Clonal Selection Algorithm (CLONALG).The calibration problem was formulated as determining the network model parameters such that the best match between measured and predicted data is obtained. The model parameters to be determined include pipe roughness values, valve closures, nodal demands, pump controls and valve settings. The artificial immune algorithm used in this work evolves a population of candidate solutions using the clonal selection principle. The main components of CLONALG include fitness based cloning and maturation of cloned population. The proposed model was applied to calibrate the C-Town network. The network calibration parameters obtained, when input into the C-Town hydraulic model, produced reasonably good match between the predicted and the observed tank water levels and pump station flows. Various performance measures were calculated and presented in the paper .

Solving optimal pump control problem using max-min ant system

Given a water distribution network, where customer demands, initial tank levels and electricity tariffs are known, the goal is to find the optimal pump schedule over a time period, typically 24 hours, such that the cost of energy consumed by pumps (CE) and maintenance costs are minimised and constraints are satisfied. The electricity tariff is typically divided into an expensive peak and cheaper off-peak periods, while the actual amount of energy consumed by a pump depends on several dynamic factors. For a given schedule, its energy cost can be calculated using a hydraulic simulator (EPANET [1] in our case). On the other hand, maintenance costs are typically assumed to increase with the number of pump switches (NS), since frequent switching, that is, turning on a pump which was previously off, causes wear and tear. Typically, this objective is incorporated as an additional constraint. In our approach, this constraint is implicitly enforced by the representation. As for system constraints, such as mass and energy balance equations, and tank minimum and maximum levels, they are implicitly enforced by EPANET. Operational constraints must be explicitly handled: (i) zero total volume deficit, defined as the total sum for all tanks of positive difference in percentage between the initial and final volume of water in a tank; (ii) zero pressure deficit, since consumers must be supplied water at adequate pressures; and (iii) no warnings reported by the simulator.