Water Resources Management

, Volume 27, Issue 5, pp 1249–1261 | Cite as

Multiobjective Pump Scheduling Optimization Using Harmony Search Algorithm (HSA) and Polyphonic HSA

  • Ioannis P. KougiasEmail author
  • Nicolaos P. Theodossiou


Harmony Search Algorithm (HSA) is a metaheuristic method that has attracted the scientific interest since its first presentation in 2001. It is a music inspired method, imitating the music creation process in order to find optimal solutions in complicated problems. HSA’s successful application on single – objective optimization problems has resulted to an increasing interest in the implementation of HSA towards multiobjective optimization. The authors have adjusted HSA in order to deal successfully with multi-criteria water management problems. This adjustment has resulted to the creation of Multiobjective – HSA (MO-HSA). In addition, they have designed the multiobjective variant Polyphonic-HSA (Poly-HSA), which is inspired by the independent development of different voices in music and borrows elements from Swarm Intelligence and the single-objective variant Global-Best HSA. In the first part of this paper, both methods are presented in detail. Moreover, the performance of the proposed Algorithms is evaluated using standard multiobjective test – functions. ZDT and DTLZ multiobjective tests have been chosen and indicators such as Hypervolume, C – metric and diversity metric – Δ have been used to measure the convergence to the optimal front and the diversity of the solutions obtained by the proposed methods. In the second part, MO-HSA and Poly-HSA have been introduced towards the optimization of a pump scheduling problem. The objectives considered are water supply, pumping cost, electric power peak demand and pump maintenance cost. Both methods converged to non-dominated fronts and provided excellent results which are presented in 3d figures, indicating that these methods can be effectively used in multiobjective water management problems.


Water management Pump scheduling Multiobjective optimization Pareto dominance Harmony Search Algorithm 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Division of Hydraulics and Environmental Engineering, Department of Civil EngineeringAristotle University of ThessalonikiThessalonikiGreece

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