Hybrid discrete dynamically dimensioned search (HD‐DDS) algorithm for water distribution system design optimization

Abstract

[1] The dynamically dimensioned search (DDS) continuous global optimization algorithm by Tolson and Shoemaker (2007) is modified to solve discrete, single-objective, constrained water distribution system (WDS) design problems. The new global optimization algorithm for WDS optimization is called hybrid discrete dynamically dimensioned search (HD-DDS) and combines two local search heuristics with a discrete DDS search strategy adapted from the continuous DDS algorithm. The main advantage of the HD-DDS algorithm compared with other heuristic global optimization algorithms, such as genetic and ant colony algorithms, is that its searching capability (i.e., the ability to find near globally optimal solutions) is as good, if not better, while being significantly more computationally efficient. The algorithm's computational efficiency is due to a number of factors, including the fact that it is not a population-based algorithm and only requires computationally expensive hydraulic simulations to be conducted for a fraction of the solutions evaluated. This paper introduces and evaluates the algorithm by comparing its performance with that of three other algorithms (specific versions of the genetic algorithm, ant colony optimization, and particle swarm optimization) on four WDS case studies (21-to 454-dimensional optimization problems) on which these algorithms have been found to perform well. The results obtained indicate that the HD-DDS algorithm outperforms the state-of-the-art existing algorithms in terms of searching ability and computational efficiency. In addition, the algorithm is easier to use, as it does not require any parameter tuning and automatically adjusts its search to find good solutions given the available computational budget.

Performance Study of Differential Evolution with Various Mutation Strategies Applied to Water Distribution System Optimization

“…It is observed from Table 1 that DE1, DE4 and DE5 performed at least as well as, if not better than HD-DDS, GA and PSO in terms of frequency with which the best known solution was found. In terms of efficiency, DE1 and DE4 performed similarly with HD-DDS (Tolson et al 2009). Dandy et al (2010).…”

“…In addition, DE1 and DE4 outperformed other optimization techniques, such as HD-DDS (Tolson et al 2009), GA and PSO (Dandy et al 2010) in terms of robustness and efficiency. Thus, DE1 and DE4 can be viewed as being well-suited to water distribution system optimization.…”

“…This can be explained in that it appears that the DE2 and DE3 were more likely to be trapped by local optimal solutions and hence result in premature convergence. Table 1 also gives the statistical results of HD-DDS (Tolson et al 2009), GA (Dandy et al 2010) and particle swarm optimization (PSO) (Dandy et al 2010) applied to the NYTP case study. It is observed from Table 1 that DE1, DE4 and DE5 performed at least as well as, if not better than HD-DDS, GA and PSO in terms of frequency with which the best known solution was found.…”

“…DE1, DE3 and DE4 significantly outperformed HD-DDS (Tolson et al 2009) in terms of frequency with which the best solution was found and the average cost solution based on 50 different trials. Dandy et al (2010).…”

“…Murphy and Simpson (1992) were first to introduce genetic algorithms (GAs) for water network optimization; Cunha and Sousa (2001) used simulated annealing to optimize WDSs; Geem et al (2002) developed a harmony search model for optimizing WDSs; Eusuff and Lansey (2003) proposed a shuffled frog leaping algorithm (SFLA) for network optimization; and Maier et al (2003) applied an Ant Colony Optimization approach to optimize WDSs. More recently, Tolson et al (2009) developed a new algorithm (the hybrid discrete dynamically dimensioned search algorithm HD-DDS) to optimize WDSs. These techniques have been successfully applied to a number of optimization problems and have been demonstrated to be more effective in finding optimal solutions compared with deterministic optimization techniques.…”