ABSTRACT:The genetic algorithm technique is a relatively new optimization technique. In this paper we present a methodology for optimizing pipe networks using genetic algorithms. Unknown decision variables are coded as binary strings. We investigate a three-operator genetic algorithm comprising reproduction, crossover, and mutation. Results are compared with the techniques of complete enumeration and nonlinear programming. We apply the optimization techniques to a case study pipe network. The genetic algorithm technique finds the global optimum in relatively few evaluations compared to the size of the search space. INTRODUCTIONThe construction and maintenance of pipelines for water supply costs many millions of dollars every year. As funds for the development of new infrastructure become increasingly scarce, there is an increasing desire to achieve the highest level of effectiveness for each dollar spent. Traditionally, the design of water distribution networks has been based on experience. However, there is now a significant (and growing) body of literature devoted to optimization of pipe networks.

Abstract. An improved genetic algorithm (GA) formulation for pipe network optimization has been developed. The new GA uses variable power scaling of the fitness function. The exponent introduced into the fitness function is increased in magnitude as the GA computer run proceeds. In addition to the more commonly used bitwise mutation operator, an adjacency or creeping mutation operator is introduced. Finally, Gray codes rather than binary codes are used to represent the set of decision variables which make up the pipe network design. Results are presented comparing the performance of the traditional or simple GA formulation and the improved GA formulation for the New York City tunnels problem. The case study results indicate the improved GA performs significantly better than the simple GA. In addition, the improved GA performs better than previously used traditional optimization methods such as linear, dynamic, and nonlinear programming methods and an enumerative search method. The improved GA found a solution for the New York tunnels problem which is the lowest-cost feasible discrete size solution yet presented in the literature.

ABSTRACT:During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the optimal design and operation of water distribution systems. More recently, ant colony optimization algorithms (ACOAs), which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to a number of benchmark combinatorial optimization problems. In this paper, a formulation is developed which enables ACOAs to be used for the optimal design of water distribution systems.This formulation is applied to two benchmark water distribution system optimization problems and the results are compared with those obtained using genetic algorithms. The findings of this study indicate that ACOAs should be considered as an alternative to GAs for the optimal design of water distribution systems, as they outperformed GAs for the two case studies considered both in terms of computational efficiency and their ability to find near global optimal solutions.

ABSTRACT:During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the optimal design and operation of water distribution systems. More recently, ant colony optimization algorithms (ACOAs), which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to a number of benchmark combinatorial optimization problems. In this paper, a formulation is developed which enables ACOAs to be used for the optimal design of water distribution systems.This formulation is applied to two benchmark water distribution system optimization problems and the results are compared with those obtained using genetic algorithms. The findings of this study indicate that ACOAs should be considered as an alternative to GAs for the optimal design of water distribution systems, as they outperformed GAs for the two case studies considered both in terms of computational efficiency and their ability to find near global optimal solutions.

This paper reviews a number of unsteady friction models for transient pipe flow. Two distinct unsteady friction models, the Zielke and the Brunone models, are investigated in detail. The Zielke model, originally developed for transient laminar flow, has been selected to verify its effectiveness for "low Reynolds number" transient turbulent flow. The Brunone model combines local inertia and wall friction unsteadiness. This model is verified using the Vardy's analytically deduced shear decay coefficient C* to predict the Brunone's friction coefficient k rather than use the traditional trial and error method for estimating k. The two unsteady friction models have been incorporated into the method of characteristics water hammer algorithm. Numerical results from the quasi-steady friction model and the Zielke and the Brunone unsteady friction models are compared with results of laboratory measurements for water hammer cases with laminar and low Reynolds number turbulent flows. Conclusions about the range of validity for the three friction models are drawn. In addition, the convergence and stability of these models are addressed. RESUMELe papier passe en revue un certain nombre de modeles de friction non permanente en ecoulement transitoire en conduite. Deux modeles de friction non permanente, celui de Zielke et celui de Brunone sont investigues en details. Le modele de Zielke, developpe a l'origine pour les ecoulements transitoires laminaires, a ete selectionne pour tester l'efficacite du modele pour les ecoulements transitoires turbulents a faible nombre de Reynolds. Le modele de Brunone combine la variation de l'inertie locale et de la friction de paroL Ce modele est verifie en utilisant Ie coefficient C* d'amortissement du cisaillement de Vardy dCduit analytiquement pour predire Ie coefficient de friction k de Brunone, plutot que la method traditionnelle par essais et erreurs pour estimer k. Les deux modeles de friction non permanente ont ete incorpores dans un algorithme de calcul du coup de belier par la methode des caracteristiques. Les resultats numeriques obtenus a partir d'un modele de friction quasi permanente et a partir des modeles non permanents de Zielke et de Brunone sont compares avec des resultats de mesures en laboratoire pour des ecoulements laminaires ou turbulents a faible nombre de Reynolds. Des conclusions sont tirees sur les domaines de validite des trois modeles de friction. En complement, la convergence et la stabilite des modeles sont abordees. IntroductionTraditionally the steady or quasi-steady friction terms are incorporated into the standard water hammer algorithms. This assumption is satisfactory for slow transients where the wall shear stress has a quasi-steady behaviour. Experimental validation of steady friction models for rapid transients [1,2,3,4,5] previously has shown significant discrepancies in attenuation and phase shift of pressure traces when the computational results are compared to the results of measurements. The discrepancies are introduced by a difference in ve...