Shuffled Frog Leaping Algorithm (SFLA) is a meta-heuristic for solving discrete optimization problems. Here it is applied to determine optimal discrete pipe sizes for new pipe networks and for network expansions. SFLA is a population based, cooperative search metaphor inspired by natural memetics. The algorithm uses memetic evolution in the form of infection of ideas from one individual to another in a local search. The local search is similar in concept to particle swarm optimization. A shuffling strategy allows for the exchange of information between local searches to move toward a global optimum. This paper summarizes the development of SFLANET, a computer model that links SFLA and the hydraulic simulation software EPANET and its library functions. Application of SFLANET to literature network design problems is then described. Although the algorithm is in its initial stages of development, promising results were obtained.

A memetic meta-heuristic called the shuffled frog-leaping algorithm (SFLA) has been developed for solving combinatorial optimization problems. The SFLA is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The SFLA consists of a set of interacting virtual population of frogs partitioned into different memeplexes. The virtual frogs act as hosts or carriers of memes where a meme is a unit of cultural evolution. The algorithm performs simultaneously an independent local search in each memeplex. The local search is completed using a particle swarm optimization-like method adapted for discrete problems but emphasizing a local search. To ensure global exploration, the virtual frogs are periodically shuffled and reorganized into new memplexes in a technique similar to that used in the shuffled complex evolution algorithm. In addition, to provide the opportunity for random generation of improved information, random virtual frogs are generated and substituted in the population.The algorithm has been tested on several test functions that present difficulties common to many global optimization problems. The effectiveness and suitability of this algorithm have also been demonstrated by applying it to a groundwater model calibration problem and a water distribution system design problem. Compared with a genetic algorithm, the experimental results in terms of the likelihood of convergence to a global optimal solution and the solution speed suggest that the SFLA can be an effective tool for solving combinatorial optimization problems.

Several models that can be used to optimally size water distribution pipes were applied to a hypothetical system. The results are summarized in this paper. The models produced solutions with costs that were within 10% of one another, although the solutions were quite different. While the models were helpful in sizing pipes, some manual calculations and a good deal of engineering judgment were required to apply them.

This paper presents the basic framework for a model that can be used to determine the optimal (least‐cost) design of a water distribution system subject to continuity, conservation of energy, nodal head bounds, and reliability constraints. Reliability is defined as the probability of satisfying nodal demands and pressure heads for various possible pipe failures (breaks) in the water distribution system. The overall model includes three that are linked: a steady‐state simulation model, a reliability model, and an optimization model. The simulation model is used to implicitly solve the continuity and energy constraints and is used in the reliability model to define minimum cut sets. The reliability model, which is based on a minimum cut‐set method, determines the values of system and nodal reliability. The optimization model is based on a generalized reduced‐gradient method. Examples are used to illustrate the model.

Calibration is a process of comparing model results with field data and making the appropriate adjustments so that both results agree. Calibration methods can involve formal optimization methods or manual methods in which the modeler informally examines alternative model parameters. The development of a calibration framework typically involves the following: (1) definition of the model variables, coefficients, and equations; (2) selection of an objective function to measure the quality of the calibration; (3) selection of the set of data to be used for the calibration process; and (4) selection of an optimization/manual scheme for altering the coefficient values in the direction of reducing the objective function. Hydraulic calibration usually involves the modification of system demands, fine-tuning the roughness values of pipes, altering pump operation characteristics, and adjusting other model attributes that affect simulation results, in particular those that have significant uncertainty assoc...

A chance constrained model is presented for the minimum cost design of water distribution networks. This methodology attempts to account for the uncertainties in required demands, required pressure heads, and pipe roughness coefficients. The optimization problem is formulated as a nonlinear programming model which is solved using a generalized reduced gradient method. Details of the mathematical model formulation are presented along with example applications. Results illustrate that uncertainties in future demands, pressure head requirements, and pipe roughness can have significant effects on the optimal network design and cost.