Optimization

Summarized below are several of the technologies that have been employed by Optimatics in projects around the world.

Evolutionary Algorithms

Evolutionary algorithm (EA) optimization is a directed search technique that evaluates hundreds of thousands of possible solutions as it converges on the best solution alternatives.

To apply EA optimization to a water system, an EA routine is linked to a hydraulic simulation model set up for the appropriate steady-state or extended period simulation (EPS) scenarios.

The EA search then sorts through different combinations of pipe, tank, pump and valve improvements, and/or operational set points and pumping schedules. The search objective is to find the best mix of decisions to meet the utility's design and performance criteria at the least cost.

Genetic Algorithm Optimization

The Optimatics Genetic Algorithm (OGA) ® was the first Genetic Algorithm applied to water systems optimization.

Genetic Algorithm (GA) optimization is an evolutionary technique based upon the mechanisms of natural selection and genetics (Goldberg 1989). "Survival of the fittest" relentlessly drives the GA towards improved solutions. The GA process involves the selection, combination and manipulation of possible solution options (Simpson 1999).

Starting from an initial population of trial solutions (generation 0), the GA uses certain operators to derive a subsequent population of off-spring solutions (generation 1, 2, etc.). The three operators of reproduction, crossover and mutation act on successive generations to drive a process akin to natural selection. The fittest solutions in each generation have the greatest probability of surviving and then breeding to "evolve" better and better solutions. Fitness is a measure of each solution's cost and hydraulic performance.

Non-Linear Programming

In cases where the optimization problem can be converted to a series of linear programs without loss of accuracy the most appropriate technology is Non-Linear Programming (NLP). The main advantage of NLP is in its computational efficiency. Optimal solutions can be produced in a matter of minutes, making NLP useful for optimizing systems in real-time. NLP has been successfully applied to optimise the scheduling of pump operations, and in the long term management of bulk water systems.

In operations optimization the non-linear equations governing the hydraulics of pump stations, pipeline flow, water treatment plant sources, energy dissipaters and pressure reducing valves can be approximated by linear programs to produce solutions that minimize cost, energy, or a combination of both.

Distributed Computing

Distributed computing allows Optimatics to develop near-optimum solutions in hours or days rather than weeks or months. 'Distributed computing' refers to the practice of harnessing the combined processing power of a number of disparate resources into one unit.

Evolutionary Algorithms (EAs) require significant amounts of computing power in order to be effective. With the requirement of performing hundreds of thousands of hydraulic simulations on a single optimization project, the demands of Optimatics' advanced optimization technologies far exceed those that could be offered by a single processor.

Optimatics utilizes a cluster of computing nodes, dividing an optimization project into smaller computing tasks, and distributing tasks individually to each node. Tasks are then processed in parallel to achieve time efficiencies.

The distributed computing technologies of Optimatics are scalable and enable optimization processes to be run by clients on their in-house computer networks.

Artificial Neural Networks

When coupled with a GA, Artificial Neural Networks (ANNs) satisfy the requirement of achieving optimal solutions by up to 100 times faster than a stand-alone GA. Artificial Neural Networks (ANNs) can be used to approximate computationally intensive simulation models, such as EPANET and SWMM. The ANN can then be used in place of EPANET or SWMM in a Genetic Algorithm (GA) run. As ANNs are an approximation technique, they can be run in a significantly shorter amount of time than the simulation model. Therefore, when coupled with a GA, ANNs satisfy the requirement of achieving optimal solutions in a shorter time-frame. Optimal solutions are also verified with the original simulation model to ensure they satisfy hydraulic requirements. The main purpose of the ANN technology is to improve efficiency, that is, reduce computer run-time.

 

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, Mass, Addison-Wesley Pub. Co.

Simpson, A. R. (1999). Modelling of Pressure Regulating Devices - A Major Problem Yet to be Satisfactorily Solved in Hydraulic Simulation. Water Distribution Systems Conference, Division of Water Resources Planning and Management, ASCE. Tempe, Arizona, USA.