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Optimal design and rehabilitation of a water distribution system is a constrained nonlinear optimization problem. A penalty function is often employed to transform a constrained into a nonconstrained optimization problem within the framework of a genetic algorithm search. A penalty factor is used for defining the penalty function and calculating the penalty cost for the solutions with constraint violation. Effective penalty factors vary from one optimization model to another. This paper introduces a self-adaptive penalty approach to artificially evolve both the penalty factor and the design solutions. Solution robustness is proposed and quantified, along with solution fitness, for representing the boundary between the infeasible and feasible solutions of a high-dimension optimization problem. The solution space of multiple dimensions is mapped onto a 2D space, providing significant insight into the self-adaptive penalty approach, which is compared with other constraint-handling techniques tested on a benchmark example. The results show that this approach is more effective than other penalty methods used for searching for optimal and near-optimal solutions. The self-adaptive penalty approach relieves modelers from tuning the penalty function and facilitates a practical optimization modeling for water distribution design. [ABSTRACT FROM AUTHOR]

The system identification and vibration control of a cable-stayed bridge are considered difficult to achieve due to the bridge's structural complexity and system uncertainties. In this paper, based on the concept of decentralized information structures, a decentralized, nonparametric identification and control algorithm with neural networks is proposed for the purpose of suppressing the vibration of a documented six-cable-stayed bridge model induced by earthquake excitations. The control strategy proposed here uses the stay cables as active tendons to provide control forces through appropriate actuators. Each individual actuator is controlled by a decentralized neuro-controller that only uses local information. The feature of decentralized control simplifies the implementation of the control algorithms and makes decentralized control easy to practice and cost effective. The effectiveness of the decentralized identification and control algorithm based on neural networks is evaluated through numerical simulations. And the adaptability of the decentralized neurocontrollers for different kinds of earthquake excitations and for a damaged cable-stayed bridge model is demonstrated via numerical simulations. [ABSTRACT FROM AUTHOR]