constrained optimization

The tuned liquid column damper (TLCD) having a uniform cross-sectional tube of U-shaped, occupied with liquid is used as a vibrational response mitigation device. The tuned liquid column ball damper (TLCBD) is a modified TLCD, where, an immovable orifice, positioned at the middle part of the horizontal portion, is replaced by a metal ball. Different studies on the unconstrained optimization performance of TLCBD subjected to the stochastic earthquake have been performed where limitations on the maximum amplitude of liquid present in the vertical portion of the tube were not imposed. In the case of the high magnitude of earthquake and space constraint, the excessive liquid movement might get generated in the vertical portion of the tube which can create challenging circumstances. This can be taken care of by restricting the liquid movement up to a certain limit. The present investigation considers the optimum performance of the structure with TLCBD for mitigating the vibrational response with limited liquid movement in the vertical portion of the tube. A numerical study has been carried out to demonstrate the difference between constrained and unconstrained optimization of structure-TLCBD system. Numerical results show the influence of constraining cases on optimum parameters and performance behavior of the structure-TLCBD system.

The non-convex behavior presented by nonlinear systems limits the application of classical optimization techniques to solve optimal control problems for these kinds of systems. This paper proposes a hybrid algorithm, namely BA-SD, by combining Bee algorithm (BA) with steepest descent (SD) method for numerically solving nonlinear optimal control (NOC) problems. The proposed algorithm includes the merits of BA and SD simultaneously. The motivation of presenting the proposed algorithm includes that BA is showed to converge to the region that global optimum is settled, rapidly during the initial stages of its search. However, around global optimum, the search process will become slowly. In contrast, SD method has low ability to convergence to local optimum, but it can achieve faster convergent speed around global optimum and the convergent accuracy can be higher. In the proposed algorithm, at the beginning step of search procedure, BA is utilized to find a near optimum solution. In this case, the hybrid algorithm is used to enhance global search ability. When the change in fitness value is smaller than a predefined value, the searching procedure is switched to SD to accelerate the search procedure and find an accurate solution. In this way, the algorithm finds an optimum solution more accurately. Simulations demonstrate the feasibility of the proposed algorithm.