SUMMARYAn upper bound or a lower bound of the MultipleChoice Knapsack Problem can be calculated by solving LP relaxation. In 1979, Sinha and Zoltners proposed a branchand-bound algorithm for solving the Multiple-Choice Knapsack Problem, and provided a method to obtain the strict upper bound. In this paper, we propose a new calculation method to obtain a stricter upper bound than the upper bound of SinhaZoltners and compare the results of the two methods.
Until now, no formula has been derived for computing the acoustic parameters of the transmitting and receiving systems in the actual piezoelectric telephone handset of small size and light weight. The lack of such a formula was a significant hindrance to the design of the handset.
In this paper, estimation of these parameters is made possible by the application of the nonlinear optimization technique. In this optimization problem, convergence is extremely slow since there is a magnitude difference of about 1010 among the parameters. Hence, for each parameter, a hypothetical maximum and minimum are assumed so that the problem is replaced with a hypothetical conditional optimization problem.
By means of the change of variables, the variable ranges of all the parameters are aligned. At the same time, the problem is transformed back to the optimization problem without constraints so that the convergence is accelerated.
Since the performance function is constructed in which all the measured characteristics of the transmitting and receiving sensitivities under different measurement conditions are used as esimating information, the resultant optimization problem is of a significant size. The simulation characteristics computed based on the obtained estimation values agreed well with the measured characteristics. This implies that the estimated value derived by the present method is useful in actual design of the handset.
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