The branch-and-bound method was originally developed to cope with difficulties caused by discontinuous design variables in linear programming. When the branch-an~-bound method is applied to solve nonlinear programming (NLP) problems with a large number of mixed discontinuous and continuous design variables. the slow rate of convergence becomes a major drawback of the method. In thIs study. a number of enhancements are proposed to speed up the rate of convergence of the conventIOnal branch-an~~bound algorithm. Three NLP in the form of truss-design examples ar~tested to compare the capabilitIes and effIcIency of the proposed enhancements. It is shown that of the five CrIterIa for arranglllg the order III which the deSign variables are branched. the criterion of maximum cost difference dramatically reduces the number of branch nodes. thereby reducing the total number of continuous-optimization runs executed. Moreover. neighboring search. a branching procedure restricted in the neighborhood of the contllluous optImum. IS proven to be effective in speeding up the convergence. Investigation also shows that branching several deSign varIables simultaneously is not as efficient as sequentially branching one variable at a time. The proposed enhancements are incorporated along with a sequential quadratic programming algorithm mto a software package that IS shown to be very useful in the optimal design of engineering structures.

In this paper, we consider the problem of computing the smallest enclosing circle. An efficient cutting plane algorithm is derived. It is based on finding the valid cut and reducing the problem into solving a series of linear programs. The numerical performance of this algorithm outperforms other existing algorithms in our computational experiments.

In this paper, a double-random phase-encoding technique-based text encryption and hiding method is proposed. First, the secret text is transformed into a 2-dimensional array and the higher bits of the elements in the transformed array are used to store the bit stream of the secret text, while the lower bits are filled with specific values. Then, the transformed array is encoded with double-random phase-encoding technique. Finally, the encoded array is superimposed on an expanded host image to obtain the image embedded with hidden data. The performance of the proposed technique, including the hiding capacity, the recovery accuracy of the secret text, and the quality of the image embedded with hidden data, is tested via analytical modeling and test data stream. Experimental results show that the secret text can be recovered either accurately or almost accurately, while maintaining the quality of the host image embedded with hidden data by properly selecting the method of transforming the secret text into an array and the superimposition coefficient. By using optical information processing techniques, the proposed method has been found to significantly improve the security of text information transmission, while ensuring hiding capacity at a prescribed level.

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