In this paper, an optimization model with an objective function as monomial subject to a system of the fuzzy relation equations with max-bounded difference (maxBD) composition operator is presented. We firstly determine its feasible solution set. Then some special characteristics of its feasible domain and the optimal solutions are studied. Some procedures for reducing and decomposing the probl...

This paper develops a simple bounding procedure for the optimal value of a posynomial geometric programming (GP) problem when some of the coefficients for terms in the problem’s objective function are estimated with error. The bound may be computed even before the problem is solved and it is shown analytically that the optimum value is very insensitive to errors in the coefficients; for example...

Topology optimization is a method to find the best distribution of material in a given design domain. The use of topology optimization for structural design often leads to slender structures which are sensitive to geometric imperfections such as the misplacement or misalignment of material. A robust approach to topology optimization is therefore presented which takes into account these geometri...

Linear Programming 15 after kd successful rounds, 2k (H) nek=3. This implies that the above algorithm terminates in at most 3d lnn successful rounds. Since each round takes O(dd) time to compute xR and O(dn) time to compute V , the expected running time of the algorithm is O((d2n+dd+1) log n). By combining this algorithm with a randomized recursive algorithm, Clarkson improved the expected runn...

In this paper we review the recent progress in the design of efficient algorithms for several geometric optimization problems in manufacturing processes. We first describe the strong geometric characteristics of optimization problems in manufacturing. Three illustrative problems are then presented in details: the shortest contour touring problem in laminated object manufacturing, the minimum to...

We review the recent progress in the design of e cient algorithms for various problems in geometric optimization. The emphasis in this survey is on the techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, prune-and-search techniques for linear programming and related problems, and LP-type problems and their e cient solution.