A Fuzzy Approach for Determining a Feasible Point in a Constrained Problem

In an engineering design process, it is often desirable or even necessary to find a feasible starting point before finding the actual optimal design. The identification of unapparent feasible points provides problem insight with little computational cost. In addition, some optimization algorithms either require, or function more efficiently with, an initial point that satisfies all constraints. The advantages of using an initial feasible design are especially evident with complex structural problems and with problems that involve potential safety concerns such as the design of large pressure vessels. Although some methods are available, literature concerning the development and use of feasible-point determination is scarce. In this paper, fuzzy function theory is used to develop a novel, simple, and efficient algorithm for determining a feasible point by starting with a potentially infeasible point. Each constraint is written in fuzzy form with a newly developed membership function. The resulting optimization problem is easily solved using conventional techniques. This approach is applied to structural and manufacturing problems, including the design of a general pressure vessel. When compared with an established method, the new approach is successful and more than twenty-five times faster with larger problems.