The interior-point methods have emerged as highly efficient procedures for solving linear programming problems in recent years. The interior point methods have superior theoretical properties as well as observed computational advantages over simplex methods at solving large linear programming problems and are found to be immune to degeneracy. It is a common observation in literature that most nonlinear programming methods that work well for small and medium sized problems are not able to solve large-scale problems efficiently. It is to be expected that interior-point methods, when used in an adaptive sequential linear programming strategy, might prove to be a powerful engineering optimization tool. The development of an adaptive sequential linear programming algorithm, based on an infeasible primal-dual path-following interior-point algorithm and fuzzy heuristics, is considered in this work for the solution of large-scale engineering design optimization problems. Several numerical examples are considered to demonstrate the effectiveness and efficiency of the present method. The examples include a part stamping problem, a turbine rotor design problem, and an optimal control problem related to tidal power generation. The number of design variables and constraints range from 12 to 402 and 20 to 20,300, respectively, for the part stamping problem. The turbine rotor problem involves 905 variables and 1081 constraints, and the optimal control problem has 2002 variables and 1001 constraints. The numerical results clearly demonstrate the superiority of the interior-point methods compared with the well-known simplex-based linear solver in solving large-scale optimum design problems. The superior performance of the present method is shown in terms of both computational time and the ability to handle degenerate problems.
ASJC Scopus subject areas
- Aerospace Engineering