Optimum Structural Design of Internal Combustion Engine Systems by Branch-and-Bound Algorithm

Abstract

This paper develops an alternative optimization approach for systematic design of a parametrized engine system and illustrates the procedure through application to a novel conversion device, the patented Stiller-Smith mechanism (1, 2). Using simultaneous interplay between a simulation scheme, presented in detail elsewhere (3), and an optimization scheme, the proposed structural design process integrates the multiple objectives of structural design. Developed here in detail, optimization involves intermediate continuous optimization via a penalty function method, and integer or discrete programming through the branch-and-bound algorithm. The ensuing application illustrates the approach by optimizing a 16-cylinder Stiller-Smith engine for minimum weight-power and dimensions-power ratios under several types of constraints. In the context of a multi-objective constrained non-linear programming problem, the design example proceeds through three stages: (a) preliminary, in which the designer applies the simulation scheme to obtain the system response variables from the design requirements to reflect trade-off relationships among multiple design objectives; (b) secondary, the intermediate continuous optimal design stage, in which a penalty function method is used to specify constraints within a general range to allow variation in the choice of parameters; and (c) final, in which the branch-and-bound algorithm constrains integer variables to take integer values and discrete variables to take discrete values, thereby arriving at an optimal design.