This paper presents a constrained multiobjective (multicriterion, vector) optimization methodology by integrating a Pareto genetic algorithm (GA) and a fuzzy penalty function method. A Pareto GA generates a Pareto optimal subset from which a robust and compromise design can be selected. This Pareto GA consists of five basic operators: reproduction, crossover, mutation, niche, and the Pareto-set filter. The niche and the Paretoset filter are defined, and fitness for a multiobjective optimization problem is constructed. A fuzzy-logic penalty function method is developed with a combination of deterministic, probabilistic, and vague environments that are consistent with GA operation theory based on randomness and probability. Using this penalty function method, a constrained multiobjective optimization problem is transformed into an unconstrained one. The functions of a point (string, individual) thus transformed contain information on a point's status (feasible or infeasible), position in a search space, and distance from a Pareto optimal set. Sample cases investigated in this work include a multiobjective integrated structural and control design of a truss, a 72-bar space truss with two criteria, and a four-bar truss with three criteria. Numerical experimental results demonstrate that the proposed method is highly efficient and robust.


Civil, Architectural and Environmental Engineering

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2024 American Society of Civil Engineers, All rights reserved.

Publication Date

01 Jan 1997