Pareto-Optimal Solutions for a Truss Problem

Abstract

Most optimization problems, particularly those in engineering design, require the simultaneous optimization of more than one objective function. In this context, the solutions of these problems are based on the Pareto frontier construction. Substantial efforts have been made in recent years to develop methods for the construction of Pareto frontiers that guarantee uniform distribution and exclude the non-Pareto and local Pareto points. The Normal Boundary Intersection (NBI) is a recent contribution that generates a well-distributed Pareto frontier efficiently. Nevertheless, this method should be combined with a global optimization method to ensure the convergence to the global Pareto frontier. This paper proposes the NBI method using Adaptive Simulated Annealing (ASA) algorithm, namely NBI-ASA as a global nonlinear multi-objective optimization method. A well known benchmark multi-objective problem has been chosen from the literature to demonstrate the validity of the proposed method, applicability of the method for structural problems has been tested through a truss problem and promising results were obtained. The results indicate that the proposed method is a powerful search and multi-objective optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms.

Cheetah Optimizer for Multi-objective Optimization Problems

“…The main objectives for this problem are to minimize the volume of structure and displacement at P 1 . The design variables involved are the cross-sectional area of all four points (P 1 -P 4 ) [43]. The Mathematical minimize :…”