Lexicographic Multi-Objective Optimization Approach for Welding Flux System Design

Multiple response optimization of welding flux performance has been found to be cost effective and useful for the achievement of the best balance among conflicting welding flux quality attributes. Many multi-criteria optimization methods (MCOM) have been applied in flux formulation situations where flux quality attributes are of comparable importance. However, information on applications of MCOM to flux design situations where quality attributes are in hierarchical order of importance is scarce in the open literature. In this study, a Lexicographic Multi-objective Optimization (LMO) model was proposed for handling flux design situations in which the attributes are in hierarchical order of importance. The model was applied using data from literature. Two priority levels were used: acicular ferrite (AF) maximization was assigned first priority while the maximization of polygonal ferrite (PF) content and weld-metal impact toughness (WIT) were assigned second priority subject to oxygen content constraint of 250 – 350ppm. The respective solutions for AF, PF, WIT and oxygen content were 51.19%, 21.80%, 23.70J at -20oC and 315ppm. The corresponding flux formulation was CaO (25.90) MgO (15.00) CaF2 (31.10) and Al2O3 (8.00%). Various priority structures were used to explore trade-off options and to generate three more pareto efficient solutions from which the flux formulator can select the most preferred one. The proposed model has filled the existing gap in the literature being a pioneering work in the application of lexicographic multi-objective optimization method in welding flux design.