Multi-objective weighted average algorithm: a novel algorithm for multi-objective optimization problems and its application in engineering problems

Abstract

Numerous meta-heuristic algorithms struggle with degraded performance when addressing multi-objective optimization problems due to the challenge of balancing two goals: accurately estimating Pareto-optimal solutions and ensuring their broad distribution across objectives. While the Weighted Average Algorithm (WAA) excels in single-objective optimization, its scalarization-based mechanism fundamentally conflicts with multi-objective requirements. To bridge this gap, we propose the Multi-Objective Weighted Average Algorithm (MOWAA) with three key innovations: (1) a hybrid exploration-exploitation mechanism integrating adaptive mutation and crossover operations; (2) an elitist archive management system using efficient non-dominated sorting across three critical solution sets; and (3) a novel roulette-wheel-based leader selection strategy that dynamically balances convergence and diversity. To verify the performance of the developed MOWAA, the numerical benchmark test functions (CEC2009, ZDT and DTLZ) and four engineering problems (the Binh and Korn (BNH), Constraint (CONSTR), Srinivas and Deb (SRN), and 10-bar Truss (BAR TRUSS)) are used in comparison with three multi-objective optimization algorithms. The results show that MOWAA achieves better optimization performance than comparative algorithms, with Pareto-optimal solutions exhibiting excellent convergence and coverage. Finally, applying MOWAA to an Artificial Neural Network (ANN) model using an experimental dataset on surface waviness (in mm) of Wire Arc Additive Manufacturing (WAAM) components enhances predictive accuracy by balancing optimization of prediction error and variance. Compared to single-objective optimization methods, the MOWAA approach effectively captures the complex relationships between process parameters and waviness in the WAAM process.