Multi-Objective Evolutionary Optimization Algorithm for Profit-Maximization and Risk Minimization in Business Operations

Abstract

The management of business operations is becoming more and more focused on achieving simultaneous optimization of conflicting objectives (profit maximization, risk minimization, regulatory compliance, and sustainability) while also managing complex operational constraints. Traditional single-objective optimization and multi-criteria optimization based on scalarization do not utilize the inherent trade-off structure present in these types of situations.  Developed a Multi-Objective Evolutionary Optimization (MOEO) Algorithm for Business Operations (MOEO-BO) that uses the NSGA-III non-dominated sorted approach to optimize the following six objectives at once: net profit (f₁), Conditional Value-at-Risk (f₂), operational risk index (f₃), Return on Invested Capital (f₄), ESG compliance (f₅), and exposure to market volatility (f₆). The algorithm has been validated on 65 real-world business units within six industrial sectors, yielding a Hypervolume indicator of 0.847 and an Inverted Generational Distance of 0.0028, outperforming both NSGA-III (HV = 0.793), NSGA-II (HV = 0.761), MOEA/D (HV = 0.778), and SPEA2 (HV = 0.742).  The MOEO-BO algorithm, when applied to businesses in the manufacturing, retail, financial services, healthcare, technology, and logistics sectors, resulted in an aggregate profit increase of 37.5%, with an overall risk reduction of 39.4% from baseline operational strategies.  Ablation studies demonstrated that each of the following attributes contributed significantly to the solution quality: maintaining diverse reference points (+10.1% Hypervolume, 73.4% Generational Distance improvement), Augmented Lagrangian repairs (+3.9% Hypervolume), and using a six-objective formulation (+31.2% over the single-objective formulation).  The MOEO-BO algorithm enables enterprise decision makers to create a Pareto-optimal strategy frontier, providing explicit means for managing trade-offs in the face of uncertainties.