Balancing Deterministic, Stochastic, and Nature-Inspired Metaheuristics in Budget-Constrained Global Optimization: Theory, Applications, and Cross-Domain Implications

Abstract

Global optimization has emerged as a central methodological challenge across engineering, finance, energy systems, and management sciences, particularly in contexts characterized by nonconvex landscapes, high dimensionality, uncertainty, and limited computational or financial budgets. Over the past two decades, the field has witnessed the parallel evolution of deterministic algorithms, stochastic optimization methods, and nature-inspired metaheuristics, each grounded in distinct theoretical assumptions and practical trade-offs. This article develops a comprehensive, theory-driven analysis of the efficiency, robustness, and applicability of these optimization paradigms under constrained evaluation budgets. Drawing strictly on established literature, the study synthesizes insights from comparative global optimization theory, expensive black-box optimization, human- and nature-inspired metaheuristics, and application-driven optimization in energy systems, portfolio management, and index tracking. Rather than offering a superficial comparison, the article deeply interrogates why and how certain classes of algorithms succeed or fail under different structural conditions, including smoothness, uncertainty, sparsity, and real-world constraints. The methodology relies on conceptual synthesis, cross-domain abstraction, and descriptive analytical reasoning rather than mathematical formalism, thereby making the discussion accessible while retaining rigor. The results highlight that no single optimization paradigm dominates universally; instead, efficiency emerges from the alignment between problem structure, information availability, and algorithmic exploration–exploitation balance. The discussion further explores limitations, theoretical tensions between determinism and randomness, and future research directions, particularly in hybrid and adaptive optimization frameworks. By unifying insights from computational optimization and applied decision-making domains, this article contributes a holistic perspective on global optimization under limited budgets, with implications for both theory and practice.