IWOO: Wave Optics Optimizer Improved with Hybrid Strategies for Numerical Optimization and Engineering Applications

This paper provides a historical analysis of the IEEE CEC Single Objective Optimization competition results (2010-2024). We analyze how benchmark functions shaped winning algorithms, identifying the 2014 introduction of dense rotation matrices as a key performance filter. This design choice introduced parameter non-separability, reduced effectiveness of coordinate-dependent methods (PSO, GA), and established the dominance of Differential Evolution variants capable of preserving the rotational invariance of their difference vectors, specifically L-SHADE. Post-2020 analysis reveals a shift towards high complexity hybrid optimizers that combine different mechanisms (e.g., Eigenvector Crossover, Societal Sharing, Reinforcement Learning) to maximize ranking stability. We conclude by identifying structural similarities between these modern benchmarks and Variational Quantum Algorithm landscapes, suggesting that evolved CEC solvers possess the specific adaptive capabilities required for quantum control.

This paper presents a novel population-based metaheuristic, Indian Wedding System Optimization (IWSO), inspired by the socio-cultural dynamics of traditional Indian weddings. IWSO models the matchmaking process driven by collaboration among families, candidates, and matchmakers as a guided, selective search framework for solving complex optimization problems. The algorithm introduces two key innovations: (i) a matchmaker-guided influence strategy, where elite solutions direct the evolution of weaker candidates, enhancing convergence without external parameters; and (ii) an adaptive elimination and reinitialization mechanism that maintains diversity and prevents premature convergence by replacing underperforming individuals. IWSO employs a weighted multi-objective fitness function and analytically derived time and space complexity, benchmarked against existing optimization approaches such as Genetic Algorithm (GA), Partical Swarm Optimization (PSO), Differential Evolution (DE), Cuckoo Search (CS), etc. Extensive experiments on benchmark high-dimensional and multimodal test functions demonstrate superior performance of IWSO in terms of convergence speed, solution quality, and robustness.

Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal warm-start iterates, reporting iteration reductions of 30-46%. We show that these reported gains rest on an inappropriate evaluation baseline: prior methods benchmark against the flat start $V_m = 1, V_a = 0$, whereas the solver's actual default - the variable-bound midpoint $(l+u)/2$ - is near-optimal for log-barrier centrality. Against this corrected baseline, no primal-only warm-start method reduces solver iterations. We trace the failure to a geometric property of interior-point methods: primal prediction accuracy is anticorrelated with convergence speed, and providing the ground-truth optimal solution $x^*$ without dual variables causes the solver to diverge. Oracle experiments establish that the complete primal-dual-barrier state $(x^*, λ^*, z^*, μ^*)$ reduces IPOPT iterations from 23 to 3 - an 85% reduction that is structurally inaccessible to primal-only methods. To enable rigorous evaluation of warm-start methods on this task, we release a benchmark suite comprising dual-labeled AC-OPF datasets with IPOPT-extracted solutions, a corrected evaluation protocol, and WARP - a topology-conditioned encode-process-decode interaction network that predicts the full interior-point state $(\hat{x}, \hatλ, \hat{z}, \hatμ)$ on the heterogeneous constraint graph. WARP achieves a 76% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.