A Longitudinal Analysis of the CEC Single-Objective Competitions (2010-2024) and Implications for Variational Quantum Optimization

Abstract

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.

Figures (7)

• Figure 1: Longitudinal evolution of algorithm families in CEC Competitions (2010–2024). Stacked bars illustrate the percentage distribution of all participating entries by category, with text annotations identifying the top-five-ranked algorithms for each year. To address the structural hybridization characteristic of post-2020 solvers, algorithmic classification follows a strict "Primary Search Engine" protocol. Solvers are categorized based on the specific evolutionary mechanism that consumes the majority ($>50\%$) of the maximum function evaluation budget. To accurately capture evolutionary trajectories, the DE family is subdivided into Canonical/Adaptive, SHADE Lineage, Societal/Multi-Population, and Driven Ensembles. Under this protocol, multi-component architectures are classified by their dominant foundational logic; for instance, ensembles that rely on DE as their core exploration framework but periodically trigger Covariance Matrix Adaptation to navigate rotated valleys (e.g., EA4eigN100 ) are classified as DE-Driven Ensembles rather than generic hybrids. This granular taxonomy confirms a structural shift from early algorithmic diversity to the sustained dominance of highly specialized DE architectures.
• Figure 2: Publication volume across three primary search clusters. The blue line establishes the baseline of the optimization community. The orange line tracks the "Quantum Revolution", starting around 2015-2016 when NISQ devices became a major research focus. The green line illustrates the intersection of quantum computing and optimization.
• Figure 3: Parameter concentration in QAOA for Max-Cut on 3-regular graphs with unweighted ($w_{ij} = 1$) and weighted ($w_{ij} \in \{\pm 1, \pm 2, \pm 3\}$) edges using circuit depth $p = 4$. (a) PCA visualization of optimization trajectories identifying local minimum (blue), maximum (red), and random initialization (white) points on a 10-qubit graph instance. Panel (b) reveals that the local minima (left columns) possess non-separable, rotated valley structures that persist across increasing problem dimensions ($N=4$ to $20$). Source: rudolph2021orqvizvisualizin
• Figure 4: Hardware-efficient ansatz with $L=1$ entangling layer for $N=10$ qubits. The circuit utilizes $R_y$ rotation gates and a linear CNOT staircase to produce a 20-dimensional parameter space.
• Figure 5: Optimizer convergence on the 10-qubit $L=1$ Ising VQA landscape. (left) Under exact statevector simulation, several advanced metaheuristics successfully navigate the underparameterized landscape to reach the global minimum. (right) Under noisy conditions, modern CEC variants demonstrate superior robustness, maintaining convergence despite stochastic fluctuations in the energy expectation values.