The optimization of independent automotive suspension systems, which is one of the main pillars of the vehicle performance and comfort, is currently going through a revolutionary change due to the development of artificial intelligence and quantum computing. This paper aims to review the multi-objective optimization of suspension parameters including camber, caster, and toe to discuss the complex design issues that arise from geometric and dynamic considerations. Some of the most common computational methodologies, which are Genetic Algorithms, Particle Swarm Optimization, and Gradient Descent, are discussed in this paper along with the new quantum computing techniques such as Gate-Based quantum computing and Quantum Annealing (QA). In addition, this review incorporates information from the practice of automotive manufacturers who have incorporated the use of artificial intelligence and quantum computing in their suspension systems. However, there are still some issues remaining, such as the computational cost, real-time flexibility, and the applicability of theoretical concepts to actual engineering structures. Some potential future research directions are introduced in this paper, such as hybrid optimization approaches, quantum techniques, and adaptive materials, which are considered as potential directions for future development. This systematic review presents a conceptual framework for researchers and engineers to follow, stressing the importance of interdisciplinarity in the development of intelligent suspension systems with performance objectives that are capable of adjusting to various road conditions. The findings of this work underscore the growing importance of complex computational techniques in modern automotive industry and highlight their potential to shape future developments based on emerging trends and industry practices.

The double wishbone suspension (DWS) system is widely used in automotive engineering because of its favorable kinematic properties, which affect vehicle dynamics, handling, and ride comfort; hence, it is important to have an accurate 3D model, simulation, and analysis of the system in order to optimize its design. This requires efficient computational tools for parametric study. The development of effective computational tools that support parametric exploration stands as an essential requirement. Our research demonstrates a complete Wolfram Mathematica system that creates parametric 3D kinematic models and conducts simulations, performs analyses, and generates interactive visualizations of DWS systems. The system uses homogeneous transformation matrices to establish the spatial relationships between components relative to a global coordinate system. The symbolic geometric parameters allow designers to perform flexible design exploration and the kinematic constraints create an algebraic equation system. The numerical solution function NSolve computes linkage positions from input data, which enables fast evaluation of different design parameters. The integrated 3D visualization module based on Mathematica’s manipulate function enables users to see immediate results of geometric configurations and parameter effects while calculating exact 3D coordinates. The resulting robust, systematic, and flexible computational environment integrates parametric 3D design, kinematic simulation, analysis, and dynamic visualization for DWS, serving as a valuable and efficient tool for engineers during the design, development, assessment, and optimization phases of these complex automotive systems.

The double wishbone suspension (DWS) system is widely used in automotive engineering because of its favorable kinematic properties which affect vehicle dynamics, handling, and ride comfort; hence, it is important to have an accurate 3D model, simulation, and analysis of the system in order to optimize its design which requires efficient computational tools for parametric study. The development of effective computational tools which support parametric exploration stands as an essential requirement. Our research demonstrates a complete Wolfram Mathematica system which creates parametric 3D kinematic models and conducts simulations and analyses and generates interactive visualizations of DWS systems. The system uses homogeneous transformation matrices to establish the spatial relationships between components relative to a global coordinate system. The symbolic geometric parameters allow designers to perform flexible design exploration and the kinematic constraints create an algebraic equation system. The numerical solution function NSolve computes linkage positions from input data which enables fast evaluation of different design parameters. The integrated 3D visualization module based on Mathematica′s manipulate function enables users to see immediate results of geometric configurations and parameter effects while calculating exact 3D coordinates. The resulting robust, systematic, and flexible computational environment integrates parametric 3D design, kinematic simulation, analysis, and dynamic visualization for DWS, serving as a valuable and efficient tool for engineers during the design, development, assessment, and optimization phases of these complex automotive systems.

The design of multi-link vehicle suspension systems, such as the 3D double-wishbone, presents a critical challenge in automotive engineering. The process constitutes a high-dimensional, nonlinearly constrained optimization problem where traditional gradient-based methods often fail by converging to suboptimal local minima. This paper introduces a novel two-stage hybrid optimization framework designed to overcome this limitation by intelligently integrating quantum-inspired and classical techniques. The methodology explicitly defines a QUBO (Quadratic Unconstrained Binary Optimization) stage and an SQP (Sequential Quadratic Programming) stage. Stage 1 addresses the complex kinematic constraint problem by formulating it as a QUBO, which is then solved using Simulated Annealing to perform a global search, guaranteeing a physically feasible starting point. Subsequently, Stage 2 takes this feasible solution and employs an SQP algorithm to perform a high-precision local refinement, tuning the geometry to meet specific performance targets for camber and caster curves. The framework successfully converged to a design with a near-zero performance objective of 7.08 × 10⁻¹⁴. The efficacy of this hybrid approach is highlighted by the dramatic improvement from the high-error initial solution found by Simulated Annealing to the final, high-precision result from the SQP refinement. We conclude that this QUBO-SQP framework is a powerful and validated methodology for solving complex, real-world engineering design problems, effectively bridging the gap between global exploration and local precision.

The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus, that affect variational quantum algorithms, and transfers well into the fault-tolerant era, as it requires only a limited number of arbitrary angle gates. Despite its potential, the algorithm has seen limited implementation efforts, presumably due to its abstract formulation. In this work, we provide a detailed instruction on implementing the quantum step operator for arbitrary backtracking instances. For a single controlled diffuser of a binary backtracking tree with depth n , our implementation requires only 6 n +14 CX gates. We detail the process of constructing accept and reject oracles for Sudoku problems using our interface to quantum backtracking. The presented code is written using Qrisp, a high-level quantum programming language, making it executable on most current physical backends and simulators. Subsequently, we perform several simulator based experiments and demonstrate solving 4× 4 Sudoku instances with up to nine empty fields. This is, to the best of our knowledge, the first instance of a compilable implementation of this generality, marking a significant and exciting step forward in quantum software engineering.

Large-scale graphs underpin critical applications such as financial fraud detection, citation analysis, and biomedical discovery, where link prediction is often performed under severe label scarcity, class imbalance, and operational cost constraints. Recent large language models (LLMs) provide powerful semantic priors that can augment graph learning; however, naïvely querying LLMs is computationally expensive, and direct distillation of their outputs into compact graph models can degrade predictive reliability. In this work, we propose a budgeted LLM-assisted framework for graph link prediction that explicitly accounts for both predictive performance and calibration. The framework consists of four stages: (i) training a backbone graph neural network (GNN) using available labeled edges, (ii) selectively querying an LLM under a fixed query budget, (iii) distilling LLM-provided soft supervision into a lightweight student predictor, and (iv) learning a calibration-aware gating model that adaptively combines base and student predictions on a per-edge basis. The proposed gate relies only on inexpensive uncertainty- and structure-aware signals, such as predictive entropy and node degree, to determine when LLM supervision is likely to be beneficial. We evaluate the proposed approach using both ranking and reliability metrics, including ROC-AUC, Average Precision (AP), Expected Calibration Error (ECE), and Brier score. Experiments on four benchmark datasets—Elliptic, Cora, PubMed, and OGBN-Arxiv—demonstrate that the learned gate consistently improves ranking performance over both the base GNN and the LLM-distilled student under the same query budget, while substantially reducing calibration error. These results highlight that selective, calibration-aware LLM supervision offers a practical and trustworthy pathway for improving graph link prediction in cost-sensitive real-world settings.