Models and Dataset

<b>P3DE (Parameter-less Population Pyramid with Deep Ensemble):</b><br>P3DE is a hybrid feature selection framework that combines the Parameter-less Population Pyramid (P3) metaheuristic optimization algorithm with a deep ensemble of autoencoders. Designed for high-dimensional biological data, P3DE dynamically evaluates candidate feature subsets using an ensemble of autoencoders with different activation functions (Sigmoid, Tanh, ReLU). Ensemble weights are computed based on initial, historical, and functional reconstruction performance. This parameter-free, adaptive architecture enhances exploration and avoids overfitting, making P3DE a robust tool for biomarker discovery in gene expression datasets.<br><b>TJO (Tom and Jerry Optimization):</b><br>TJO is a nature-inspired metaheuristic algorithm that models the predator-prey dynamics of the cartoon characters Tom (predator) and Jerry (prey). Operating in a binary search space, TJO simulates intelligent and evasive movements of the prey to guide the population toward optimal solutions. The algorithm does not rely on predefined control parameters like crossover or mutation rates, which makes it lightweight and easy to implement for various feature selection and optimization tasks.<br><b>RAO (Rao Optimization Algorithm):</b><br>RAO is a parameter-less optimization algorithm that updates solutions based on simple arithmetic operations involving the best and worst individuals in the population. Unlike conventional evolutionary algorithms, RAO does not use mechanisms such as crossover, mutation, or selection. Its simplicity and lack of algorithm-specific parameters make it computationally efficient and easy to apply in high-dimensional problems such as gene selection for cancer classification.

<b>P3DE：无参数种群金字塔结合深度集成学习（Parameter-less Population Pyramid with Deep Ensemble）:</b><br>P3DE是一种混合特征选择框架，将无参数种群金字塔（Parameter-less Population Pyramid，P3）元启发式优化算法与自编码器深度集成模型相结合。该框架专为高维生物数据设计，通过采用不同激活函数（Sigmoid、Tanh、ReLU）的自编码器集成动态对候选特征子集进行评估。集成权重基于初始性能、历史性能与功能重构性能计算得出。这种无参数自适应架构能够增强探索能力并避免过拟合，使P3DE成为基因表达数据集生物标志物发现的可靠工具。<br><b>TJO：汤姆与杰瑞优化算法（Tom and Jerry Optimization）:</b><br>TJO是一种受自然启发的元启发式算法，以卡通角色汤姆（捕食者）与杰瑞（猎物）的捕食者-猎物动态交互关系为建模原型。该算法工作于二进制搜索空间，通过模拟猎物的智能规避行为引导种群向最优解逼近。该算法无需依赖交叉率、突变率等预定义控制参数，因此轻量化且易于在各类特征选择与优化任务中部署。<br><b>RAO：Rao优化算法（Rao Optimization Algorithm）:</b><br>RAO是一种无参数优化算法，通过基于种群内最优与最差个体的简单算术运算更新候选解。与传统进化算法不同，RAO无需使用交叉、突变或选择等演化机制。其简洁的设计与无算法专属控制参数的特性使其计算效率极高，且易于在癌症分类基因选择等高维优化问题中应用。