进化计算领域文章更新主要包括以下六大方向如下：
基础理论（包括遗传算法、进化策略、遗传编程、群智能等算法设计、理论研究、基准测试、进化思想、算法软件、综述等）
进化优化（包括黑盒优化、多目标优化、约束优化、噪声优化、多任务优化、多模态优化、迁移优化、大规模优化、昂贵优化、学习优化等）
组合优化（包括进化神经组合优化、进化机器人、路线规划、布局布线、工业控制、调度等）
神经进化（包含进化神经网络的参数、超参数、架构、规则等）
进化学习（包括进化特征选择、强化学习、多目标学习、公平性学习、联邦学习、进化计算机视觉、进化自然语言处理、进化数据挖掘等）
应用研究（工业、网络、安全、物理、生物、化学等）
文章来源主要包括：
1. IEEE CIS: CIM, TEVC, TNNLS, TFS, TAI, TETCI, CEC
2. IEEE CS/SMC: TPAMI, TKDE, TPDS, TCYB, TSMC, Proc. IEEE
3. ACM: TELO, GECCO, FOGA, ICML
4. MIT: ECJ, ARTL, JMLR, NIPS
5. Elsevier/Springer: AIJ, SWEVO, SCIS, PPSN
6. AAAI/MK/OR: AAAI, IJCAI, ICLR
7. Else: NMI, NC, PNAS, Nature, Science, ArXiv
基础理论
Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithms, IEEE TEVC
https://ieeexplore.ieee.org/document/10637292
Evolutionary Reinforcement Learning (ERL), which integrates Evolutionary Algorithms (EAs) and Reinforcement Learning (RL) for optimization, has demonstrated remarkable performance advancements. By fusing both approaches, ERL has emerged as a promising research direction. This survey offers a comprehensive overview of the diverse research branches in ERL. Specifically, we systematically summarize recent advancements in related algorithms and identify three primary research directions: EA-assisted Optimization of RL, RL-assisted Optimization of EA, and synergistic optimization of EA and RL. Following that, we conduct an in-depth analysis of each research direction, organizing multiple research branches. We elucidate the problems that each branch aims to tackle and how the integration of EAs and RL addresses these challenges. In conclusion, we discuss potential challenges and prospective future research directions across various research directions. To facilitate researchers in delving into ERL, we organize the algorithms and codes involved on https://github.com/yeshenpy/Awesome-Evolutionary-Reinforcement-Learning
进化优化
Exact Calculation of Inverted Generational Distance, IEEE TEVC
https://ieeexplore.ieee.org/document/10636749
Inverted Generational Distance (IGD) is an important performance indicator in the field of multi-objective optimization (MOO). Although it has been widely used for decades, applying IGD for fair and accurate performance evaluation remains challenging, with the biggest obstacle being the selection of the reference set. IGD generally represents the distance between the solution set and the Pareto front (PF). Since the real PF is often an infinite set, even if it is known, it is difficult to apply it directly to the calculation of IGD. As a workaround, past research typically samples a finite set, i.e., the reference set, from the PF as an approximation, indirectly used in the IGD calculation. This inevitably introduces a systematic error, which we refer to as discretization error. In this paper, we prove an upper bound for the discretization error, demonstrating that if the reference set is sufficiently dense and uniformly distributed on the entire PF, the discretization error will converge to zero. Additionally, we propose a numerical method for the exact calculation of IGD and IGD+. When the analytical expression of the PF is known, this method allows for the direct calculation of IGD and IGD+ using the real PF, thus avoiding discretization error.
An Adaptive Multi-Strategy Algorithm Based on Extent of Environmental Change for Dynamic Multiobjective Optimization, IEEE TEVC
https://ieeexplore.ieee.org/document/10633735
The most obvious characteristic of dynamic multi-objective optimization problems (DMOPs) is the time-varying Pareto-optimal set (POS) or/and Pareto-optimal front (POF). This kind of problem poses a higher challenge to evolutionary algorithms, as it requires populations to rapidly track and converge the updated POF in new environments. Differing from the superposition of several strategies in the literatures, we propose an adaptive multi-strategy algorithm based on the extent of environmental change, called AMEEC, to effectively handle various dynamic changes. AMEEC chooses the corresponding strategies for different environmental changes adaptively. When the environment changes moderately or similarly, the prediction based on clustered center points, POS manifold prediction, and generation of random solutions based on ideal points are employed to relocate the population individuals in the new environment. Otherwise, the trend prediction model is employed to predict the knee points of each part and the center points of each cluster, and to adaptively adjust the area of random solutions based on ideal and nadir points focuses on enhancing the diversity of population members. The proposed AMEEC is tested comprehensively on nineteen benchmark problems compared with six state-of-the-art algorithms. All algorithms use RM-MEDA (a regularity model-based multi-objective estimation of distribution algorithm) as a static optimizer. The experimental results demonstrate that AMEEC can achieve good convergence, diversity, and distribution, and is more competitive in dealing with dynamic problems.
A Hierarchical and Ensemble Surrogate-Assisted Evolutionary Algorithm With Model Reduction for Expensive Many-Objective Optimization, IEEE TEVC
https://ieeexplore.ieee.org/document/10630664
The Kriging model has been widely used in regression-based surrogate-assisted evolutionary algorithms (SAEAs) for expensive multiobjective optimization by using one model to approximate one objective, and the fusion of all the models forms the fitness surrogate. However, when tackling expensive many-objective optimization problems, too many models are required to construct such a fitness surrogate, which incurs cumulative prediction uncertainty and higher computational cost. Considering that the fitness surrogate works to predict different objective values to help select promising solutions with good convergence and diversity, this article proposes a novel model reduction idea to change the many-models-based fitness surrogate to a two-models-based indicator surrogate (TIS) that directly approximates convergence and diversity indicators. Based on TIS, a hierarchical and ensemble surrogate-assisted evolutionary algorithm (HES-EA) is proposed with three stages. Firstly, the HES-EA transforms the many objectives of the real-evaluated solutions into two indicators (i.e., the convergence and diversity indicators) and divides these solutions into different clusters. Secondly, a HES consisting of a cluster surrogate and different TISs is trained through these clustered solutions and their indicators. Thirdly, during the optimization process, the HES can predict the candidate solutions’ cluster information via the cluster surrogate and indicator information via the TISs. Promising solutions can thus be selected based on the predicted information via a clustering-based sequential selection strategy without real fitness evaluation consumption. Compared with state-of-the-art SAEAs on three widely used benchmark suites up to 184 instances and one real-world application, HES-EA shows its superiority in both optimization performance and computational cost.
Promoting Objective Knowledge Transfer: A Cascaded Fuzzy System for Solving Dynamic Multiobjective Optimization Problems, IEEE TFS
https://ieeexplore.ieee.org/document/10634796
In this paper, a novel dynamic multiobjective optimization algorithm (DMOA) with a cascaded fuzzy system (CFS) is developed, which aims to promote objective knowledge transfer from an innovative perspective of comprehensive information characterization. This development seeks to overcome the bottleneck of negative transfer in evolutionary transfer optimization (ETO)-based algorithms. Specifically, previous Pareto solutions, center- and knee-points of multi-subpopulation are adaptively selected to establish the source domain, which are then assigned soft labels through the designed CFS, based on a thorough evaluation of both convergence and diversity. A target domain is constructed by centroid feed-forward of multi-subpopulation, enabling further estimations on learning samples with the assistance of the kernel mean matching (KMM) method. By doing so, the property of non-independently identically distributed data is considered to enhance efficient knowledge transfer. Extensive evaluation results demonstrate the reliability and superiority of the proposed CFS-DMOA in solving dynamic multiobjective optimization problems (DMOPs), showing significant competitiveness in terms of mitigating negative transfer as compared to other state-of-the-art ETO-based DMOAs. Moreover, the effectiveness of the soft labels provided by CFS in breaking the “either/or” limitation of hard labels is validated, facilitating a more flexible and comprehensive characterization of historical information, thereby promoting objective and effective knowledge transfer.
An Indicator-Based Many-Objective Evolutionary Algorithm With Adaptive Reference Points Assisted by Growing Neural Gas Network, IEEE TETCI
https://ieeexplore.ieee.org/document/10636788
Many-objective optimization problems (MaOPs) pose significant challenges to the traditional multi-objective evolutionary algorithms (MOEAs) due to the loss of selection pressure. Recently, specific many-objective evolutionary algorithms (MaOEAs) have been proposed to solve MaOPs, among which the indicator-based MaOEAs are easy-to-use with good versatility. Inverted generational distance (IGD) is a reliable performance indicator to quantify the performance of MOEAs and MaOEAs. However, the bottleneck of applying IGD as the selection indicator in MaOEAs is the high dependence on the reference points specification over the Pareto front (PF). Most existing studies use the non-dominated solutions or the uniformly sampled points on the hyperplane as the reference points, which show poor adaptation in solving problems with various PF shapes. To address this issue, we propose to adaptively learn the distribution of the reference points using growing neural gas (GNG) network. To this end, a modified online GNG is designed to learn the topological structure of the PF using both the solutions stored in an external archive and the current population as the training data. The neurons in the GNG network and the normalized solutions in the archive are seen as the approximated reference points, based on which the IGD indicator contribution of each solution can be calculated to guide the evolutionary search. The experimental studies compare the proposed algorithm with eight state-of-the-art MaOEAs on solving 21 benchmark MaOPs. The results demonstrate that the proposed algorithm can achieve highly competitive performance when solving problems with both regular and irregular PFs.
Surrogate-Assisted Search with Competitive Knowledge Transfer for Expensive Optimization
https://arxiv.org/abs/2408.07176
Expensive optimization problems (EOPs) have attracted increasing research attention over the decades due to their ubiquity in a variety of practical applications. Despite many sophisticated surrogate-assisted evolutionary algorithms (SAEAs) that have been developed for solving such problems, most of them lack the ability to transfer knowledge from previously-solved tasks and always start their search from scratch, making them troubled by the notorious cold-start issue. A few preliminary studies that integrate transfer learning into SAEAs still face some issues, such as defective similarity quantification that is prone to underestimate promising knowledge, surrogate-dependency that makes the transfer methods not coherent with the state-of-the-art in SAEAs, etc. In light of the above, a plug and play competitive knowledge transfer method is proposed to boost various SAEAs in this paper. Specifically, both the optimized solutions from the source tasks and the promising solutions acquired by the target surrogate are treated as task-solving knowledge, enabling them to compete with each other to elect the winner for expensive evaluation, thus boosting the search speed on the target task. Moreover, the lower bound of the convergence gain brought by the knowledge competition is mathematically analyzed, which is expected to strengthen the theoretical foundation of sequential transfer optimization. Experimental studies conducted on a series of benchmark problems and a practical application from the petroleum industry verify the efficacy of the proposed method. The source code of the competitive knowledge transfer is available at this https URL.
组合优化
An Iterated Greedy Algorithm With Reinforcement Learning for Distributed Hybrid FlowShop Problems With Job Merging, IEEE TEVC
https://ieeexplore.ieee.org/document/10637266
The distributed hybrid flowshop scheduling problems (DHFSP) widely exist in various industrial production processes, and thus have received widespread attention. However, the existing research mainly focuses on inter-factory and inter-machine collaboration, but ignores collaborative processing between jobs. Therefore, this paper considers rescheduling DHFSP with job merging and reworking (DHFRPJM), and establishes a mixed integer linear programming model. The objective is to minimize the makespan. Based on problem-specific knowledge, a decoding heuristic and initialization strategy considering job merging are designed. An acceleration strategy based on critical path is adopted to save computational effort of iterated greedy algorithm. A local search strategy based on a deep reinforcement learning algorithm further improves the performance of the algorithm. Experimental results based on actual production data show that the proposed algorithm outperforms other algorithms in closely related literature.
神经进化
Automatic Design of Deep Graph Neural Networks With Decoupled Mode, IEEE TNNLS
https://ieeexplore.ieee.org/document/10636846
Graph neural networks (GNNs), a class of deep learning models designed for performing information interaction on non-Euclidean graph data, have been successfully applied to node classification tasks in various applications such as citation networks, recommender systems, and natural language processing. Graph node classification is an important research field for node-level tasks in graph data mining. Recently, due to the limitations of shallow GNNs, many researchers have focused on designing deep graph learning models. Previous GNN architecture search works only solve shallow networks (e.g., less than four layers). It is challenging and nonefficient to manually design deep GNNs for challenges like over-smoothing and information squeezing, which greatly limits their capabilities on large-scale graph data. In this article, we propose a novel neural architecture search (NAS) method for designing deep GNNs automatically and further exploit the application potential on various node classification tasks. Our innovations lie in two aspects, where we first redesign the deep GNNs search space for architecture search with a decoupled mode based on propagation and transformation processes, and we then formulate and solve the problem as a multiobjective optimization to balance accuracy and computational efficiency. Experiments on benchmark graph datasets show that our method performs very well on various node classification tasks, and exploiting large-scale graph datasets further validates that our proposed method is scalable.
KAN versus MLP on Irregular or Noisy Functions
https://arxiv.org/abs/2408.07906
In this paper, we compare the performance of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions. We control the number of parameters and the size of the training samples to ensure a fair comparison. For clarity, we categorize the functions into six types: regular functions, continuous functions with local non-differentiable points, functions with jump discontinuities, functions with singularities, functions with coherent oscillations, and noisy functions. Our experimental results indicate that KAN does not always perform best. For some types of functions, MLP outperforms or performs comparably to KAN. Furthermore, increasing the size of training samples can improve performance to some extent. When noise is added to functions, the irregular features are often obscured by the noise, making it challenging for both MLP and KAN to extract these features effectively. We hope these experiments provide valuable insights for future neural network research and encourage further investigations to overcome these challenges.
Massive Dimensions Reduction and Hybridization with Meta-heuristics in Deep Learning
https://arxiv.org/abs/2408.07194
Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In this modern deep learning era, the state-of-the-art DNN models have millions and billions of parameters, including weights and biases, making them huge-scale optimization problems in terms of search space. Tuning a huge number of parameters is a challenging task that causes vanishing/exploding gradients and overfitting; likewise, utilized loss functions do not exactly represent our targeted performance metrics. A practical solution to exploring large and complex solution space is meta-heuristic algorithms. Since DNNs exceed thousands and millions of parameters, even robust meta-heuristic algorithms, such as Differential Evolution, struggle to efficiently explore and converge in such huge-dimensional search spaces, leading to very slow convergence and high memory demand. To tackle the mentioned curse of dimensionality, the concept of blocking was recently proposed as a technique that reduces the search space dimensions by grouping them into blocks. In this study, we aim to introduce Histogram-based Blocking Differential Evolution (HBDE), a novel approach that hybridizes gradient-based and gradient-free algorithms to optimize parameters. Experimental results demonstrated that the HBDE could reduce the parameters in the ResNet-18 model from 11M to 3K during the training/optimizing phase by metaheuristics, namely, the proposed HBDE, which outperforms baseline gradient-based and parent gradient-free DE algorithms evaluated on CIFAR-10 and CIFAR-100 datasets showcasing its effectiveness with reduced computational demands for the very first time.
进化学习
Deep Learning: a Heuristic Three-stage Mechanism for Grid Searches to Optimize the Future Risk Prediction of Breast Cancer Metastasis Using EHR-based Clinical Data
https://arxiv.org/abs/2408.07673
A grid search, at the cost of training and testing a large number of models, is an effective way to optimize the prediction performance of deep learning models. A challenging task concerning grid search is the time management. Without a good time management scheme, a grid search can easily be set off as a mission that will not finish in our lifetime. In this study, we introduce a heuristic three-stage mechanism for managing the running time of low-budget grid searches, and the sweet-spot grid search (SSGS) and randomized grid search (RGS) strategies for improving model prediction performance, in predicting the 5-year, 10-year, and 15-year risk of breast cancer metastasis. We develop deep feedforward neural network (DFNN) models and optimize them through grid searches. We conduct eight cycles of grid searches by applying our three-stage mechanism and SSGS and RGS strategies. We conduct various SHAP analyses including unique ones that interpret the importance of the DFNN-model hyperparameters. Our results show that grid search can greatly improve model prediction. The grid searches we conducted improved the risk prediction of 5-year, 10-year, and 15-year breast cancer metastasis by 18.6%, 16.3%, and 17.3% respectively, over the average performance of all corresponding models we trained using the RGS strategy. We not only demonstrate best model performance but also characterize grid searches from various aspects such as their capabilities of discovering decent models and the unit grid search time. The three-stage mechanism worked effectively. It made our low-budget grid searches feasible and manageable, and in the meantime helped improve model prediction performance. Our SHAP analyses identified both clinical risk factors important for the prediction of future risk of breast cancer metastasis, and DFNN-model hyperparameters important to the prediction of performance scores.
Impacts of Darwinian Evolution on Pre-trained Deep Neural Networks
https://arxiv.org/abs/2408.05563
Darwinian evolution of the biological brain is documented through multiple lines of evidence, although the modes of evolutionary changes remain unclear. Drawing inspiration from the evolved neural systems (e.g., visual cortex), deep learning models have demonstrated superior performance in visual tasks, among others. While the success of training deep neural networks has been relying on back-propagation (BP) and its variants to learn representations from data, BP does not incorporate the evolutionary processes that govern biological neural systems. This work proposes a neural network optimization framework based on evolutionary theory. Specifically, BP-trained deep neural networks for visual recognition tasks obtained from the ending epochs are considered the primordial ancestors (initial population). Subsequently, the population evolved with differential evolution. Extensive experiments are carried out to examine the relationships between Darwinian evolution and neural network optimization, including the correspondence between datasets, environment, models, and living species. The empirical results show that the proposed framework has positive impacts on the network, with reduced over-fitting and an order of magnitude lower time complexity compared to BP. Moreover, the experiments show that the proposed framework performs well on deep neural networks and big datasets.
应用研究
Migrant Resettlement by Evolutionary Multi-objective Optimization, IEEE TAI
https://ieeexplore.ieee.org/document/10636230
Migration has been a universal phenomenon, which brings opportunities as well as challenges for global development. As the number of migrants (e.g., refugees) increases rapidly, a key challenge faced by each country is the problem of migrant resettlement. This problem has attracted scientific research attention, from the perspective of maximizing the employment rate. Previous works mainly formulated migrant resettlement as an approximately submodular optimization problem subject to multiple matroid constraints and employed the greedy algorithm, whose performance, however, may be limited due to its greedy nature. In this paper, we propose a new framework called Migrant Resettlement by Evolutionary Multi-objective Optimization (MR-EMO), which reformulates migrant resettlement as a bi-objective optimization problem that maximizes the expected number of employed migrants and minimizes the number of dispatched migrants simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve the bi-objective problem. We implement MR-EMO using three MOEAs: the popular Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) as well as the theoretically grounded Global Simple Evolutionary Multi-objective Optimizer (GSEMO). To further improve the performance of MR-EMO, we propose a specific MOEA, called Global Simple Evolutionary Multi-objective Optimizer using matrix-Swap mutation and Repair mechanism (GSEMO-SR), which has a better ability to search for feasible solutions. We prove that MR-EMO using either GSEMO or GSEMO-SR can achieve better theoretical guarantees than the previous greedy algorithm. Experimental results under the interview and coordination migration models clearly show the superiority of MR-EMO (with either NSGA-II, MOEA/D, GSEMO or GSEMO-SR) over previous algorithms, and that using GSEMO-SR leads to the best performance of MR-EMO.
Compact Multi-tasking Multi-chromosome Genetic Algorithm for Heuristic Selection in Ontology Matching, IEEE TAI
https://ieeexplore.ieee.org/document/10634573
Ontology Matching (OM) is critical for knowledge integration and system interoperability on the semantic web, tasked with identifying semantically related entities across different ontologies. Despite its importance, the complexity of terminology semantics and the large number of potential matches present significant challenges. Existing methods often struggle to balance between accurately capturing the multifaceted nature of semantic relationships and computational efficiency. This work introduces a novel approach, a compact multi-tasking multi-chromosome genetic algorithm for Heuristic Selection (HS) in OM, designed to navigate the nuanced hierarchical structure of ontologies and diverse entity mapping preferences. Our method combines compact genetic algorithms with multi-chromosome optimization for entity sequencing and assigning HS, alongside an adaptive knowledge transfer mechanism to finely balance exploration and exploitation efforts. Evaluated on the Ontology Alignment Evaluation Initiative’s benchmark, our algorithm demonstrates superior ability to produce high-quality ontology alignments efficiently, surpassing comparative methods in both effectiveness and efficiency. These findings underscore the potential of advanced genetic algorithms in enhancing OM processes, offering significant contributions to the broader AI field by improving the interoperability and knowledge integration capabilities of semantic web technologies.
An improved continuous-encoding-based multiobjective evolutionary algorithm for community detection in complex networks, IEEE TAI
https://ieeexplore.ieee.org/document/10634576
Community detection is a fundamental and widely studied field in network science. To perform community detection, various competitive multiobjective evolutionary algorithms have been proposed. It is worth noting that the latest continuous encoding method transforms the original discrete problem into a continuous one, which can achieve better community partitioning. However, the original continuous encoding ignored important structural features of nodes, such as the clustering coefficient, resulting in poor initial solutions and reduced the performance of community detection. Therefore, we propose a simple scheme to effectively utilize node structure feature vectors to enhance community detection. Specifically, a continuous encoding and clustering coefficient-based multiobjective evolutionary algorithm called CECC-Net is proposed. In CECC-Net, the clustering coefficient vector performs the Hadamard product with a continuous vector (i.e., a concatenation of the continuous variables x associated with the edges), resulting in an improved initial individual. Then, applying the nonlinear transformation to the continuous-valued individual yields a discrete-valued community grouping solution. Furthermore, a corresponding adaptive operator is designed as an essential part of this scheme to mitigate the negative effects of feature vectors on population diversity. The effectiveness of the proposed scheme was validated through ablation and comparative experiments. Experimental results on synthetic and real-world networks demonstrate that the proposed algorithm has competitive performance in comparison with several state-of-the-art EA-based community detection algorithms.
Hardening Active Directory Graphs via Evolutionary Diversity Optimization based Policies, ACM TELO
https://dl.acm.org/doi/10.1145/3688401
Active Directory (AD) is the default security management system for Windows domain networks. An AD environment can be described as a cyber-attack graph, with nodes representing computers, accounts, etc., and edges indicating existing accesses or known exploits that enable attackers to move from one node to another. This paper explores a Stackelberg game model between one attacker and one defender on an AD attack graph. The attacker’s goal is to maximize their chances of successfully reaching the destination before getting detected. The defender’s aim is to block a constant number of edges to minimize the attacker’s chance of success. The paper shows that the problem is #P-hard and, therefore, intractable to solve exactly. To defend the AD graph from cyber attackers, this paper proposes two defensive approaches. In the first approach, we convert the attacker’s problem to an exponential sized Dynamic Program that is approximated by a Neural Network (NN). Once trained, the NN serves as an efficient fitness function for defender’s Evolutionary Diversity Optimization based defensive policy. The diversity emphasis on the defender’s solution provides a diverse set of training samples, improving the training accuracy of our NN for modeling the attacker. In the second approach, we propose a RL based policy to solve the attacker’s problem and Critic network assisted Evolutionary Diversity Optimization based defensive policy to solve defender’s problem. Experimental results on synthetic AD graphs show that the proposed defensive policies are scalable, highly effective, approximate attacker’s problem accurately, and generate good defensive plans.
Enhanced Optimization Strategies to Design an Underactuated Hand Exoskeleton
https://arxiv.org/abs/2408.07384
Exoskeletons can boost human strength and provide assistance to individuals with physical disabilities. However, ensuring safety and optimal performance in their design poses substantial challenges. This study presents the design process for an underactuated hand exoskeleton (U-HEx), first including a single objective (maximizing force transmission), then expanding into multi objective (also minimizing torque variance and actuator displacement). The optimization relies on a Genetic Algorithm, the Big Bang-Big Crunch Algorithm, and their versions for multi-objective optimization. Analyses revealed that using Big Bang-Big Crunch provides high and more consistent results in terms of optimality with lower convergence time. In addition, adding more objectives offers a variety of trade-off solutions to the designers, who might later set priorities for the objectives without repeating the process - at the cost of complicating the optimization algorithm and computational burden. These findings underline the importance of performing proper optimization while designing exoskeletons, as well as providing a significant improvement to this specific robotic design.
