This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and boundary conditions, demonstrating its accuracy and ability to find approximate solutions efficiently. This framework offers a promising, scalable solution for finding approximate solutions to differential equations, with the potential for future improvements in computational performance and applicability to more complex systems involving vector-valued objectives.

Natural terrain complexity often necessitates agile movements like jumping in animals to improve traversal efficiency. To enable similar capabilities in quadruped robots, complex real-time jumping maneuvers are required. Current research does not adequately address the problem of online omnidirectional jumping and neglects the robot's kinodynamic constraints during trajectory generation. This paper proposes a general and complete cascade online optimization framework for omnidirectional jumping for quadruped robots. Our solution systematically encompasses jumping trajectory generation, a trajectory tracking controller, and a landing controller. It also incorporates environmental perception to navigate obstacles that standard locomotion cannot bypass, such as jumping from high platforms. We introduce a novel jumping plane to parameterize omnidirectional jumping motion and formulate a tightly coupled optimization problem accounting for the kinodynamic constraints, simultaneously optimizing CoM trajectory, Ground Reaction Forces (GRFs), and joint states. To meet the online requirements, we propose an accelerated evolutionary algorithm as the trajectory optimizer to address the complexity of kinodynamic constraints. To ensure stability and accuracy in environmental perception post-landing, we introduce a coarse-to-fine relocalization method that combines global Branch and Bound (BnB) search with Maximum a Posteriori (MAP) estimation for precise positioning during navigation and jumping. The proposed framework achieves jump trajectory generation in approximately 0.1 seconds with a warm start and has been successfully validated on two quadruped robots on uneven terrains. Additionally, we extend the framework's versatility to humanoid robots.

This paper aims to make a mark in the future of sustainable robotics, where efficient algorithms are required to carry out tasks like environmental monitoring and precision agriculture efficiently. We proposed a hybrid algorithm that combines Artificial Bee Colony (ABC) with Levy flight to optimize adaptive sensor placement alongside an important notion of hotspots from domain knowledge experts. By enhancing exploration and exploitation, our approach significantly improves the identification of critical hotspots. This algorithm also finds its usecases for broader search and rescue operations applications, demonstrating its potential in optimization problems across various domains.

The main challenge of multimodal optimization problems is identifying multiple peaks with high accuracy in multidimensional search spaces with irregular landscapes. This work proposes the Multiple Global Peaks Big Bang-Big Crunch (MGP-BBBC) algorithm, which addresses the challenge of multimodal optimization problems by introducing a specialized mechanism for each operator. The algorithm expands the Big Bang-Big Crunch algorithm, a state-of-the-art metaheuristic inspired by the universe's evolution. Specifically, MGP-BBBC groups the best individuals of the population into cluster-based centers of mass and then expands them with a progressively lower disturbance to guarantee convergence. During this process, it (i) applies a distance-based filtering to remove unnecessary elites such that the ones on smaller peaks are not lost, (ii) promotes isolated individuals based on their niche count after clustering, and (iii) balances exploration and exploitation during offspring generation to target specific accuracy levels. Experimental results on twenty multimodal benchmark test functions show that MGP-BBBC generally performs better or competitively with respect to other state-of-the-art multimodal optimizers.

From ancient to modern times, acoustic structures have been used to control the propagation of acoustic waves. However, the design of the acoustic structures has remained widely a time-consuming and computational resource-consuming iterative process. In recent years, Deep Learning has attracted unprecedented attention for its ability to tackle hard problems with huge datasets, which has achieved state-of-the-art results in various tasks. In this work, an acoustic structure design method is proposed based on deep learning. Taking the design of multi-order Helmholtz resonator for instance, we experimentally demonstrate the effectiveness of the proposed method. Our method is not only able to give a very accurate prediction of the geometry of the acoustic structures with multiple strong-coupling parameters, but also capable of improving the performance of evolutionary approaches in optimization for a desired property. Compared with the conventional numerical methods, our method is more efficient, universal and automatic, which has a wide range of potential applications, such as speech enhancement, sound absorption and insulation.

Opposition-based learning (OBL) is an effective approach to improve the performance of metaheuristic optimization algorithms, which are commonly used for solving complex engineering problems. This chapter provides a comprehensive review of the literature on the use of opposition strategies in metaheuristic optimization algorithms, discussing the benefits and limitations of this approach. An overview of the opposition strategy concept, its various implementations, and its impact on the performance of metaheuristic algorithms are presented. Furthermore, case studies on the application of opposition strategies in engineering problems are provided, including the optimum locating of control systems in tall building. A shear frame with Magnetorheological (MR) fluid damper is considered as a case study. The results demonstrate that the incorporation of opposition strategies in metaheuristic algorithms significantly enhances the quality and speed of the optimization process. This chapter aims to provide a clear understanding of the opposition strategy in metaheuristic optimization algorithms and its engineering applications, with the ultimate goal of facilitating its adoption in real-world engineering problems.

Metaheuristics are stochastic optimization algorithms that mimic natural processes to find optimal solutions to complex problems. The success of metaheuristics largely depends on the ability to effectively explore and exploit the search space. Memory mechanisms have been introduced in several popular metaheuristic algorithms to enhance their performance. This chapter explores the significance of memory in metaheuristic algorithms and provides insights from well-known algorithms. The chapter begins by introducing the concept of memory, and its role in metaheuristic algorithms. The key factors influencing the effectiveness of memory mechanisms are discussed, such as the size of the memory, the information stored in memory, and the rate of information decay. A comprehensive analysis of how memory mechanisms are incorporated into popular metaheuristic algorithms is presented, and concludes by highlighting the importance of memory in metaheuristic performance and providing future research directions for improving memory mechanisms. The key takeaways are that memory mechanisms can significantly enhance the performance of metaheuristics by enabling them to explore and exploit the search space effectively and efficiently, and that the choice of memory mechanism should be tailored to the problem domain and the characteristics of the search space.

An improved bilinear fuzzy genetic algorithm (BFGA) is introduced in this chapter for the design optimization of steel structures with semi-rigid connections. Semi-rigid connections provide a compromise between the stiffness of fully rigid connections and the flexibility of fully pinned connections. However, designing such structures is challenging due to the non-linear behavior of semi-rigid connections. The BFGA is a robust optimization method that combines the strengths of fuzzy logic and genetic algorithm to handle the complexity and uncertainties of structural design problems. The BFGA, compared to standard GA, demonstrated to generate highquality solutions in a reasonable time. The application of the BFGA is demonstrated through the optimization of steel structures with semi-rigid connections, considering the weight, and performance criteria. The results show that the proposed BFGA is capable of finding optimal designs that satisfy all the design requirements and constraints. The proposed approach provides a promising solution for the optimization of complex structures with non-linear behavior.

Evolutionary Multi-Objective Optimization Algorithms (EMOAs) are widely employed to tackle problems with multiple conflicting objectives. Recent research indicates that not all objectives are equally important to the decision-maker (DM). In the context of interactive EMOAs, preference information elicited from the DM during the optimization process can be leveraged to identify and discard irrelevant objectives, a crucial step when objective evaluations are computationally expensive. However, much of the existing literature fails to account for the dynamic nature of DM preferences, which can evolve throughout the decision-making process and affect the relevance of objectives. This study addresses this limitation by simulating dynamic shifts in DM preferences within a ranking-based interactive algorithm. Additionally, we propose methods to discard outdated or conflicting preferences when such shifts occur. Building on prior research, we also introduce a mechanism to safeguard relevant objectives that may become trapped in local or global optima due to the diminished correlation with the DM-provided rankings. Our experimental results demonstrate that the proposed methods effectively manage evolving preferences and significantly enhance the quality and desirability of the solutions produced by the algorithm.

Symbolic regression, a task discovering the formula best fitting the given data, is typically based on the heuristical search. These methods usually update candidate formulas to obtain new ones with lower prediction errors iteratively. However, since formulas with similar function shapes may have completely different symbolic forms, the prediction error does not decrease monotonously as the search approaches the target formula, causing the low recovery rate of existing methods. To solve this problem, we propose a novel search objective based on the minimum description length, which reflects the distance from the target and decreases monotonically as the search approaches the correct form of the target formula. To estimate the minimum description length of any input data, we design a neural network, MDLformer, which enables robust and scalable estimation through large-scale training. With the MDLformer's output as the search objective, we implement a symbolic regression method, SR4MDL, that can effectively recover the correct mathematical form of the formula. Extensive experiments illustrate its excellent performance in recovering formulas from data. Our method successfully recovers around 50 formulas across two benchmark datasets comprising 133 problems, outperforming state-of-the-art methods by 43.92%.