Closed-form differential equations, including partial differential equations and higher-order ordinary differential equations, are one of the most important tools used by scientists to model and better understand natural phenomena. Discovering these equations directly from data is challenging because it requires modeling relationships between various derivatives that are not observed in the data (equation-data mismatch) and it involves searching across a huge space of possible equations. Current approaches make strong assumptions about the form of the equation and thus fail to discover many well-known systems. Moreover, many of them resolve the equation-data mismatch by estimating the derivatives, which makes them inadequate for noisy and infrequently sampled systems. To this end, we propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations. We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently. Finally, we demonstrate empirically that it can discover many well-known equations that are beyond the capabilities of current methods.

Interstitial diffusion is a pivotal process that governs the phase stability and irradiation response of materials in non-equilibrium conditions. In this work, we study sluggish and chemically-biased interstitial diffusion in Fe-Ni concentrated solid solution alloys (CSAs) by combining machine learning (ML) and kinetic Monte Carlo (kMC), where ML is used to accurately and efficiently predict the migration energy barriers on-the-fly. The ML-kMC reproduces the diffusivity that was reported by molecular dynamics results at high temperatures. With this powerful tool, we find that the observed sluggish diffusion and the "Ni-Ni-Ni"-biased diffusion in Fe-Ni alloys are ascribed to a unique "Barrier Lock" mechanism, whereas the "Fe-Fe-Fe"-biased diffusion is influenced by a "Component Dominance" mechanism. Inspired by the mentioned mechanisms, a practical AvgS-kMC method is proposed for conveniently and swiftly determining interstitial-mediated diffusivity by only relying on the mean energy barriers of migration patterns. Combining the AvgS-kMC with the differential evolutionary algorithm, an inverse design strategy for optimizing sluggish diffusion properties is applied to emphasize the crucial role of favorable migration patterns.

Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and $\sigma_8$. We learn the ratio between an existing low-accuracy fitting function for $P(k)$ and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2% between $k = 9\times10^{-3} - 9 \, h{\rm \, Mpc^{-1}}$ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. We also provide a simple analytic approximation for $\sigma_8$ with a similar accuracy, with a root mean squared fractional error of just 0.4% when evaluated across the same range of cosmologies. This function is easily invertible to obtain $A_{\rm s}$ as a function of $\sigma_8$ and the other cosmological parameters, if preferred. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

This paper investigates the optimization problem of scheduling autonomous mobile robots (AMRs) in hospital settings, considering dynamic requests with different priorities. The primary objective is to minimize the daily service cost by dynamically planning routes for the limited number of available AMRs. The total cost consists of AMR's purchase cost, transportation cost, delay penalty cost, and loss of denial of service. To address this problem, we have established a two-stage mathematical programming model. In the first stage, a tabu search algorithm is employed to plan prior routes for all known medical requests. The second stage involves planning for real-time received dynamic requests using the efficient insertion algorithm with decision rules, which enables quick response based on the time window and demand constraints of the dynamic requests. One of the main contributions of this study is to make resource allocation decisions based on the present number of service AMRs for dynamic requests with different priorities. Computational experiments using Lackner instances demonstrate the efficient insertion algorithm with decision rules is very fast and robust in solving the dynamic AMR routing problem with time windows and request priority. Additionally, we provide managerial insights concerning the AMR's safety stock settings, which can aid in decision-making processes.

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA.

There are many combinatorial optimization problems whose solutions are best represented by permutations. The classic traveling salesperson seeks an optimal ordering over a set of cities. Scheduling problems often seek optimal orderings of tasks or activities. Although some evolutionary approaches to such problems utilize the bit strings of a genetic algorithm, it is more common to directly represent solutions with permutations. Evolving permutations directly requires specialized evolutionary operators. Over the years, many crossover and mutation operators have been developed for solving permutation problems with evolutionary algorithms. In this paper, we survey the breadth of evolutionary operators for permutations. We implemented all of these in Chips-n-Salsa, an open source Java library for evolutionary computation. Finally, we empirically analyze the crossover operators on artificial fitness landscapes isolating different permutation features.

The rise of renewables coincides with the shift towards Electrical Vehicles (EVs) posing technical and operational challenges for the energy balance of the local grid. Nowadays, the energy grid cannot deal with a spike in EVs usage leading to a need for more coordinated and grid aware EVs charging and discharging strategies. However, coordinating power flow from multiple EVs into the grid requires sophisticated algorithms and load-balancing strategies as the complexity increases with more control variables and EVs, necessitating large optimization and decision search spaces. In this paper, we propose an EVs fleet coordination model for the day ahead aiming to ensure a reliable energy supply and maintain a stable local grid, by utilizing EVs to store surplus energy and discharge it during periods of energy deficit. The optimization problem is addressed using Harris Hawks Optimization (HHO) considering criteria related to energy grid balancing, time usage preference, and the location of EV drivers. The EVs schedules, associated with the position of individuals from the population, are adjusted through exploration and exploitation operations, and their technical and operational feasibility is ensured, while the rabbit individual is updated with a non-dominated EV schedule selected per iteration using a roulette wheel algorithm. The solution is evaluated within the framework of an e-mobility service in Terni city. The results indicate that coordinated charging and discharging of EVs not only meet balancing service requirements but also align with user preferences with minimal deviations. The assessment of the determined solutions' quality and efficacy shows promising outcomes, with convergence after 100 iterations reflected in a generational distance of 0.35 and a Pareto front error of 1.01, while the distribution of solutions exhibits strong hypervolume thus covering a significant portion of the objective space.

Despite the recent success in a plethora of hyperparameter optimization (HPO) methods for machine learning (ML) models, the intricate interplay between model hyperparameters (HPs) and predictive losses (a.k.a fitness), which is a key prerequisite for understanding HPO, remain notably underexplored in our community. This results in limited explainability in the HPO process, rendering a lack of human trust and difficulties in pinpointing algorithm bottlenecks. In this paper, we aim to shed light on this black box by conducting large-scale fitness landscape analysis (FLA) on 1,500 HP loss landscapes of 6 ML models with more than 11 model configurations, across 67 datasets and different levels of fidelities. We reveal the first unified, comprehensive portrait of their topographies in terms of smoothness, neutrality and modality. We also show that such properties are highly transferable across datasets and fidelities, providing fundamental evidence for the success of multi-fidelity and transfer learning methods. These findings are made possible by developing a dedicated FLA framework that incorporates a combination of visual and quantitative measures. We further demonstrate the potential of this framework by analyzing the NAS-Bench-101 landscape, and we believe it is able to faciliate fundamental understanding of a broader range of AutoML tasks.

Optimization problems find widespread use in both single-objective and multiobjective scenarios. In practical applications, users aspire for solutions that converge to the region of interest (ROI) along the Pareto front (PF). While the conventional approach involves approximating a fitness function or an objective function to reflect user preferences, this paper explores an alternative avenue. Specifically, we aim to discover a method that sidesteps the need for calculating the fitness function, relying solely on human feedback. Our proposed approach entails conducting direct preference learning facilitated by an active dueling bandit algorithm. The experimental phase is structured into three sessions. Firstly, we assess the performance of our active dueling bandit algorithm. Secondly, we implement our proposed method within the context of Multi-objective Evolutionary Algorithms (MOEAs). This research presents a novel interactive preference-based MOEA framework that not only addresses the limitations of traditional techniques but also unveils new possibilities for optimization problems. In optimization problems, algorithms typically converge to the Pareto front (PF), yet users aim for convergence in their specific region of interest (ROI).

This paper studies the scheduling of autonomous mobile robots (AMRs) at hospitals where the stochastic travel times and service times of AMRs are affected by the surrounding environment. The routes of AMRs are planned to minimize the daily cost of the hospital (including the AMR fixed cost, penalty cost of violating the time window, and transportation cost). To efficiently generate high-quality solutions, some properties are identified and incorporated into an improved tabu search (I-TS) algorithm for problem-solving. Experimental evaluations demonstrate that the I-TS algorithm outperforms existing methods by producing high-quality solutions. Based on the characteristics of healthcare requests and the AMR working environment, scheduling AMRs reasonably can effectively provide medical services, improve the utilization of medical resources, and reduce hospital costs.