BUSTLE: a Versatile Tool for the Evolutionary Learning of STL Specifications from Data.

Describing the properties of complex systems that evolve over time is a crucial requirement for monitoring and understanding them. Signal Temporal Logic (STL) is a framework that proved to be effective for this aim because it is expressive and allows state properties as human-readable formulae. Crafting STL formulae that fit a particular system is, however, a difficult task. For this reason, a few approaches have been proposed recently for the automatic learning of STL formulae starting from observations of the system. In this paper, we propose BUSTLE (Bi-level Universal STL Evolver), an approach based on evolutionary computation for learning STL formulae from data. BUSTLE advances the state-of-the-art because it (i) applies to a broader class of problems, in terms of what is known about the state of the system during its observation, and (ii) generates both the structure and the values of the parameters of the formulae employing a bi-level search mechanism (global for the structure, local for the parameters). We consider two cases where (a) observations of the system in both anomalous and regular state are available, or (b) only observations of regular state are available. We experimentally evaluate BUSTLE on problem instances corresponding to the two cases and compare it against previous approaches. We show that the evolved STL formulae are effective and human-readable: the versatility of BUSTLE does not come at the cost of lower effectiveness.

Leader-follower equilibria to examine investment decisions in grid resilience-enhancing measures.

Large-area, long-duration power outages are increasingly common in the United States, and cost the economy billions of dollars each year. Building a strategy to enhance grid resilience requires an understanding of the optimal mix of preventive and corrective actions, the inefficiencies that arise when self-interested parties make resilience investment decisions, and the conditions under which regulators may facilitate the realization of efficient market outcomes. We develop a bi-level model to examine the mix of preventive and corrective measures that enhances grid resilience to a severe storm. The model represents a Stackelberg game between a regulated utility (leader) that may harden distribution feeders before a long-duration outage and/or deploy restoration crews after the disruption, and utility customers with varying preferences for reliable power (followers) who may invest in backup generators. We show that the regulator's denial of cost recovery for the utility's preventive expenditures, coupled with the misalignment between private objectives and social welfare maximization, yields significant inefficiencies in the resilience investment mix. Allowing cost recovery for a higher share of the utility's capital expenditures in preventive measures, extending the time horizon associated with damage cost recovery, and adopting a storm restoration compensation mechanism shift the realized market outcome toward the efficient solution. If about one-fifth of preventive resilience investments is approved by regulators, requiring utilities to pay a compensation of $365 per customer for a 3-day outage (about seven times the level of compensation currently offered by US utilities) provides significant incentives toward more efficient preventive resilience investments.

MetaSEM: Gene Regulatory Network Inference from Single-Cell RNA Data by Meta-Learning.

Regulators in gene regulatory networks (GRNs) are crucial for identifying cell states. However, GRN inference based on scRNA-seq data has several problems, including high dimensionality and sparsity, and requires more label data. Therefore, we propose a meta-learning GRN inference framework to identify regulatory factors. Specifically, meta-learning solves the parameter optimization problem caused by high-dimensional sparse data features. In addition, a few-shot solution was used to solve the problem of lack of label data. A structural equation model (SEM) was embedded in the model to identify important regulators. We integrated the parameter optimization strategy into the bi-level optimization to extract the feature consistent with GRN reasoning. This unique design makes our model robust to small-scale data. By studying the GRN inference task, we confirmed that the selected regulators were closely related to gene expression specificity. We further analyzed the GRN inferred to find the important regulators in cell type identification. Extensive experimental results showed that our model effectively captured the regulator in single-cell GRN inference. Finally, the visualization results verified the importance of the selected regulators for cell type recognition.

Optimal allocation and transaction of waste load permits for transboundary basin: A Bi-level programming approach based on node-arc.

Inadequate water quality exacerbates global water resources scarcity. Hence, water quality of the river basin is increasingly perceived as a global obstacle to sustainable development because of the limited water carrying capacity. Efficient waste load permits (WLPs) allocation plays a critical role in enhancing water quality by controlling the emission cap. Considering transboundary water pollution and transaction among regions, a bi-level objective model is proposed to analyze the WLPs allocation based on the node-arc method. Motivated by alleviating regional development differences, the watershed management committee concentrates on equitable distribution of WLPs to regions. Furthermore, regional authorities focus on how to guarantee the maximum economic development and balance the WLPs emissions from the municipal, industrial, and agricultural sectors. Practicality and efficiency of the constructed model is demonstrated by applying it to Tuojiang River Basin. Through the analysis of the results, three management recommendations are proposed for Tuojiang River: strengthening the prevention of agricultural non-point source pollution, sticking to the cooperation between upstream and downstream regions, and speeding up the construction of sewage environmental tax system. The results illustrate that as the proposed method can control the total amount of sewage, it could provide decision-making references for the amelioration of water environment.

Generic Structure Extraction with Bi-Level Optimization for Graph Structure Learning.

Currently, most Graph Structure Learning (GSL) methods, as a means of learning graph structure, improve the robustness of GNN merely from a local view by considering the local information related to each edge and indiscriminately applying the mechanism across edges, which may suffer from the local structure heterogeneity of the graph (i.e., the uneven distribution of inter-class connections over nodes). To overcome the drawbacks, we extract the graph structure as a learnable parameter and jointly learn the structure and common parameters of GNN from the global view. Excitingly, the common parameters contain the global information for nodes features mapping, which is also crucial for structure optimization (i.e., optimizing the structure relies on global mapping information). Mathematically, we apply a generic structure extractor to abstract the graph structure and transform GNNs in the form of learning structure and common parameters. Then, we model the learning process as a novel bi-level optimization, i.e., Generic Structure Extraction with Bi-level Optimization for Graph Structure Learning (GSEBO), which optimizes GNN parameters in the upper level to obtain the global mapping information and graph structure is optimized in the lower level with the global information learned from the upper level. We instantiate the proposed GSEBO on classical GNNs and compare it with the state-of-the-art GSL methods. Extensive experiments validate the effectiveness of the proposed GSEBO on four real-world datasets.

The promise of dawn: Microalgae photoacclimation as an optimal control problem of resource allocation.

Photosynthetic microorganisms are known to adjust their photosynthetic capacity according to light intensity. This so-called photoacclimation process is thought to maximize growth at equilibrium, but its dynamics under varying conditions remains less understood. To tackle this problem, microalgae growth and photoacclimation are represented by a (coarse-grained) resource allocation model. Using optimal control theory (the Pontryagin maximum principle) and numerical simulations, we determine the optimal strategy of resource allocation to maximize microalgal growth rate over a time horizon. We show that, after a transient, the optimal trajectory approaches the optimal steady state, a behavior known as the turnpike property. Then, a bi-level optimization problem is solved numerically to estimate model parameters from experimental data. The fitted trajectory represents well a Dunaliella tertiolecta culture facing a light down-shift. Finally, we study photoacclimation dynamics under day/night cycle. In the optimal trajectory, the synthesis of the photosynthetic apparatus surprisingly starts a few hours before dawn. This anticipatory behavior has actually been observed both in the laboratory and in the field. This shows the algal predictive capacity and the interest of our method which predicts this phenomenon.

Novel metaheuristic based on multiverse theory for optimization problems in emerging systems.

Finding an optimal solution for emerging cyber physical systems (CPS) for better efficiency and robustness is one of the major issues. Meta-heuristic is emerging as a promising field of study for solving various optimization problems applicable to different CPS systems. In this paper, we propose a new meta-heuristic algorithm based on Multiverse Theory, named MVA, that can solve NP-hard optimization problems such as non-linear and multi-level programming problems as well as applied optimization problems for CPS systems. MVA algorithm inspires the creation of the next population to be very close to the solution of initial population, which mimics the nature of parallel worlds in multiverse theory. Additionally, MVA distributes the solutions in the feasible region similarly to the nature of big bangs. To illustrate the effectiveness of the proposed algorithm, a set of test problems is implemented and measured in terms of feasibility, efficiency of their solutions and the number of iterations taken in finding the optimum solution. Numerical results obtained from extensive simulations have shown that the proposed algorithm outperforms the state-of-the-art approaches while solving the optimization problems with large feasible regions.

A bi-level chance-constrained programming method for quantifying the effectiveness of water-trading to water-food-ecology nexus in Amu Darya River basin of Central Asia.

Issues of water scarcity, food crisis, and ecological degradation pose great challenges to the sustainable development of Central Asia. In this study, a bi-level chance-constrained programming (BCCP) method is developed for planning water-food-ecology (WFE) nexus system of the Amu Darya River basin, where the efficiency of water-trading mechanism and the impact of uncertain water-availability are examined. This is the first attempt for planning WFE nexus system by incorporating chance-constrained programming (CCP) within a bi-level optimization framework. BCCP can reflect the risk of violating probabilistic constraint under uncertainty as well as balance the tradeoff between two-level decision makers in the WFE nexus system. Under trading scheme, multiple scenarios in association with different food demand, ecological-water requirement, and water availability are examined. Major findings are: (i) compared with that under non-trading, system benefits would increase [3.9, 20.4]% under trading scenarios, disclosing that water trading is an effective mechanism for the study basin; (ii) when food demand increases 10.5%, water allocated to ecological use would decrease [0.9, 2.7]% under all scenarios, revealing that agriculture can squeeze ecological water; (iii) both system benefit and water allocation would increase with p level, implying there is a tradeoff between system benefit and system-failure risk. These findings can gain insight into the interaction between two-level stakeholders and objectives as well as provide decision support for WFE nexus synergetic management.

Clustering approaches for visual knowledge exploration in molecular interaction networks.

BACKGROUND: Biomedical knowledge grows in complexity, and becomes encoded in network-based repositories, which include focused, expert-drawn diagrams, networks of evidence-based associations and established ontologies. Combining these structured information sources is an important computational challenge, as large graphs are difficult to analyze visually. RESULTS: We investigate knowledge discovery in manually curated and annotated molecular interaction diagrams. To evaluate similarity of content we use: i) Euclidean distance in expert-drawn diagrams, ii) shortest path distance using the underlying network and iii) ontology-based distance. We employ clustering with these metrics used separately and in pairwise combinations. We propose a novel bi-level optimization approach together with an evolutionary algorithm for informative combination of distance metrics. We compare the enrichment of the obtained clusters between the solutions and with expert knowledge. We calculate the number of Gene and Disease Ontology terms discovered by different solutions as a measure of cluster quality. Our results show that combining distance metrics can improve clustering accuracy, based on the comparison with expert-provided clusters. Also, the performance of specific combinations of distance functions depends on the clustering depth (number of clusters). By employing bi-level optimization approach we evaluated relative importance of distance functions and we found that indeed the order by which they are combined affects clustering performance. Next, with the enrichment analysis of clustering results we found that both hierarchical and bi-level clustering schemes discovered more Gene and Disease Ontology terms than expert-provided clusters for the same knowledge repository. Moreover, bi-level clustering found more enriched terms than the best hierarchical clustering solution for three distinct distance metric combinations in three different instances of disease maps. CONCLUSIONS: In this work we examined the impact of different distance functions on clustering of a visual biomedical knowledge repository. We found that combining distance functions may be beneficial for clustering, and improve exploration of such repositories. We proposed bi-level optimization to evaluate the importance of order by which the distance functions are combined. Both combination and order of these functions affected clustering quality and knowledge recognition in the considered benchmarks. We propose that multiple dimensions can be utilized simultaneously for visual knowledge exploration.

Robust mutant strain design by pessimistic optimization.

BACKGROUND: Flux Balance Analysis (FBA) based mathematical modeling enables in silico prediction of systems behavior for genome-scale metabolic networks. Computational methods have been derived in the FBA framework to solve bi-level optimization for deriving "optimal" mutant microbial strains with targeted biochemical overproduction. The common inherent assumption of these methods is that the surviving mutants will always cooperate with the engineering objective by overproducing the maximum desired biochemicals. However, it has been shown that this optimistic assumption may not be valid in practice. METHODS: We study the validity and robustness of existing bi-level methods for strain optimization under uncertainty and non-cooperative environment. More importantly, we propose new pessimistic optimization formulations: P-ROOM and P-OptKnock, aiming to derive robust mutants with the desired overproduction under two different mutant cell survival models: (1) ROOM assuming mutants have the minimum changes in reaction fluxes from wild-type flux values, and (2) the one considered by OptKnock maximizing the biomass production yield. When optimizing for desired overproduction, our pessimistic formulations derive more robust mutant strains by considering the uncertainty of the cell survival models at the inner level and the cooperation between the outer- and inner-level decision makers. For both P-ROOM and P-OptKnock, by converting multi-level formulations into single-level Mixed Integer Programming (MIP) problems based on the strong duality theorem, we can derive exact optimal solutions that are highly scalable with large networks. RESULTS: Our robust formulations P-ROOM and P-OptKnock are tested with a small E. coli core metabolic network and a large-scale E. coli iAF1260 network. We demonstrate that the original bi-level formulations (ROOM and OptKnock) derive mutants that may not achieve the predicted overproduction under uncertainty and non-cooperative environment. The knockouts obtained by the proposed pessimistic formulations yield higher chemical production rates than those by the optimistic formulations. Moreover, with higher uncertainty levels, both cellular models under pessimistic approaches produce the same mutant strains. CONCLUSIONS: In this paper, we propose a new pessimistic optimization framework for mutant strain design. Our pessimistic strain optimization methods produce more robust solutions regardless of the inner-level mutant survival models, which is desired as the models for cell survival are often approximate to real-world systems. Such robust and reliable knockout strategies obtained by the pessimistic formulations would provide confidence for in-vivo experimental design of microbial mutants of interest.

Bi-Level Optimization for De-Icing Position Allocation and Unmanned De-Icing Vehicle Fleet Routing Problem.

Aircraft icing due to severe cold and local factors increases the risk of flight delays and safety issues. Therefore, this study focuses on optimizing de-icing allocation and adapting to dynamic flight schedules at medium to large airports. Moreover, it aims to establish a centralized de-icing methodology employing unmanned de-icing vehicles to achieve the dual objectives of minimizing flight delay times and enhancing airport de-icing efficiency. To achieve these goals, a mixed-integer bi-level programming model is formulated, where the upper-level planning guides the allocation of de-icing positions and the lower-level planning addresses the collaborative scheduling of the multiple unmanned de-icing vehicles. In addition, a two-stage algorithm is introduced, encompassing a Mixed Variable Neighborhood Search Genetic Algorithm (MVNS-GA) as well as a Multi-Strategy Enhanced Heuristic Greedy Algorithm (MSEH-GA). Both algorithms are rigorously assessed through horizontal comparisons. This demonstrates the effectiveness and competitiveness of these algorithms. Finally, a model simulation is conducted at a major northwestern hub airport in China, providing empirical evidence of the proposed approach's efficiency. The results show that research offers a practical solution for optimizing the use of multiple unmanned de-icing vehicles in aircraft de-icing tasks at medium to large airports. Therefore, delays are mitigated, and de-icing operations are improved.

Embedding channel pruning within the CNN architecture design using a bi-level evolutionary approach.

Remarkable advancements have been achieved in machine learning and computer vision through the utilization of deep neural networks. Among the most advantageous of these networks is the convolutional neural network (CNN). It has been used in pattern recognition, medical diagnosis, and signal processing, among other things. Actually, for these networks, the challenge of choosing hyperparameters is of utmost importance. The reason behind this is that as the number of layers rises, the search space grows exponentially. In addition, all known classical and evolutionary pruning algorithms require a trained or built architecture as input. During the design phase, none of them consider the process of pruning. In order to assess the effectiveness and efficiency of any architecture created, pruning of channels must be carried out before transmitting the dataset and computing classification errors. For instance, following pruning, an architecture of medium quality in terms of classification may transform into an architecture that is both highly light and accurate, and vice versa. There exist countless potential scenarios that could occur, which prompted us to develop a bi-level optimization approach for the entire process. The upper level involves generating the architecture while the lower level optimizes channel pruning. Evolutionary algorithms (EAs) have proven effective in bi-level optimization, leading us to adopt the co-evolutionary migration-based algorithm as a search engine for our bi-level architectural optimization problem in this research. Our proposed method, CNN-D-P (bi-level CNN design and pruning), was tested on the widely used image classification benchmark datasets, CIFAR-10, CIFAR-100 and ImageNet. Our suggested technique is validated by means of a set of comparison tests with regard to relevant state-of-the-art architectures.

A bi-level multi-objective programming model for water resources management under compound uncertainties in Dongjiang River Basin, Greater Bay Area of China.

To facilitate regional water resources allocation, an integrated bi-level multi-objective programming (IBMP) model with dual random fuzzy variables was developed in this research The proposed model was derived through incorporating dual random fuzzy variables, multi-objective programming, and interval parameter programming within a bi-level optimization framework. This approach improved upon the previous bi-level programming methods and had two advantages. Firstly, it was capable of reflecting tradeoffs among multiple conflict preferences for water related bi-level hierarchical decision-making processes. Secondly, random fuzzy variables were used to tackle the dual uncertainties in both sides of the constraints, which were characterize as probability density functions and discrete intervals. Then, a real-world water resources planning problem was employed for illustrating feasibility of the application of IBMP model in Dongjiang river watershed of south China. Results reflected the alternative decisions for water allocation schemes under a set of probability levels and fuzzy α - cut levels, which can support in-depth analysis of tradeoffs among multiple levels and objective values. Moreover, modeling comparison analysis was undertaken to illustrate the performances of the proposed model.

A flexible employee recruitment and compensation model: A bi-level optimization approach.

The growing practice of flexible work following the COVID-19 pandemic is likely to have a significant impact on management and human resource (HR) practices. In this paper, we propose a novel bi-level mathematical programming model that can serve as a decision support tool for firms in real-life settings to improve recruitment and compensation decisions associated with hybrid and flexible work plans. The proposed model is composed of two levels: the first level reflects the company's goal of maximizing profitability by offering competitive salaries to candidates. The second level reflects the candidate's goal of minimizing the gap between their desired salary and the perceived benefits of a preferred flexible plan. We show that the model provides an exact solution based on a mixed integer formulation and present a computational analysis based on changing candidate behaviors in response to the firm's strategy, thus demonstrate how the problem's parameters influence the decision policy. Our proposed model leads to efficient managerial practices, compared to conventional models that utilize a single non-flexible plan. Results indicate that introducing a flexible work plan leads to an improvement of up to 59 percent in the firm's profitability. We apply the optimal solution of the bi-level model to a real-world case study of a company recruiting software engineers. Results demonstrate the applicability of the optimal solution to a real-world dataset. This paper advances knowledge by proposing a novel bi-level model for effective recruitment and compensation decisions in real-world flexible workforce settings.

Joint design and compression of convolutional neural networks as a Bi-level optimization problem.

Over the last decade, deep neural networks have shown great success in the fields of machine learning and computer vision. Currently, the CNN (convolutional neural network) is one of the most successful networks, having been applied in a wide variety of application domains, including pattern recognition, medical diagnosis and signal processing. Despite CNNs' impressive performance, their architectural design remains a significant challenge for researchers and practitioners. The problem of selecting hyperparameters is extremely important for these networks. The reason for this is that the search space grows exponentially in size as the number of layers increases. In fact, all existing classical and evolutionary pruning methods take as input an already pre-trained or designed architecture. None of them take pruning into account during the design process. However, to evaluate the quality and possible compactness of any generated architecture, filter pruning should be applied before the communication with the data set to compute the classification error. For instance, a medium-quality architecture in terms of classification could become a very light and accurate architecture after pruning, and vice versa. Many cases are possible, and the number of possibilities is huge. This motivated us to frame the whole process as a bi-level optimization problem where: (1) architecture generation is done at the upper level (with minimum NB and NNB) while (2) its filter pruning optimization is done at the lower level. Motivated by evolutionary algorithms' (EAs) success in bi-level optimization, we use the newly suggested co-evolutionary migration-based algorithm (CEMBA) as a search engine in this research to address our bi-level architectural optimization problem. The performance of our suggested technique, called Bi-CNN-D-C (Bi-level convolution neural network design and compression), is evaluated using the widely used benchmark data sets for image classification, called CIFAR-10, CIFAR-100 and ImageNet. Our proposed approach is validated by means of a set of comparative experiments with respect to relevant state-of-the-art architectures.

Bayesian Optimization for Design of Multi-Actuator Soft Catheter Robots.

Catheter-based diagnosis and therapy have grown increasingly in recent years due to their improved clinical outcomes including decreased morbidity, shorter recovery time and minimally invasiveness compared to open surgeries. Although the scalability, customizability, and diversity of soft catheter robots are widely recognized, designers and roboticists still lack comprehensive techniques for modeling and designing them. This difficulty arises due to their continuum nature, which makes characterizing the properties and predicting a soft catheter's behavior challenging, complicating robot design tasks. In this paper, we propose modeling multi-actuator soft catheters to enable alignment with desired vessel shapes near the target area. We develop mathematical models to simulate the catheter's positioning due to the moments exerted by multiple pneumatic actuators along the catheter and use those models to compare optimization approaches that can achieve catheter alignment along a desired vessel shape. Specifically, our approach proposes finding the optimal geometric and material properties for a multi-actuator soft catheter robot using a bi-level optimization framework. The upper-level optimization process uses a modified Bayesian technique to seek the optimal geometric and material properties of the soft catheter, which minimize the deviance of the actuated catheter from a desired vessel shape, while the lower-level optimization process uses a gradient-based technique to obtain the actuator moments required to achieve that vessel shape. The results demonstrate the capability of our proposed multi-actuator soft catheter to align with the desired vessel shapes, and show that the proposed framework which is in the context of Bayesian optimization has the potential to expedite the design process.

Patient-specific hyperparameter learning for optimization-based CT image reconstruction.

We propose a hyperparameter learning framework that learnspatient-specifichyperparameters for optimization-based image reconstruction problems for x-ray CT applications. The framework consists of two functional modules: (1) a hyperparameter learning module parameterized by a convolutional neural network, (2) an image reconstruction module that takes as inputs both the noisy sinogram and the hyperparameters from (1) and generates the reconstructed images. As a proof-of-concept study, in this work we focus on a subclass of optimization-based image reconstruction problems with exactly computable solutions so that the whole network can be trained end-to-end in an efficient manner. Unlike existing hyperparameter learning methods, our proposed framework generates patient-specific hyperparameters from the sinogram of the same patient. Numerical studies demonstrate the effectiveness of our proposed approach compared to bi-level optimization.

Analysis of false data injection attacks in power systems: A dynamic Bayesian game-theoretic approach.

False data injection (FDI) attack is a malicious kind of cyber attack that targets state estimators of power systems. In this paper, a dynamic Bayesian game-theoretic approach is proposed to analyze FDI attacks with incomplete information. In this approach, players' payoffs are identified according to a proposed bi-level optimization model, and the prior belief of the attacker's type is constantly updated based on history profiles and relationships between measurements. It is proven that the type belief and Bayesian Nash equilibrium are convergent. The stability and reliability of this approach can be guaranteed by the law of large numbers and the central limit theorem. The time complexity and space complexity are O(nmnsnl) and O(1), respectively. Numerical results show that the average success rate to identify at-risk load measurements is 98%. The defender can efficiently allocate resources to at-risk load measurements using the dynamic Bayesian game-theoretic approach.

Incorporating a constructed wetland system into a water pollution emissions permit system: a case study from the Chaohu watershed, China.

Water pollution emissions permit systems (WPEPS) and constructed wetland systems (CWS) are widely but independently used to balance regional economic development and ecosystem health. In this paper, a watershed scale framework that incorporates a CWS into a WPEPS is proposed for regional economic and ecosystem health sustainability. A strategy that integrates three allocation principles: per capita emissions, economic utility, and water quality contributions, is established for the initial CWS-incorporated WPEPS emissions permit allocations. To quantitatively verify the effectiveness of the CWS-incorporated WPEPS, a bi-level optimization model is formulated, in which fuzzy random variables are employed to describe the system uncertainties. The model is then applied to a practical case in the Chaohu watershed, China, to assess the effects of changing watershed management targets, from which practical insights are obtained on the initial emissions permit allocation strategies and the CWS coordination effects. It has proved that the integrated watershed management of the CWS-incorporated WPEPS is more able to rationally allocate the limited water pollution emissions permits and better balance the Chaohu watershed economic development to ensure ecological health sustainability. The CWS-incorporated WPEPS model under uncertainty can be used to guide local governments when formulating their sustainable watershed management strategies.

DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems.

The Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework is presented for addressing the optimization of bi-level mixed-integer nonlinear programming problems. In this framework, bi-level optimization problems are approximated as single-level optimization problems by collecting samples of the upper-level objective and solving the lower-level problem to global optimality at those sampling points. This process is done through the integration of the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper-level objective, and to consecutively approximate and optimize bi-level mixed-integer nonlinear programming problems that are challenging to solve using exact methods. The performance of DOMINO is assessed through solving numerous bi-level benchmark problems, a land allocation problem in Food-Energy-Water Nexus, and through employing different data-driven optimization methodologies, including both local and global methods. Although this data-driven approach cannot provide a theoretical guarantee to global optimality, we present an algorithmic advancement that can guarantee feasibility to large-scale bi-level optimization problems when the lower-level problem is solved to global optimality at convergence.