HIERARCHICAL BAYESIAN-BASED GLOBAL OPTIMIZATION ALGORITHM WITH ADAPTIVE CONVERGENCE

Abstract

HIERARCHICAL BAYESIAN-BASED GLOBAL OPTIMIZATION ALGORITHM WITH ADAPTIVE CONVERGENCE ABSTRACT The present invention is designed to solve complex global optimization problems. The system utilizes a multi-layer Bayesian framework to model optimization variables and their interdependencies, providing probabilistic estimates at each layer. An adaptive convergence module dynamically adjusts convergence parameters based on real-time progress, enhancing both accuracy and speed of optimization. The method iteratively refines the search space by integrating feedback from an evaluation engine that assesses candidate solutions using an objective function. Additionally, a search space refinement module focuses the optimization process on promising regions, preventing premature convergence to local optima. The system can handle multi-objective optimization, outputting a set of Pareto-optimal solutions. The invention's adaptive approach ensures that it remains effective across varying complexities and problem sizes, making it suitable for real-world applications in diverse fields, such as machine learning, logistics, and engineering optimization.

Specification

Description:HIERARCHICAL BAYESIAN-BASED GLOBAL OPTIMIZATION ALGORITHM WITH ADAPTIVE CONVERGENCE

FIELD OF THE INVENTION

[001] Various embodiments of the present invention generally relate to global optimization techniques. More particularly, the invention relates to hierarchical Bayesian-based global optimization algorithm with adaptive convergence.

BACKGROUND OF THE INVENTION

[002] Global optimization is a critical area of research and application in various fields, including engineering, finance, logistics, and artificial intelligence. The objective of global optimization is to identify the best solution from a set of feasible solutions in complex, high-dimensional spaces where traditional optimization techniques may struggle. Many optimization problems are characterized by non-linearity, multi-modality, and high dimensionality, making them particularly challenging to solve efficiently.

[003] Traditional optimization methods, such as gradient descent and simplex algorithms, often rely on deterministic approaches that may become trapped in local optima, leading to sub-optimal solutions. Additionally, these methods typically require a good initial guess and may not effectively explore the entire solution space. As a result, there is a growing need for more sophisticated techniques that can handle the complexities of real-world optimization problems.

[004] Bayesian optimization has emerged as a powerful probabilistic approach that addresses some of these challenges. By modeling the optimization process with a probabilistic framework, Bayesian optimization can incorporate prior knowledge and uncertainty, making it particularly well-suited for complex and expensive objective functions. However, traditional Bayesian optimization techniques may still struggle with high-dimensional problems and the efficient exploration of the solution space.
[005] Hierarchical modeling offers a promising solution by allowing for the representation of optimization variables at multiple levels of abstraction. This enables a more efficient partitioning of the solution space, facilitating targeted searches that can better navigate complex landscapes. By combining hierarchical modeling with Bayesian inference, it is possible to capture both global trends and local characteristics of the optimization problem, leading to improved performance.

[006] Furthermore, adaptive convergence strategies represent a significant advancement in optimization methodologies. Traditional fixed convergence techniques may not adequately respond to the dynamic nature of optimization problems, often leading to premature convergence or slow progress. By employing reinforcement learning principles, adaptive convergence strategies can adjust convergence parameters in real time, optimizing the balance between exploration and exploitation throughout the optimization process.

[007] The present invention aims to combine hierarchical Bayesian modeling with adaptive convergence strategies to create a robust global optimization algorithm. This innovative approach seeks to address the limitations of traditional optimization methods and enhance the efficiency, speed, and accuracy of identifying globally optimal solutions across a wide range of complex optimization problems.
SUMMARY OF THE INVENTION

[008] The invention relates to a hierarchical Bayesian-based global optimization algorithm designed to effectively tackle complex optimization problems by combining hierarchical modeling, Bayesian inference, and adaptive convergence strategies. This innovative approach provides a systematic framework for exploring large and intricate solution spaces while improving both convergence speed and accuracy.

[009] The algorithm begins by constructing a hierarchical Bayesian model that identifies optimization variables and establishes relationships across multiple layers, facilitating a comprehensive representation of the problem. Initial probabilistic estimates for candidate solutions are generated using Bayesian inference, allowing for the integration of prior knowledge and uncertainty.
[010] The method incorporates an evaluation engine that assesses candidate solutions against defined objectives, generating performance feedback that informs subsequent iterations. A key feature of the invention is the search space refinement process, which iteratively narrows the focus of optimization based on feedback, concentrating computational resources on the most promising regions.

[011] Adaptive convergence is achieved through a dynamic adjustment of convergence parameters, optimizing the speed and accuracy of the algorithm in real time. This adaptive mechanism enhances the algorithm's ability to respond to varying problem complexities and prevents premature convergence to sub-optimal solutions.

[012] Overall, the hierarchical Bayesian-based global optimization algorithm provides a robust and efficient framework for identifying globally optimal solutions across diverse and challenging optimization landscapes, making it a valuable tool in fields such as engineering, finance, and artificial intelligence.

[013] One or more advantages of the prior art are overcome, and additional advantages are provided through the invention. Additional features are realized through the technique of the invention. Other embodiments and aspects of the disclosure are described in detail herein and are considered a part of the invention.

BRIEF DESCRIPTION OF THE FIGURES

[014] The accompanying figures where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the invention.

[015] FIG. 1 is a diagram that illustrates a system for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, in accordance with an embodiment of the invention.

[016] FIG. 2 is a diagram that illustrates a flow diagram with a method for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, in accordance with an embodiment of the invention.

[017] Skilled artisans will appreciate the elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[018] While various embodiments of the invention have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions may occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed. It shall be understood that different aspects of the invention can be appreciated individually, collectively, or in combination with each other.

[019] FIG. 1 is a diagram that illustrates a system 100 for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, in accordance with an embodiment of the invention.

[020] Referring to FIG. 1, the system 100 the comprises a memory 102, a processor 104, one or more communication interfaces 106, a communication bus 108, one or more edge devices 110, Blockchain network 112, Adaptive learning module 114, Privacy preserving protocol 116, and a communication module 116.

[021] The memory 102 often referred to as RAM (Random Access Memory), is the component of a computer system that provides temporary storage for data and instructions that the processor needs to access quickly. It holds the information required for running programs and performing calculations. The memory 102 can be thought of as a workspace where the processor can read from and write to data.

[022] The processor 104 referred to as the Central Processing Unit (CPU), is the "brain" of the computer system. It carries out instructions, performs calculations, and manages the flow of data within the system. The processor 104 fetches instructions and data from memory, processes them, and produces results.

[023] The one or more communication interfaces 106 refer to the various methods and protocols used to transfer data between different systems, devices, or components. These interfaces can be hardware-based, software-based, or a combination of both.

[024] The memory 102 and the processor 104 are connected through buses, which are electrical pathways for transferring data and instructions.

[025] The communication bus 108 plays a vital role in enabling effective and efficient communication within a system. It establishes the foundation for exchanging information, coordinating actions, and synchronizing operations among different components, ensuring the system functions as an integrated whole.

[026] The present invention relates to a Hierarchical Bayesian-Based Global Optimization Algorithm with Adaptive Convergence designed to tackle complex global optimization problems through an innovative approach combining hierarchical modeling, Bayesian inference, adaptive convergence strategies, and iterative search space refinement. In an embodiment, the system is designed to efficiently explore large, complex solution spaces while improving convergence speed and accuracy.

[027] Hierarchical Model Construction Module
[028] In an embodiment, the hierarchical model construction module builds a multi-layer Bayesian framework for representing optimization variables and their dependencies. This framework uses a layered architecture where higher layers represent broader, coarse-grained aspects of the solution space, while lower layers focus on finer details. Each layer captures a different level of abstraction, allowing the system to account for both global and local characteristics of the optimization problem.

[029] The hierarchical model incorporates prior knowledge about the problem in the form of prior distributions for each optimization variable. These distributions are updated iteratively as new information is obtained during the optimization process. The hierarchical structure is particularly beneficial for high-dimensional problems, as it allows for efficient partitioning of the solution space, making it easier to focus computational resources on areas of interest.

[030] Bayesian Inference Engine
[031] In an embodiment, the Bayesian inference engine is responsible for generating probabilistic estimates for candidate solutions at each layer of the hierarchical model. The engine applies Bayesian inference to calculate the posterior distribution of the solution space by integrating new data (e.g., results from the evaluation engine) with the prior distributions defined by the hierarchical model.

[032] The Bayesian inference engine continuously updates these estimates based on feedback from the evaluation process, effectively guiding the search towards high-probability regions of the solution space. This engine also ensures that the system balances exploration (searching new areas) and exploitation (refining existing promising solutions), minimizing the risk of getting trapped in local optima.

[033] Adaptive Convergence Module
[034] In an embodiment, the adaptive convergence module dynamically adjusts the convergence parameters of the optimization process based on real-time progress. Unlike traditional fixed convergence methods, this module employs a reinforcement learning-based feedback mechanism to monitor the performance of the system. If the optimization process stagnates, the module can adjust convergence thresholds, learning from previous iterations to optimize the convergence rate.

[035] The adaptive convergence module ensures that the system can handle a wide variety of optimization problems, from simple to highly complex. It accelerates convergence when the optimization is progressing smoothly and slows it down for fine-tuning when the solution is nearing an optimum. This adaptive nature significantly enhances both speed and accuracy, ensuring that the system does not prematurely converge to sub-optimal solutions.

[036] Search Space Refinement Module
[037] In an embodiment, the search space refinement module iteratively narrows the focus of the optimization process by refining the search space based on feedback from the Bayesian inference engine. Initially, the system explores the entire solution space using a broad search strategy. As candidate solutions are evaluated, the search space is narrowed to focus on the most promising regions, while regions deemed less promising are deprioritized.

[038] This module can be enhanced using genetic algorithm-based techniques to explore and refine sub-regions of the search space. The genetic algorithm introduces mechanisms like crossover and mutation to generate new candidate solutions, helping the system avoid getting stuck in local optima. This hybrid approach ensures that the search remains diverse while concentrating efforts on regions likely to yield globally optimal solutions.

[039] Evaluation Engine
[040] In an embodiment, the evaluation engine computes the objective function for each candidate solution, providing real-time feedback on the performance of these solutions. The evaluation is based on the specific goals of the global optimization problem, such as minimizing or maximizing a particular variable or set of variables.

[041] The evaluation engine plays a crucial role in assessing candidate solutions' fitness and updating the Bayesian inference engine with new data. In some embodiments, the evaluation engine supports multi-objective optimization, allowing the system to handle multiple, potentially conflicting objectives simultaneously. By identifying Pareto-optimal solutions, the evaluation engine enables the system to provide trade-offs between different performance metrics.

[042] Control Module
[043] In an embodiment, the control module orchestrates the interaction between the hierarchical model construction module, Bayesian inference engine, adaptive convergence module, search space refinement module, and evaluation engine. It manages the iterative cycles of the optimization process, ensuring that each component functions synergistically.

[044] The control module oversees the flow of data between the components, ensuring that probabilistic estimates, feedback, and updates are appropriately timed and integrated. It also monitors the overall progress of the optimization process and adjusts the operations of individual components as needed to maintain system efficiency and effectiveness.

[045] FIG. 2 is a diagram that illustrates a flow diagram 200 with a method for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, in accordance with an embodiment of the invention.

[046] The present invention provides a method for global optimization employing a hierarchical Bayesian-based algorithm with adaptive convergence. The method aims to efficiently navigate complex solution spaces to identify globally optimal solutions through a series of systematic steps.

[047] Step 202: Hierarchical Bayesian Model Construction In this initial step, a hierarchical Bayesian model is constructed by identifying the optimization variables pertinent to the problem at hand. This involves establishing relationships among these variables across multiple layers of the model, effectively reflecting the complexity of the global optimization problem. Higher layers encapsulate broader aspects of the solution space, while lower layers focus on detailed interactions between variables. This structured approach allows for a comprehensive representation of dependencies and facilitates targeted optimization.

[048] Step 204: Generating Initial Probabilistic Estimates Once the hierarchical model is in place, the next step involves generating initial probabilistic estimates for each candidate solution. This is achieved through Bayesian inference, utilizing prior distributions defined for the identified optimization variables. The estimates provide a foundational understanding of the solution space, highlighting potential candidate solutions' likelihood of performance based on historical or theoretical insights.

[049] Step 206: Evaluation of Candidate Solutions Following the generation of probabilistic estimates, the method involves evaluating the objective function associated with each candidate solution. This evaluation provides essential performance feedback, which assesses how well each solution aligns with the optimization goals, such as maximizing or minimizing specific variables. The performance metrics derived from this step are critical for guiding subsequent refinement processes.

[050] Step 208: Iterative Search Space Refinement In this step, the search space is refined iteratively by incorporating the performance feedback obtained from the evaluation process. The Bayesian model is updated to reflect new insights, specifically adjusting prior distributions to emphasize the most promising regions of the solution space. This dynamic narrowing of focus enhances the efficiency of the optimization process, allowing computational resources to concentrate on areas more likely to yield optimal solutions.

[051] Step 210: Adaptive Convergence Adjustment The method then includes dynamically adjusting the convergence parameters of the optimization process using an adaptive convergence strategy. This adjustment is informed by the real-time progress of the optimization, allowing the system to optimize both convergence speed and accuracy. If the optimization process shows signs of stagnation, the adaptive mechanism modifies convergence thresholds to either accelerate or slow the optimization as necessary, ensuring a balanced approach that prevents premature convergence to sub-optimal solutions.

[052] Step 212: Iterative Process Continuation Finally, the method iteratively repeats the processes of generating probabilistic estimates, refining the search space, and adjusting convergence parameters. This cycle continues until a globally optimized solution is identified, ensuring that the method maintains a robust exploration-exploitation balance throughout the optimization journey.
[053] advantages of the hierarchical Bayesian-based global optimization algorithm with adaptive convergence:

[054] Efficient Exploration of Solution Spaces: The hierarchical model construction allows for a structured exploration of complex solution spaces, enabling the algorithm to effectively identify relevant areas without exhaustive searches.

[055] Dynamic Adaptation: The adaptive convergence module adjusts optimization parameters in real-time based on the progress of the algorithm, enhancing both convergence speed and accuracy. This flexibility allows the system to respond effectively to varying problem complexities.

[056] Improved Convergence Speed: By leveraging reinforcement learning techniques, the method minimizes stagnation and optimizes the convergence rate, ensuring faster identification of optimal solutions.

[057] Enhanced Accuracy: The integration of Bayesian inference continuously updates probabilistic estimates based on performance feedback, which helps refine the search and focus on high-probability regions, thus improving the accuracy of the solutions.

[058] Multi-layered Perspective: The hierarchical structure captures both global and local characteristics of the optimization problem, enabling a more comprehensive understanding of variable interactions and dependencies.

[059] Robust Handling of High-Dimensional Problems: The algorithm's capability to partition the solution space efficiently makes it particularly effective for high-dimensional optimization problems, which are often challenging for traditional methods.

[060] Integration of Prior Knowledge: The use of prior distributions allows the algorithm to incorporate existing knowledge about the optimization problem, enhancing the initial estimates and guiding the search process more effectively.

[061] Support for Multi-Objective Optimization: The evaluation engine's ability to handle multiple conflicting objectives simultaneously facilitates the identification of Pareto-optimal solutions, providing valuable trade-offs for decision-making.

[062] Hybrid Approach for Local Optima Avoidance: The search space refinement module, potentially enhanced with genetic algorithm techniques, introduces diversity in candidate solutions, reducing the risk of the algorithm getting trapped in local optima.

[063] Systematic and Iterative Improvement: The method's iterative process ensures continuous refinement of solutions, leading to progressively better results as the optimization progresses.

[064] Those skilled in the art will realize that the above-recognized advantages and other advantages described herein are merely exemplary and are not meant to be a complete rendering of all of the advantages of the various embodiments of the present invention.

[065] In the foregoing complete specification, specific embodiments of the present invention have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present invention. Accordingly, the specification and the figures are to be regarded in an illustrative rather than a restrictive sense. All such modifications are intended to be included with the scope of the present invention and its various embodiments.
 
, Claims:I/WE CLAIM:
1. A system for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, the system comprising:
a hierarchical model construction module configured to build a multi-layer Bayesian framework for representing optimization variables and their interdependencies, wherein the framework dynamically adjusts according to the complexity of the global optimization problem;
a Bayesian inference engine configured to generate probabilistic estimates of candidate solutions at each layer of the hierarchical model based on input data and prior distributions;
an adaptive convergence module configured to analyze the optimization progress and adjust convergence parameters dynamically, enabling faster and more accurate convergence based on intermediate results;
a search space refinement module operable to iteratively refine the search space based on the output of the Bayesian inference engine, narrowing the scope to high-potential regions within the global optimization problem;
an evaluation engine configured to assess the performance of candidate solutions by computing an objective function for each, providing feedback to the Bayesian inference engine for updating prior distributions; and
a control module configured to manage interactions between the hierarchical model, inference engine, adaptive convergence module, and evaluation engine, facilitating iterative optimization cycles until the global solution is identified.
2. The system of claim 1, wherein the hierarchical model construction module further comprises a multi-fidelity modeling component that allows for the integration of data sources with varying levels of accuracy and granularity, enabling the system to prioritize high-fidelity data during optimization while incorporating lower-fidelity data when necessary.
3. The system of claim 1, wherein the adaptive convergence module utilizes a reinforcement learning-based feedback mechanism to adjust convergence thresholds dynamically, wherein the module learns optimal convergence strategies based on previous iterations of the optimization process.

4. The system of claim 1, wherein the search space refinement module employs a genetic algorithm-based search strategy to further enhance the exploration of the solution space, wherein the search space is divided into sub-regions that evolve through crossover and mutation processes.
5. The system of claim 1, wherein the evaluation engine is further configured to implement a multi-objective optimization technique, wherein the system simultaneously optimizes multiple conflicting objectives, generating a set of Pareto-optimal solutions to provide a trade-off between various performance metrics.

6. A method for global optimization using a hierarchical Bayesian-based algorithm with adaptive convergence, the method comprising:
at step 202, constructing a hierarchical Bayesian model by identifying optimization variables and establishing relationships across multiple layers based on the complexity of the global optimization problem;
at step 204, generating initial probabilistic estimates for each candidate solution using Bayesian inference based on prior distributions for the identified variables;
at step 206, evaluating the objective function for each candidate solution to generate performance feedback;
at step 208, refining the search space iteratively by incorporating performance feedback into the Bayesian model to update prior distributions and narrow the focus to promising regions;
at step 210, dynamically adjusting convergence parameters using an adaptive convergence strategy based on the progress of the optimization, wherein convergence speed and accuracy are optimized in real-time;
at step 212, iteratively repeating the steps of generating probabilistic estimates, refining the search space, and adjusting convergence parameters until a globally optimized solution is identified.

7. The method of claim 6, wherein at step 202, the hierarchical Bayesian model is constructed using multi-fidelity data sources, allowing the method to incorporate both high- and low-accuracy data to improve the robustness of the optimization process, with the higher fidelity data receiving greater weight in the inference process.

8. The method of claim 6, wherein at step 210, the adaptive convergence strategy utilizes a reinforcement learning algorithm that continuously updates convergence parameters based on real-time feedback from the optimization progress, enabling faster and more efficient convergence over time.

9. The method of claim 6, wherein at step 208, the search space refinement is performed using a hybrid optimization approach, combining Bayesian search with a genetic algorithm to explore diverse regions of the solution space and prevent premature convergence to local optima.

10. The method of claim 6, wherein at step 206, the objective function is designed to handle multi-objective optimization, allowing for the simultaneous optimization of multiple conflicting objectives, wherein the method outputs a Pareto-optimal set of solutions that provide trade-offs between the different objectives.

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