arXiv:2504.11864v1 Announce Type: new Abstract: Gray-box optimization proposes effective and efficient optimizers of general use. To this end, it leverages information about variable dependencies and the subfunction-based problem representation. These approaches were already shown effective by enabling textit{tunnelling} between local optima even if these moves require the modification of many dependent variables. Tunnelling is useful in solving the maximum satisfiability problem (MaxSat), which can be reformulated to Max3Sat. Since many real-world problems can be brought to solving the MaxSat/Max3Sat instances, it is important to solve them effectively and efficiently. Therefore, we focus on Max3Sat instances for which tunnelling fails to introduce improving moves between locally optimal high-quality solutions and the region of globally optimal solutions. We analyze the features of such instances on the ground of phase transitions. Based on these observations, we propose manipulating clause-satisfiability characteristics that allow connecting high-quality solutions distant in the solution space. We utilize multi-satisfiability characteristics in the optimizer built from typical gray-box mechanisms. The experimental study shows that the proposed optimizer can solve those Max3Sat instances that are out of the grasp of state-of-the-art gray-box optimizers. At the same time, it remains effective for instances that have already been successfully solved by gray-box.
This article, titled “Gray-box Optimization for Solving Max3Sat Instances,” explores the concept of gray-box optimization and its application in solving the maximum satisfiability problem (MaxSat), specifically focusing on Max3Sat instances. Gray-box optimization utilizes information about variable dependencies and subfunction-based problem representation to effectively and efficiently optimize general problems. The authors highlight the effectiveness of gray-box optimization in enabling “tunnelling” between local optima, even when it requires modifying multiple dependent variables. However, they also identify instances where tunnelling fails to introduce improving moves between locally optimal high-quality solutions and globally optimal solutions. By analyzing the features of these instances and studying phase transitions, the authors propose manipulating clause-satisfiability characteristics to connect high-quality solutions that are distant in the solution space. They incorporate multi-satisfiability characteristics into the optimizer built from typical gray-box mechanisms. The experimental study demonstrates that the proposed optimizer successfully solves Max3Sat instances that were previously challenging for state-of-the-art gray-box optimizers, while remaining effective for instances that have already been successfully solved by gray-box methods. Overall, this article highlights the significance of gray-box optimization in solving complex real-world problems and presents a novel approach to address challenging instances of the Max3Sat problem.
Unleashing the Power of Gray-Box Optimization: Connecting Distant Solutions in Max3Sat Instances
Gray-box optimization has emerged as a powerful technique for solving a wide range of optimization problems effectively and efficiently. By leveraging information about variable dependencies and using a subfunction-based problem representation, gray-box optimization algorithms have shown impressive results. They have enabled tunnelling between local optima, even when this requires modifying multiple dependent variables. Tunnelling is particularly useful in solving the maximum satisfiability problem (MaxSat), which can be reformulated as Max3Sat.
Given that many real-world problems can be reduced to solving MaxSat/Max3Sat instances, it becomes crucial to find effective and efficient solutions. However, there are instances in which tunnelling fails to introduce improving moves between locally optimal high-quality solutions and the region of globally optimal solutions. These instances present a challenge and require deeper analysis.
Phase Transitions and Failed Tunnelling
Our research focuses on understanding the features of Max3Sat instances for which tunnelling fails. We observe that these instances exhibit interesting characteristics known as phase transitions. Phase transitions occur when the structure of the problem undergoes drastic changes, resulting in different solution landscapes.
Based on these observations, we propose a novel approach to manipulating clause-satisfiability characteristics in Max3Sat instances. By carefully analyzing the phase transitions, we identify specific characteristics that allow us to connect high-quality solutions that are distant in the solution space.
Leveraging Multi-Satisfiability Characteristics
We harness the power of multi-satisfiability characteristics within the optimizer, leveraging the typical mechanisms of gray-box optimization. Our proposed optimizer takes into account the clause-satisfiability characteristics and uses this information to guide its search for improving solutions.
Through an extensive experimental study, we validate the effectiveness of our proposed optimizer. We compare it with state-of-the-art gray-box optimizers and demonstrate its superior performance in solving Max3Sat instances that are out of the reach of existing methods.
Furthermore, our optimizer remains effective for instances that have already been successfully solved by gray-box algorithms. This versatility makes it a valuable tool for solving a wide range of Max3Sat instances, addressing both the challenging and well-explored problem landscapes.
Conclusion
Our research sheds new light on the power of gray-box optimization in tackling Max3Sat instances. By understanding the underlying features and leveraging clause-satisfiability characteristics, we propose an innovative approach that connects distant high-quality solutions. Our experimental study confirms the effectiveness and efficiency of our proposed optimizer, outperforming state-of-the-art methods and expanding the capabilities of gray-box optimization. With its ability to handle both challenging and previously solved instances, our optimizer holds immense potential for solving a broad range of real-world problems.
The paper titled “Gray-box Optimization for Solving Max3Sat Instances” introduces a new approach to solve the maximum satisfiability problem (MaxSat) using gray-box optimization techniques. Gray-box optimization is a method that leverages information about variable dependencies and subfunction-based problem representation to effectively and efficiently optimize general problems.
One key aspect of gray-box optimization is the concept of “tunnelling” between local optima. Tunnelling allows for movement between different local optima even if it requires modifying multiple dependent variables. This feature has been shown to be effective in solving MaxSat problems, which can be reformulated as Max3Sat problems.
However, the authors note that there are instances of Max3Sat where tunnelling fails to introduce improving moves between locally optimal high-quality solutions and the region of globally optimal solutions. These instances pose a challenge as they cannot be effectively solved by existing gray-box optimizers. Therefore, the paper aims to address this limitation and propose a solution.
The authors analyze the features of these challenging Max3Sat instances and identify phase transitions as a key factor. Phase transitions refer to sudden changes in the problem’s characteristics, such as the number of satisfiable clauses, as the search progresses. Based on these observations, the authors propose manipulating clause-satisfiability characteristics to connect high-quality solutions that are distant in the solution space.
To implement this idea, the authors utilize multi-satisfiability characteristics in the optimizer built from typical gray-box mechanisms. The experimental study conducted shows promising results, demonstrating that the proposed optimizer can successfully solve Max3Sat instances that were previously out of reach for state-of-the-art gray-box optimizers. Furthermore, the optimizer remains effective for instances that have already been successfully solved by existing gray-box methods.
Overall, this paper contributes to the field of gray-box optimization by addressing the limitations of existing techniques in solving challenging Max3Sat instances. By analyzing the features of these instances and proposing a novel approach, the authors provide valuable insights into improving the effectiveness and efficiency of gray-box optimization for a wider range of real-world problems. Future research in this area could explore the application of these techniques to other combinatorial optimization problems and further investigate the underlying factors that affect the performance of gray-box optimizers.
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