论文标题
使用约束神经优化提取最佳溶液歧管
Extracting Optimal Solution Manifolds using Constrained Neural Optimization
论文作者
论文摘要
受限的优化解决方案算法仅限于基于点的解决方案。在实践中，必须满足单个或多个目标，其中目标函数和约束都可以是非凸的，从而导致多个最佳解决方案。现实世界的场景包括与隐式功能，高光谱脉络和帕累托最佳方面的相交表面。当面对非凸形表格时，本地或全球凸化是一种常见的解决方法。但是，这种方法通常仅限于严格的功能类别，从而导致对原始问题的次优点。我们提出了将最佳集合提取为大约歧管的神经解决方案，其中未修改的非凸目标和约束定义为建模者指导，域信息$ L_2 $损失函数。这促进了可解释性，因为建模者可以在其特定领域中针对已知的分析形式确认结果。我们提出了综合和现实的案例，以验证我们的方法并与已知的求解器进行比较，以便在准确性和计算效率方面进行基准标记。
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple optimal solutions. Real world scenarios include intersecting surfaces as Implicit Functions, Hyperspectral Unmixing and Pareto Optimal fronts. Local or global convexification is a common workaround when faced with non-convex forms. However, such an approach is often restricted to a strict class of functions, deviation from which results in sub-optimal solution to the original problem. We present neural solutions for extracting optimal sets as approximate manifolds, where unmodified, non-convex objectives and constraints are defined as modeler guided, domain-informed $L_2$ loss function. This promotes interpretability since modelers can confirm the results against known analytical forms in their specific domains. We present synthetic and realistic cases to validate our approach and compare against known solvers for bench-marking in terms of accuracy and computational efficiency.
