Computer Science > Neural and Evolutionary Computing
[Submitted on 13 Sep 2020 (v1), last revised 3 Jan 2021 (this version, v4)]
Title:Extracting Optimal Solution Manifolds using Constrained Neural Optimization
View PDFAbstract: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.
Submission history
From: Gurpreet Singh [view email][v1] Sun, 13 Sep 2020 15:37:44 UTC (21,000 KB)
[v2] Sat, 24 Oct 2020 16:37:04 UTC (16,005 KB)
[v3] Tue, 10 Nov 2020 04:15:20 UTC (16,005 KB)
[v4] Sun, 3 Jan 2021 18:46:54 UTC (16,005 KB)
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