Why Not? Solver-Grounded Certificates for Explainable Mission Planning

Earth Observation (EO) satellite scheduling (deciding which imaging tasks to perform and when) is a well-studied combinatorial optimization problem. Existing methods typically assume that the operational constraint model is fully specified in advance. In practice, however, constraints governing separation between observations, power budgets, and thermal limits are often embedded in engineering artefacts or high-fidelity simulators rather than in explicit mathematical models. We study EO scheduling under unknown constraints: the objective is known, but feasibility must be learned interactively from a binary oracle. Working with a simplified model restricted to pairwise separation and global capacity constraints, we introduce Conservative Constraint Acquisition~(CCA), a domain-specific procedure designed to identify justified constraints efficiently in practice while limiting unnecessary tightening of the learned model. Embedded in the Learn&Optimize framework, CCA supports an interactive search process that alternates optimization under a learned constraint model with targeted oracle queries. On synthetic instances with up to 50tasks and dense constraint networks, L&O improves over a no-knowledge greedy baseline and uses far fewer main oracle queries than a two-phase acquire-then-solve baseline (FAO). For $n\leq 30$, the average gap drops from 65--68% (Priority Greedy) to 17.7--35.8% using L&O. At $n{=}50$, where the CP-SAT reference is the best feasible solution found in 120s, L&O improves on FAO on average (17.9% vs.\ 20.3%) while using 21.3 main queries instead of 100 and about $5\times$ less execution time.

We give an attribution method for neural combinatorial-optimisation (CO) policies that (i) decomposes a decision by constraint families via LP-relaxation duals, (ii) certifies counterfactuals through a combinatorial feasibility model (implemented as a CSP feasibility-decision model), and (iii) bounds the size of a PAC-sufficient explanation with a Bonferroni-corrected Hoeffding sufficient-subset test along a greedy ordering. Across three CO problems and three seeds, our LP-anchored $Λ$-attribution matches the CF-derived signal at 96.5% on CVRPTW (n_cert=344) and 77.2% on the Orienteering Problem (n_cert=281) vs 75.0% and 35.2% for proxy gradient (paired diffs +0.215 and +0.420; McNemar exact $p \le 10^{-14}$). In the rank-aligned regime of the Flexible Job-Shop Scheduling Problem, both backends agree on every CSP-certified flip (n_cert=59), confirming the no-gain prediction. Bonferroni-PAC subsets average 5.0 nodes per step ($M=70$, $\varepsilon=δ=0.2$, $k_{\max}=25$). Reference implementation: https://github.com/sohaibafifi/neuro-co-cax

Counterfactual (CF) explanations identify changes that alter an input's classification. While existing methods produce realistic and low-cost CFs, they often fail to ensure feasibility, by suggesting non-constructive modifications or incompatible with future changes (e.g., changing an individual's race to secure a job offer). We introduce a refinement of CF explanations that explicitly enforces feasibility. Our approach is the first to efficiently generate CFs that are realistic, low-cost and feasible. We accommodate both hard feasible constraints, specified by domain knowledge users, and soft feasible constraints, inferred automatically via causal inference from the dataset. Our method, Feasible Counterfactual Explanations (FCx), is based on a modified Variational Autoencoder (VAE) optimized with a multi-factor loss function. We measure the cost of a change based on the absolute change in values (proximity) as well as the number of features changed (sparsity) while realism is measured based on the LOF for density estimation, guaranteeing that CFs reside in densely populated regions. Extensive experiments on four public datasets show that our approach matches state-of-the-art performance across multiple metrics while guaranteeing feasibility.