Beyond Feasibility: Solution-Landscape Preserving Generation of Mixed-Integer Linear Programs

Real-world Mixed-Integer Linear Programming (MILP) instances are scarce and costly to collect, limiting the training and evaluation of learning-based MILP solvers. Existing instance generation methods mainly preserve structural similarity, computational difficulty, feasibility, and boundedness. However, these properties do not ensure solution-landscape preservation: a generated instance may remain structurally similar and feasible while substantially altering the representative solutions and their distribution compared with those of the source instance. We propose Solution-Landscape Preserving Generation of Mixed-Integer Linear Programs (SLP-MILP), a controllable generation framework that explicitly incorporates source solution behavior into the generation process. SLP-MILP constructs solution-aware constraint groups based on the activation relationships between solutions and constraints as well as the constraint structure and regenerates selected groups through solution-conditioned masked generative reconstruction under an explicit structural modification budget. For each regenerated constraint direction, its right-hand side is determined by aligning the constraint-response profile with that of the original constraint on the source solution-landscape. A separate conformal retention safeguard prevents the aligned constraints from discarding excessive source probability mass. Experiments on multiple MILP families demonstrate the effectiveness of SLP-MILP in preserving solution-landscape characteristics while maintaining structural similarity.