Monolithic Encoding for Matrix System Layout Optimization: From Nested to Single-Loop Search

Matrix-system layout optimization requires joint determination of workstation combinations and workstation-area assignments. Because workstation combinations constrain feasible assignments, the problem is often formulated as bi-level optimization, requiring assignment re-optimization for each combination and allocation of the simulation-evaluation budget between two search levels. However, this hierarchy arises from the formulation rather than the layout problem itself. This paper presents a single-loop alternative to nested optimization using a monolithic encoding that integrates both decisions into a single area-indexed layout vector, eliminating the need for a predefined upper/lower evaluation-budget split. The approach is evaluated in a simulation-based automotive trim-part assembly case using six algorithmic configurations under identical evaluation budgets. Monolithic search achieved higher expected net profit than nested search with the same optimizer (A12 = 0.66, p = 0.003), and the difference was significant in the particle swarm optimization family (A12 = 0.72). A budget-split sensitivity analysis showed that nested search performance depends on the allocation of evaluations between levels, potentially requiring additional tuning, whereas the proposed single-loop search avoids this additional search burden. These comparative findings are limited to a 5 × 5 layout with hypothetical economic parameters.