Time-Adaptive Simulated Annealing with Exact-Window Optimization for the Single-Row Facility Layout Problem

Abstract

The single-row facility layout problem (SRFLP) orders unequal-length facilities on a line to minimize flow-weighted center distances. We present a time-adaptive multi-start simulated annealing (AMSA) framework that coordinates one spectral start, randomized restarts, incremental insertion and interchange moves, variable-neighborhood descent (VND), and exact fixed-exterior window optimization under a shared deadline. The primary experiment comprised 137 public instances with 8–1000 facilities and ten fixed seeds per instance, giving 1370 successful runs. Among 133 instances with traceable historical reference values, the best of ten runs reached or improved the study reference on 91 instances. The mean run-level relative gap was 0.00470%, and 57 instances produced the same objective for every seed. New controlled experiments compare six variants on 21 representative instances, nine parameter groups on six instances, serial and concurrent execution on nine instances, and four exclusive runtime stages on nine instances. Full AMSA had the best aggregate rank; only removal of adaptive time allocation differed significantly from the full method after Holm correction. All tested non-default parameter levels had paired Wilcoxon p>0.05. Profiling showed that annealing consumed 70.29%, 88.52%, and 96.69% of solver time in the small–medium, medium, and large groups, respectively. Two stored layouts below the archived reference snapshot were independently recomputed by two objective identities with zero discrepancy. These results support AMSA as a reproducible deadline-aware baseline; they do not establish superiority over recent methods evaluated on different platforms or budgets.