Contribution: This paper presents a novel two-phase algorithmic approach that decouples preference satisfaction from fairness optimization in student team formation, achieving both objectives without compromise. The method applies simulated annealing -- a core materials science technique -- to an educational challenge, demonstrating pedagogical integration of administrative processes. Background: Forming effective teams in large engineering cohorts (100+ students) requires balancing student preferences, academic fairness, and demographic diversity. Existing tools either optimize for fairness while ignoring preferences (CATME, Team-Anneal) or accommodate preferences while compromising balance (self-selection), leaving complaint rates at 5--35%. Intended Outcomes: Eliminate formal complaints, achieve near-zero GPA variance between teams, prevent gender isolation, and maintain high preference satisfaction while creating a scalable, reproducible solution applicable across engineering programs. Application Design: Phase 1 forms fixed triads through graph-theoretic clustering that maximizes mutual preferences, preserving social bonds. Phase 2 employs simulated annealing to pair triads into teams of six while optimizing GPA variance, gender balance, and size constraints. This decomposition mirrors hierarchical optimization in materials processing. Findings: Deployed across 238 students, the algorithm eliminated formal complaints entirely (vs >30% baseline), achieved GPA variance of 0.005 (vs. historical mean 9.74), eliminated gender-isolated individuals, and maintained 94.3% preference satisfaction. Validation against 82 historical grouping instances (1,538 teams, 6 academic years) confirmed significant improvement over conventional methods.

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