{ "schema_version": 1, "case": { "id": "cnc-live-scheduling", "name": "CNC scheduling with a live priority update", "domain": "Flexible manufacturing", "summary": "A nonlinear bi-objective schedule is initialized from public tables, then updated by changing one job priority while reusing accepted state.", "objective_labels": [ "Weighted nonlinear tardiness", "Energy and load" ], "sense": "minimize", "public_table_counts": { "job_machine": 54, "jobs": 18, "machines": 3 }, "tss": { "solver": "NSGA-II", "segment_counts": { "assignment": 1, "permutation": 1 }, "workbench_slots": [ "build_problem", "evaluate" ], "fixed_runtime": [ "typed initialization", "crossover", "mutation", "repair", "validation" ] }, "turns": [ { "id": "t000", "title": "Initial bi-objective schedule", "request": "Bi-objective nonlinear flexible parallel-machine scheduling: 18 jobs (table `jobs`, id column job_id) on 3 heterogeneous CNC machines (table `machines`, id column machine = m1/m2/m3). Eligibility and machine-specific processing times are in table `job_machine` (one row per (job_id, machine): processing_h p_jm, eligible in {0,1}); a job may only be assigned to a machine with eligible=1 and processing_h not NULL.\n\nDECISIONS: assignment A_j in {m1,m2,m3} of each job to exactly one eligible machine, and a processing sequence pi_m (ordered list) of the jobs assigned to each machine m.\n\nTIME EVOLUTION: On each machine m, process its jobs in the order of pi_m. For job j with predecessor i on the same machine: S_j = max(r_j, C_i); for the FIRST job on a machine (no predecessor): S_j = r_j and no setup time is incurred. Completion: C_j = S_j + s_ijm + p_jm. Setup time between consecutive jobs i then j on machine m: s_ijm = b_m * ( 1.2*I(family_i != family_j) + 0.4*I(material_i != material_j) + 0.35*|u_i - u_j| ), using family, material, setup_level columns of `jobs` and b_m of `machines`. Tardiness T_j = max(0, C_j - d_j). Makespan Cmax = max_j C_j. Machine load L_m = sum of p_jm over jobs on m + sum of s_ijm over consecutive pairs in pi_m.\n\nOBJECTIVE 1 (minimize): f1 = sum_j w_j * T_j^2 + 0.05 * Cmax^2, with w_j = priority_w of `jobs`.\nOBJECTIVE 2 (minimize): f2 = sum_m [ p_m * ( sum_{j on m} p_jm + 0.5 * sum_{consecutive pairs on m} s_ijm ) + beta_m * L_m^2 ], with p_m and beta_m from `machines`.\n\nCONSTRAINTS (violations must be penalized): each job assigned to exactly one machine and only to eligible machines; per-machine sequencing enforces S_j >= C_i for consecutive pairs (machine processes one job at a time); S_j >= r_j for all jobs; setup times exactly as the formula above; all variables nonnegative. Solve as a bi-objective minimization with solver_preference=evolutionary and report the Pareto front of nondominated schedules.", "restart": { "skill": "typed_initialization", "label": "Typed initialization", "reused": 0, "fresh_ratio": 1.0, "reason": "The first request builds the TSS Workbench and samples a typed population." }, "objectives": [ "f1", "f2" ], "population_size": 100, "pareto_size": 8, "generations": 10, "latency_seconds": 506.6, "front": [ { "objectives": [ 125.92198906249997, 868.165646375 ], "feasible": true, "sequences": { "m1": [ "J10", "J17", "J02", "J06", "J15", "J01", "J18" ], "m2": [ "J05", "J07", "J04", "J09", "J14" ], "m3": [ "J13", "J03", "J16", "J08", "J11", "J12" ] }, "assignments": { "J01": "m1", "J02": "m1", "J03": "m3", "J04": "m2", "J05": "m2", "J06": "m1", "J07": "m2", "J08": "m3", "J09": "m2", "J10": "m1", "J11": "m3", "J12": "m3", "J13": "m3", "J14": "m2", "J15": "m1", "J16": "m3", "J17": "m1", "J18": "m1" } }, { "objectives": [ 1599.8896309374998, 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Keep all other data (all other jobs, machines, job_machine eligibility and processing times), both objective definitions (f1 = sum_j w_j * T_j^2 + 0.05 * Cmax^2; f2 = sum_m [ P_m * ( sum p_jm + 0.5 * sum s_ijm ) + beta_m * L_m^2 ]), all constraints, and the evolutionary/Pareto (NSGA-II) solver route unchanged. Reuse the accepted state where valid and apply the appropriate fast restart, then return the updated Pareto front of nondominated schedules.", "restart": { "skill": "warm_restart_v1", "label": "Warm restart", "reused": 50, "fresh_ratio": 0.5, "reason": "Only priority_w of J01 changed from 2.0 to 2.5, altering objective f1 weights slightly without changing feasibility, constraints, decision structure, or objective senses. Existing schedules remain feasible and their basin is not invalidated; 50% fresh Warm repair is sufficient." }, "objectives": [ "f1", "f2" ], "population_size": 100, "pareto_size": 15, "generations": 10, "latency_seconds": 28.2, "front": [ { "objectives": [ 67.67366406250001, 869.5935321249999 ], "feasible": true, "sequences": { "m1": [ "J10", "J09", "J15", "J17", "J02", "J14", "J05" ], "m2": [ "J13", "J03", "J04", "J07", "J12", "J18" ], "m3": [ "J16", "J06", "J08", "J11", "J01" ] }, "assignments": { "J01": "m3", "J02": "m1", "J03": "m2", "J04": "m2", "J05": "m1", "J06": "m3", "J07": "m2", "J08": "m3", "J09": "m1", "J10": "m1", "J11": "m3", "J12": "m2", "J13": "m2", "J14": "m1", "J15": "m1", "J16": "m3", "J17": "m1", "J18": "m2" } }, { "objectives": [ 1366.7300721874992, 813.4101949374999 ], "feasible": true, "sequences": { "m1": [ "J17", "J15", "J02", "J09", "J10" ], "m2": [ "J14", "J05", "J18", "J07", "J04" ], "m3": [ "J16", "J06", "J08", "J01", "J11", "J12", "J13", "J03" ] }, 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