Resource Allocation via Simulated Annealing

Workload

Jobs 24

Machines 5

Cooling rate α 0.970

Schedule State

Makespan (max load)

Load std. dev.

0.00

Temperature

0.00

Iterations

How it works

This is the multiprocessor scheduling problem (P||C_max): given N jobs with processing costs w_i and M identical machines, assign each job to one machine so the makespan — the busiest machine's total load — is as small as possible. It is NP-hard for M ≥ 2, so real schedulers use heuristics rather than brute force.

load(m)  = Σ w_i for jobs i assigned to machine m
makespan = max_m load(m)
goal     = minimize makespan

The simulator solves it with simulated annealing: each iteration, one random job is proposed to move to a different random machine. If the move reduces the makespan it is always accepted; if it increases it by ΔE, it is accepted anyway with probability

P(accept) = exp(-ΔE / T)

Temperature T starts high (frequent uphill moves, escaping bad local optima) and cools each step as T ← αT. As T falls, only improving moves survive and the schedule settles near a local optimum — visible as the machine towers converging to similar heights.

Jobs / Machines — resize the problem; a new random workload is generated (weights 2–9).
Cooling rate α — how slowly temperature decays; slower cooling explores more but converges later.
Run — auto-steps the annealer; Step advances one proposal at a time; New jobs reshuffles the workload and resets T.

The same load-balancing pattern underlies cloud VM placement, CPU thread scheduling and warehouse task assignment.

Machine load tower Machine base

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