Benchmark
Results appear after an experiment.
Current: —
Order the items as a pure permutation and let a deterministic decoder insert a sack boundary whenever the next item would exceed capacity. Compare minimum-sack packing with balanced-load criteria without encoding partitions in the chromosome.
Results appear after an experiment.
Current: —
This laboratory begins with the one-dimensional Bin Packing Problem: every item has a weight and all sacks have equal capacity. The standard objective minimizes the number of sacks; the balanced extension asks how equally or tightly the sacks should be loaded when the sack count ties.
COIN learns useful adjacency and positional evidence, while ROSE estimates relative order. Visible boundaries are not genes: one deterministic decoder is shared by every algorithm.
The O(n) Next-Fit decoder scans left to right and opens a sack before an item that would exceed capacity C. Every permutation therefore decodes to a feasible packing without repair.
Let wᵢ be item weight, C capacity, B(π) decoded sack count, and Lᵦ the load of sack b.
Average unused capacity equals C−Σwᵢ/B and is therefore redundant with sack count when total weight and C are fixed. It remains visible for teaching; maximum unused capacity and load variance distinguish packings with the same B. Use lexicographic priority for the standard track or an explicit Pareto set for the MO track.
The page loads genuine BPPLIB Falkenauer U and T instances. U uses uniformly distributed item sizes; T contains triplets constructed to share a bin in an optimum. Balance objectives are explicitly labelled a balanced extension because BPPLIB reference bounds concern bin count, not variance.