Bottom-Left Fill

Constructive placement heuristic that drops each piece to the lowest-leftmost feasible position.

Also called: Bottom-Left Fill · BLF · 바텀-레프트

A constructive placement rule: each piece is positioned as low as possible, then as far left as possible, without overlap; the "fill" variant also reuses gaps left by earlier placements. Often used as the inner placement step inside a metaheuristic search. Traces to Jakobs (1996).

Claims & evidence

Every relationship is a claim with an evidence grade; applicable problem-to-problem relationships also carry an equivalence level. See the evidence policy.

A–X describes evidence reliability; E0–E4 describes mathematical similarity between problems. The two axes are independent.

Relationships to this entry 3

uses method
2D Irregular Nesting to Bottom-Left Fill
Bottom-left and bottom-left-fill placement rules are widely used constructive heuristics for irregular nesting layouts.
EvidenceB · Survey / tutorial / community
Sources
- Source grade: A — Peer-reviewed / officialOn genetic algorithms for the packing of polygons
  Citation details
  Jakobs, S. (1996). On genetic algorithms for the packing of polygons. EJOR 88(1):165-181. Origin of the bottom-left-fill placement heuristic.
uses method
2D Strip Packing to Bottom-Left Fill
Bottom-left and bottom-left-fill were introduced for rectangle strip/packing layouts and are standard constructive heuristics here.
EvidenceA · Peer-reviewed / official
Sources
- Source grade: A — Peer-reviewed / officialOn genetic algorithms for the packing of polygons
  Citation details
  Jakobs, S. (1996). On genetic algorithms for the packing of polygons. EJOR 88(1):165-181. Origin of the bottom-left-fill placement heuristic.
shares method with
First-Fit Decreasing to Bottom-Left Fill
First-fit-decreasing and bottom-left-fill are both constructive placement heuristics that place items one by one under a fixed rule.
EvidenceB · Survey / tutorial / community
Equiv.E3 · structural analogy
Sources
- Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems
  Citation details
  Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.

Relationships to this entry
Relationship	Claim	Evidence	Equiv.	Sources
uses method 2D Irregular Nesting to Bottom-Left Fill	Bottom-left and bottom-left-fill placement rules are widely used constructive heuristics for irregular nesting layouts.	B · Survey / tutorial / community	—	Source grade: A — Peer-reviewed / officialOn genetic algorithms for the packing of polygons Citation details Jakobs, S. (1996). On genetic algorithms for the packing of polygons. EJOR 88(1):165-181. Origin of the bottom-left-fill placement heuristic.
uses method 2D Strip Packing to Bottom-Left Fill	Bottom-left and bottom-left-fill were introduced for rectangle strip/packing layouts and are standard constructive heuristics here.	A · Peer-reviewed / official	—	Source grade: A — Peer-reviewed / officialOn genetic algorithms for the packing of polygons Citation details Jakobs, S. (1996). On genetic algorithms for the packing of polygons. EJOR 88(1):165-181. Origin of the bottom-left-fill placement heuristic.
shares method with First-Fit Decreasing to Bottom-Left Fill	First-fit-decreasing and bottom-left-fill are both constructive placement heuristics that place items one by one under a fixed rule.	B · Survey / tutorial / community	E3 · structural analogy	Source grade: A — Peer-reviewed / officialAn improved typology of cutting and packing problems Citation details Wäscher, G., Haußner, H., Schumann, H. (2007). An improved typology of cutting and packing problems. EJOR 183(3):1109-1130.