Source
González et al. (2025), LIT-008, arXiv 2504.10648v1 (Annals of Operations Research 350: 979–1015), read in full in NOTE-015. The journal version and the GitHub instances were not compared.
What was actually shown
The problem (§3, §4.1). Collection points have fixed sites; each gets one of eight bin combinations (capacity 1.1–5.6 m³). Waste accumulates deterministically each day, with no collection on Sunday, cyclic over the week. Visit days are a free decision, not chosen from patterns, and service time depends on the bins. The cost is weekly bin cost plus routing time. The MIQP is linearised exactly as a MILP.
Why bins follow visits. The bin needed at a point is the smallest combination at least as large as its maximum accumulation, which the longest gap between visits sets (Eqs. 2c, 2k–2m). The GA evolves only a visit mask and daily orders and derives the bins in the decoder (App. A).
The comparison (Tables 5–6). On five 12-point instances, Gurobi 10 ran 8 h on each formulation and stopped with gaps of 29.06–32.15% (MILP) and 26.15–32.34% (MIQP). The GA ran 30 times per instance (about 7.5–7.7 h in total). Mean over instances of (C_GA − C_exact)/C_exact:
| bin cost | routing cost | overall cost | |
|---|---|---|---|
| GA best vs MILP | +19.88% | −5.75% | −0.08% |
| GA mean/median vs MILP | +18.65% | −0.36% | +3.75% |
| GA best vs MIQP | +22.59% | −5.74% | +1.70% |
| GA mean/median vs MIQP | +21.24% | +1.37% | +5.61% |
Larger instances (Table 7). On 40–163 points, all 30 runs were feasible, at 0.72–5.58 h mean per run, with no bound, alternative method or current-practice baseline.
What could have come out otherwise. The GA could have matched the exact incumbents on both cost components. It systematically trades bin cost for routing cost: it finds shorter routes by visiting less often, which forces larger bins.
What this does not say
- That either method is near optimal. Both are compared with incumbents roughly 30% from Gurobi’s bound.
- That the GA “consistently” routes better than the MILP. On i.12.2 its best routing cost is 0.76% worse (NOTE-015, C5).
- That the exact bins are 26–29% cheaper. The GA’s bin excess is up to +25.62% and +28.78%, so the exact bins are up to about 20% and 22% cheaper. The paper makes the same slip (§6).
- That the tuned GA generalises. Operators were tuned on i.12.1, which is also a test instance, and the 12-point instances are subsets of the one real instance.
- That runtime grows linearly. Four points with different generation budgets and penalty weights do not establish it.
- That the bin deficit is inherent. The repair only adds visits, which may cause it; the paper does not analyse this.
Connections
The record holds no other account of vehicle routing or metaheuristic evaluation. The paper builds on Mahéo, Rossit and Kilby (2020, 2023) and is positioned against Hemmelmayr et al. (2014, 2017) and Gläser and Stücken (2021), none of which is held.