Exact and Hybrid Solutions for the Multi-Objective VM Reassignment Problem
Bibliographic record
Abstract
Machine Reassignment is a challenging problem for constraint programming (CP) and mixed integer linear programming (MILP) approaches, especially given the size of data centres. Hybrid solutions mixing CP and heuristic algorithms, such as, large neighbourhood search (CBLNS), also struggle to address the problem given its size and number of constraints. The multi-objective version of the Machine Reassignment Problem is even more challenging and it seems unlikely for CP, MILP or hybrid solutions to obtain good results in this context. As a result, the first approaches to address this problem have been based on other optimisation methods, including metaheuristics. In this paper we study three things: (i) under which conditions a mixed integer optimisation solver, such as IBM ILOG CPLEX, can be used for the Multi-objective Machine Reassignment Problem; (ii) how much of the search space can a well-known hybrid method such as CBLNS explore; and (iii) can we find a better hybrid approach combining MILP or CBLNS and an- other recent metaheuristic proposed for the problem (GeNePi). We show that MILP can handle only small or medium scale data centres, and with some relaxations, such as, an optimality tolerance gap and a limited number of directions explored in the search space. CBLNS on the other hand struggles with the problem in general but achieves reasonable performance for large instances of the problem. However, we show that our hybridisation improves both the quality of the set of solutions (CPLEX+GeNePi and CBLNS+GeNePi improve the solutions by +17.8% against CPLEX alone and +615% against CBLNS alone) and number of solutions (8.9 times more solutions than CPLEX alone and 56.76 times more solutions than CBLNS alone), while the processing time of CPLEX+GeNePi and CBLNS+GeNePi increases only by 6% and 16.4% respectively. Overall, the study shows that CPLEX+GeNePi is the best algorithm for small instances (CBLNS+GeNePi only gets 45.2% of CPLEX+GeNePi’s hypervolume) while CBLNS+GeNePi is better than the others on large instances (that CPLEX+GeNePi cannot address).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".