Team Orienteering with Time-Varying Profit
Why this work is in the frame
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Bibliographic record
Abstract
This paper studies the team orienteering problem, where the arrival time and service time affect the collection of profits. Such interactions result in a nonconcave profit function. This problem integrates the aspect of time scheduling into the routing decision, which can be applied in humanitarian search and rescue operations where the survival rate declines rapidly. Rescue teams are needed to help trapped people in multiple affected sites, whereas the number of people who could be saved depends as well on how long a rescue team spends at each site. Efficient allocation and scheduling of rescue teams is critical to ensure a high survival rate. To solve the problem, we formulate a mixed-integer nonconcave programming model and propose a Benders branch-and-cut algorithm, along with valid inequalities for tightening the upper bound. To solve it more effectively, we introduce a hybrid heuristic that integrates a modified coordinate search (MCS) into an iterated local search. Computational results show that valid inequalities significantly reduce the optimality gap, and the proposed exact method is capable of solving instances where the mixed-integer nonlinear programming solver SCIP fails in finding an optimal solution. In addition, the proposed MCS algorithm is highly efficient compared with other benchmark approaches, whereas the hybrid heuristic is proven to be effective in finding high-quality solutions within short computing times. We also demonstrate the performance of the heuristic with the MCS using instances with up to 100 customers. Summary of Contribution: Motivated by search and rescue (SAR) operations, we consider a generalization of the well-known team orienteering problem (TOP) to incorporate a nonlinear time-varying profit function in conjunction with routing and scheduling decisions. This paper expands the envelope of operations research and computing in several ways. To address the scalability issue of this highly complex combinatorial problem in an exact manner, we propose a Benders branch-and-cut (BBC) algorithm, which allows us to efficiently deal with the nonconcave component. This BBC algorithm is computationally enhanced through valid inequalities used to strengthen the bounds of the BBC. In addition, we propose a highly efficient hybrid heuristic that integrates a modified coordinate search into an iterated local search. It can quickly produce high-quality solutions to this complex problem. The performance of our solution algorithms is demonstrated through a series of computational experiments.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it