Application of a goal programming algorithm to incorporate environmental requirements in a multi-objective Columbia River Treaty Reservoir optimization model
Bibliographic record
Abstract
Due to large variability in streamflows and a lack of adequate reservoir storage capability in US territories, a treaty for the Columbia River was established between Canada and the USA in 1964. However, the treaty only considers power generation and flood control, and to address environmental issues, supplemental operating agreements have been signed each year since the 1990s. In this paper, we present a goal programming (GP) optimization algorithm to model the terms and conditions of the Supplemental Operating Agreements of the Columbia River Treaty (CRT) between BC Hydro and “United States Entities”. The GP technique is a multi-objective programming method that has been used in many different fields including reservoir optimization. After its introduction in 1961, it has been used extensively and is considered a robust modeling technique. The GP algorithm we have developed models the multi-objective problem using a combination of lexicographic and weighted goal-programming techniques. Case studies using four scenarios were performed to assess the satisfaction of environmental requirements for different target flow requirements at the US–Canadian border of the Columbia River. The GP algorithm we have developed allows for the constraints to deviate from a target value. This in turn provides modeling flexibility to handle infeasibility, typically encountered when hard constraints are included in the formulation of the optimization problem. GP can be used to investigate the trade-offs between multiple objectives by minimizing the deviation from user-specified target levels. In addition, the goal-programming formulation can represent more realistic real-time operational situations of a complex multi-reservoir system like the BC Hydro system.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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 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".