Enhancing Management Strategy Evaluation: Implementation of a TOPSIS-Based Multi-Criteria Decision-Making Framework for Harvest Control Rules
Abstract
1. Introduction
1.1. Management Strategy Evaluation Tools
- An Operation Model. An operation model reads in historical data for the “ground truth” fish biomass and simulates the population dynamics through fish population models.
- An Estimation Model. An estimation model is based on the operation model and projects the future fish biomass and fish catch, iteratively generating estimated values based on defined parameters.
- An HCR. The MSE takes in the parameters, e.g., TRP, LRP, and maximum catch, and simulates the regulatory effect of an HCR in the catch, thus further impacting the fish biomass projection.
1.2. Implementation of North Pacific Albacore MSE by the ISC
- Maintain an SSB higher than the limit reference point (LRP);
- Maintain the depletion of total biomass around the historical average depletion;
- Maintain catches above the average historical catch;
- The change in the total allowable catch between years should be relatively gradual;
- Maintain fishing intensity (F) at the target reference point with reasonable variability.
1.3. Limitations of the Weighted Sum Method and Motivation for a New Decision Support Model
2. Materials and Methods
2.1. Theoretical Background
2.1.1. Multi-Criteria Decision Making (MCDM)
2.1.2. Weighted Sum Method (WSM)
2.1.3. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Method
- Construct a normalized decision matrix r such that each entry in the matrix is calculated as follows:
- Construct a weighted normalized decision matrix with the following expression:
- Determine the positive and the negative ideal alternative from the previous matrix as follows:Positive:Negative:
- For each alternative, calculate its separation from the ideals with the following:Separation from positive ideal:Separation from negative ideal:
- For each alternative, calculate its final relative closeness to ideals with the following:The alternative with highest relative closeness is considered the best by the algorithm, given the user’s preferences, the objectives, and the alternatives’ performances.
- Preservation of multi-dimensional analytical structure until the last step. The TOPSIS method evaluates each alternative through comparisons between each of its objective parameters and the polarized ideal states. This characteristic ensures consistent geometric awareness of the underlying disparate data distributions across different objectives during evaluation.
- Geometric assessment. While TOPSIS remains a compensatory framework, i.e., allowing alternatives to make up disadvantages with strengths, its formulation with distance implies that deviation from the ideals is squared and thus more penalized compared to linear models such as the WSM. In other words, those alternatives with extremely poor performance in any objective will be more visibly demonstrated in their TOPSIS scores; the worse the performance, the heavier the penalty. This characteristic significantly reduces the chances of TOPSIS to rank imbalanced alternatives as better ones. On the other hand, since the distance is spread out on a range through geometric calculation, it would also tend to nuance the alternatives when aggregated and lower the chance of producing ties.
- Results in the scales of ideal alternatives. Due to its construction of the comparisons with respect to the best possible scenarios, the evaluative metrics could be explained in relative relationships, e.g., closeness to the ideal circumstances. This could potentially improve the explainability of the output due to its contextual relevance, while results from other formulations, such as aggregated WSM scores, cannot easily translate to sensible knowledge.
2.1.4. Sensitivity Analysis
2.2. Data Collection and Processing
2.2.1. AMPLE MSE
- The HCR inputs have the following options to choose from:
- (a)
- Blim: One value from (0.2, 0.25, 0.3, 0.4).
- (b)
- Belbow: One value from (0.6, 0.8).
- (c)
- Cmin: One value from (50, 75).
- (d)
- Cmax: One value from (125, 200).
In total, this constitutes a compilation of 32 HCRs as competing alternatives. The complete permutation table of their performances is provided in Appendix A. - The variability inputs: All variability inputs were set to 0.1.
- The HCR type was set to the threshold catch.
- The simulation was run at least 30 times, and a representative run from these runs was manually selected to collect performance metrics.
- The medium time period was the only considered set of performance metrics. The exclusion of datasets from short and long periods was due to the need for comparative simplicity.
- Stock life history was set to medium growth; stock history was set to be fully exploited; other settings were set to default values.
- Software was accessed in February 2025, Version 1.0.0.
2.2.2. NPALB MSE
2.3. Implementation of WSM and TOPSIS with User Participatory Interface
3. Results
3.1. Comparison: WSM and TOPSIS
3.1.1. AMPLE Dataset
3.1.2. NPALB Dataset
3.2. Sensitivity Analysis
3.2.1. AMPLE Dataset
3.2.2. NPALB Dataset
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
HCR | Harvest Control Rule; |
TOPSIS | Technique for Order Preference by Similarity to Ideal Solution Method; |
MSE | Management Strategy Evaluation; |
TAC | Total Allowable Catch; |
TAE | Total Allowable Effort; |
OM | Operation Model; |
EM | Estimation Model; |
SSB | Spawning Stock Biomass; |
LRP | Limit Reference Point; |
MCDM | Multi-Criteria Decision Making; |
WSM | Weighted Sum Method; |
TRP | Target Reference Point; |
ACL | Annual Catch Limit; |
ABC | Acceptable Biological Catch; |
IATTC | Inter-American Tropical Tuna Commission; |
ISC | International Scientific Committee; |
WCPFC | Western and Central Pacific Fisheries Commission. |
Appendix A. Dataset: HCR Evaluation on AMPLE [5]
HCR | Blim | Belbow | Cmin | Cmax | Prob. > LRP | Catch | Relative CPUE | Relative Effort | Catch Stability | Prox to TRP |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0.2 | 0.6 | 50 | 125 | 1 | 100 | 0.66 | 1.6 | 0.89 | 0.8 |
2 | 0.2 | 0.6 | 50 | 200 | 0.55 | 67 | 0.33 | 2.1 | 0.88 | 0.4 |
3 | 0.2 | 0.6 | 75 | 125 | 0.8 | 99 | 0.54 | 1.9 | 0.93 | 0.66 |
4 | 0.2 | 0.6 | 75 | 200 | 0 | 21 | 0.04 | 8.8 | 0.85 | 0.049 |
5 | 0.2 | 0.8 | 50 | 125 | 1 | 98 | 0.82 | 1.2 | 0.92 | 0.91 |
6 | 0.2 | 0.8 | 50 | 200 | 0.95 | 87 | 0.48 | 1.8 | 0.88 | 0.58 |
7 | 0.2 | 0.8 | 75 | 125 | 0.99 | 110 | 0.79 | 1.4 | 0.95 | 0.92 |
8 | 0.2 | 0.8 | 75 | 200 | 0.13 | 47 | 0.14 | 6.3 | 0.84 | 0.17 |
9 | 0.25 | 0.6 | 50 | 125 | 1 | 98 | 0.74 | 1.3 | 0.95 | 0.86 |
10 | 0.25 | 0.6 | 50 | 200 | 1 | 84 | 0.51 | 1.6 | 0.91 | 0.6 |
11 | 0.25 | 0.6 | 75 | 125 | 0.99 | 98 | 0.64 | 1.5 | 0.97 | 0.75 |
12 | 0.25 | 0.6 | 75 | 200 | 0.38 | 52 | 0.19 | 5.5 | 0.88 | 0.22 |
13 | 0.25 | 0.8 | 50 | 125 | 1 | 97 | 0.91 | 1 | 0.96 | 0.93 |
14 | 0.25 | 0.8 | 50 | 200 | 1 | 92 | 0.63 | 1.5 | 0.92 | 0.74 |
15 | 0.25 | 0.8 | 75 | 125 | 1 | 100 | 0.85 | 1.2 | 0.98 | 0.95 |
16 | 0.25 | 0.8 | 75 | 200 | 0.81 | 82 | 0.44 | 1.9 | 0.95 | 0.51 |
17 | 0.3 | 0.6 | 50 | 125 | 1 | 99 | 0.76 | 1.3 | 0.94 | 0.9 |
18 | 0.3 | 0.6 | 50 | 200 | 1 | 90 | 0.59 | 1.5 | 0.89 | 0.69 |
19 | 0.3 | 0.6 | 75 | 125 | 1 | 100 | 0.71 | 1.4 | 0.96 | 0.83 |
20 | 0.3 | 0.6 | 75 | 200 | 0.91 | 83 | 0.49 | 1.7 | 0.93 | 0.58 |
21 | 0.3 | 0.8 | 50 | 125 | 1 | 97 | 0.95 | 1 | 0.96 | 0.88 |
22 | 0.3 | 0.8 | 50 | 200 | 1 | 96 | 0.7 | 1.4 | 0.93 | 0.82 |
23 | 0.3 | 0.8 | 75 | 125 | 1 | 100 | 0.86 | 1.2 | 0.97 | 0.93 |
24 | 0.3 | 0.8 | 75 | 200 | 0.99 | 87 | 0.54 | 1.6 | 0.95 | 0.63 |
25 | 0.4 | 0.6 | 50 | 125 | 1 | 95 | 0.71 | 1.3 | 0.78 | 0.87 |
26 | 0.4 | 0.6 | 50 | 200 | 1 | 92 | 0.64 | 1.5 | 0.53 | 0.76 |
27 | 0.4 | 0.6 | 75 | 125 | 1 | 100 | 0.68 | 1.4 | 0.86 | 0.83 |
28 | 0.4 | 0.6 | 75 | 200 | 0.89 | 90 | 0.58 | 1.6 | 0.77 | 0.71 |
29 | 0.4 | 0.8 | 50 | 125 | 1 | 100 | 0.91 | 1.1 | 0.87 | 0.89 |
30 | 0.4 | 0.8 | 50 | 200 | 1 | 95 | 0.71 | 1.3 | 0.78 | 0.86 |
31 | 0.4 | 0.8 | 75 | 125 | 1 | 99 | 0.8 | 1.2 | 0.92 | 0.93 |
32 | 0.4 | 0.8 | 75 | 200 | 0.97 | 99 | 0.65 | 1.5 | 0.83 | 0.79 |
Appendix B. Graphs: Change in HCR Rankings with AMPLE Dataset
Appendix C. Dataset: TAC HCR Evaluation with NPALB by ISC [4]
hcr | TRP | LRP | SSB Thre Shold | Frac Tion F | odds SSB > LRP | odds SSB > 20% SSBo | odds SSB > 7.7% SSBo | odds SSB > 7.7% SSBo | Deple Tion > Minimum Historical | Annual Catch > Historical | Med Term > Historical | Long Term > Historical | Catch Stability | No Management Change | f Target over f |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | F50 | 0.2 | 0.3 | 0.25 | 0.92 | 0.92 | 0.92 | 0.99 | 0.7 | 0.63 | 0.64 | 0.68 | 0.7 | 0.77 | 0.88 |
2 | F50 | 0.14 | 0.3 | 0.25 | 0.96 | 0.92 | 0.92 | 0.98 | 0.7 | 0.62 | 0.64 | 0.68 | 0.72 | 0.77 | 0.89 |
3 | F50 | 0.08 | 0.3 | 0 | 0.98 | 0.91 | 0.92 | 0.98 | 0.7 | 0.62 | 0.64 | 0.67 | 0.75 | 0.76 | 0.89 |
4 | F50 | 0.14 | 0.2 | 0.25 | 0.96 | 0.91 | 0.92 | 0.98 | 0.7 | 0.63 | 0.65 | 0.68 | 0.78 | 0.91 | 0.88 |
5 | F50 | 0.08 | 0.2 | 0 | 0.98 | 0.91 | 0.92 | 0.98 | 0.69 | 0.65 | 0.67 | 0.71 | 0.82 | 0.91 | 0.87 |
6 | F40 | 0.14 | 0.2 | 0.25 | 0.93 | 0.87 | 0.9 | 0.97 | 0.68 | 0.64 | 0.61 | 0.73 | 0.63 | 0.87 | 1.06 |
7 | F40 | 0.08 | 0.2 | 0 | 0.97 | 0.88 | 0.9 | 0.97 | 0.68 | 0.66 | 0.63 | 0.75 | 0.66 | 0.88 | 1.05 |
8 | F40 | 0.08 | 0.14 | 0 | 0.96 | 0.86 | 0.9 | 0.96 | 0.67 | 0.67 | 0.63 | 0.75 | 0.7 | 0.92 | 1.02 |
9 | F50 | 0.2 | 0.3 | 0.5 | 0.91 | 0.91 | 0.92 | 0.98 | 0.7 | 0.63 | 0.66 | 0.68 | 0.75 | 0.76 | 0.89 |
10 | F50 | 0.14 | 0.3 | 0.5 | 0.96 | 0.92 | 0.92 | 0.99 | 0.7 | 0.62 | 0.64 | 0.69 | 0.74 | 0.77 | 0.89 |
11 | F50 | 0.08 | 0.3 | 0.25 | 0.99 | 0.92 | 0.92 | 0.99 | 0.7 | 0.63 | 0.67 | 0.69 | 0.79 | 0.77 | 0.89 |
12 | F50 | 0.14 | 0.2 | 0.5 | 0.96 | 0.91 | 0.92 | 0.98 | 0.7 | 0.64 | 0.66 | 0.7 | 0.82 | 0.91 | 0.88 |
13 | F50 | 0.08 | 0.2 | 0.25 | 0.98 | 0.91 | 0.92 | 0.98 | 0.69 | 0.65 | 0.66 | 0.71 | 0.82 | 0.91 | 0.87 |
14 | F40 | 0.14 | 0.2 | 0.5 | 0.92 | 0.86 | 0.9 | 0.96 | 0.67 | 0.65 | 0.63 | 0.73 | 0.67 | 0.86 | 1.02 |
15 | F40 | 0.08 | 0.2 | 0.25 | 0.97 | 0.87 | 0.9 | 0.97 | 0.67 | 0.66 | 0.64 | 0.74 | 0.67 | 0.87 | 1.01 |
16 | F40 | 0.08 | 0.14 | 0.25 | 0.96 | 0.86 | 0.9 | 0.96 | 0.67 | 0.66 | 0.65 | 0.75 | 0.71 | 0.92 | 1.03 |
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Year | Fish Catch (Pound) | Dollars |
---|---|---|
2010 | 25,519,780 | 28,778,100 |
2011 | 24,358,199 | 43,346,942 |
2012 | 30,722,107 | 45,851,105 |
2013 | 28,523,378 | 41,942,710 |
2014 | 27,316,224 | 32,793,729 |
2015 | 24,906,966 | 29,395,030 |
2016 | 23,024,227 | 37,680,810 |
2017 | 16,464,156 | 34,847,851 |
2018 | 15,326,874 | 24,936,506 |
2019 | 16,797,242 | 27,985,757 |
2020 | 15,790,675 | 24,106,123 |
2021 | 7,921,173 | 15,969,360 |
2022 | 16,278,851 | 35,245,038 |
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Liu, J.; Song, Z.; Xie, Y.; Zhang, Z. Enhancing Management Strategy Evaluation: Implementation of a TOPSIS-Based Multi-Criteria Decision-Making Framework for Harvest Control Rules. Fishes 2025, 10, 140. https://doi.org/10.3390/fishes10040140
Liu J, Song Z, Xie Y, Zhang Z. Enhancing Management Strategy Evaluation: Implementation of a TOPSIS-Based Multi-Criteria Decision-Making Framework for Harvest Control Rules. Fishes. 2025; 10(4):140. https://doi.org/10.3390/fishes10040140
Chicago/Turabian StyleLiu, Jikun, Zhenlei Song, Yuhang Xie, and Zhe Zhang. 2025. "Enhancing Management Strategy Evaluation: Implementation of a TOPSIS-Based Multi-Criteria Decision-Making Framework for Harvest Control Rules" Fishes 10, no. 4: 140. https://doi.org/10.3390/fishes10040140
APA StyleLiu, J., Song, Z., Xie, Y., & Zhang, Z. (2025). Enhancing Management Strategy Evaluation: Implementation of a TOPSIS-Based Multi-Criteria Decision-Making Framework for Harvest Control Rules. Fishes, 10(4), 140. https://doi.org/10.3390/fishes10040140