?? ??? ?????? ?? ?? ????? ??? ? ?? ????? ILP(?? ?? ???) ????, A* ????? ??? ?? ????? Branch and Bound ????? ??? ??? ??????. ?? ????? ??? ??? ??? ???? ??????? ILP ? Branch and Bound ??? ??? ????? ????? A* ??? ?? ???? ?? ???????.
?? ??: ????? ?? ?? ?? ??? ??? ???? ???, ?? ?? ? ?? ???? ???????. ?????? ???? ???, ?? ??? ???? ????? ?? ???? ?????.
???? ??
??? ? ?? ???? ??? ?? ???? ?????.
goos: linux goarch: amd64 pkg: github.com/sosalejandro/<my-project>/<my-package>/pkg cpu: 13th Gen Intel(R) Core(TM) i7-13700HX BenchmarkGenerateReportILP-24 724 1694029 ns/op 30332 B/op 181 allocs/op BenchmarkGenerateReportILPParallel-24 6512 187871 ns/op 34545 B/op 184 allocs/op BenchmarkGenerateReportLocal-24 2 851314106 ns/op 559466456 B/op 7379756 allocs/op BenchmarkBranchGenerateReportLocal-24 101449 12106 ns/op 29932 B/op 165 allocs/op BenchmarkGenerateReportLocalParallel-24 3 349605952 ns/op 559422440 B/op 7379837 allocs/op BenchmarkBranchGenerateReportLocalParallel-24 120543 10755 ns/op 29933 B/op 165 allocs/op PASS coverage: 81.4% of statements ok github.com/sosalejandro/<my-project>/<my-package>/pkg 11.121s
???? ??
?? ????? ??? ??? ??? ???? ??????? ???(?, ? ??? ???? ??)? ???? ?????.
ILP ? ?? ? ???? ?? ?? ??:
plan := []Plan{
{ID: "1", Times: 100},
{ID: "2", Times: 150},
{ID: "3", Times: 200},
{ID: "8", Times: 50},
{ID: "9", Times: 75},
{ID: "10", Times: 80},
{ID: "11", Times: 90},
{ID: "12", Times: 85},
{ID: "13", Times: 60},
{ID: "14", Times: 110},
}
A* ?? ???:
plan := []Plan{
{ID: "1", Times: 1},
{ID: "2", Times: 1},
{ID: "3", Times: 5},
{ID: "8", Times: 5},
{ID: "9", Times: 5},
{ID: "10", Times: 5},
{ID: "11", Times: 9},
{ID: "12", Times: 5},
{ID: "13", Times: 5},
{ID: "14", Times: 5},
}
???? ??
??? ????? ???? ??? ??? ??? ???? ?? ? ??? ?? ? ?? ??(?, Times ?? ?)? ??? ?????.
? ??:
- ILP ? ?? ? ??? ??:
100 + 150 + 200 + 50 + 75 + 80 + 90 + 85 + 60 + 110 = 1000
- A* ??:
1 + 1 + 5 + 5 + 5 + 5 + 9 + 5 + 5 + 5 = 46
??? ??:
ILP Iterations / A* Iterations = 1000 / 46 ≈ 21.74
?? ILP? Branch and Bound ??? A* ??? ?? ?? 21.74? ? ?? ??? ????? ?????.
?? ??
???? ??? ?? ???? ??? ??? ?????.
| Benchmark | Runs | ns/op | B/op | allocs/op | Total Time (ns) |
|---|---|---|---|---|---|
| BenchmarkGenerateReportILP-24 | 724 | 1,694,029 | 30,332 | 181 | ≈ 1,225,836,996 |
| BenchmarkGenerateReportILPParallel-24 | 6,512 | 187,871 | 34,545 | 184 | ≈ 1,223,607,552 |
| BenchmarkBranchGenerateReportLocal-24 | 101,449 | 12,106 | 29,932 | 165 | ≈ 1,224,505,394 |
| BenchmarkGenerateReportLocal-24 | 2 | 851,314,106 | 559,466,456 | 7,379,756 | ≈ 1,702,628,212 |
| BenchmarkGenerateReportLocalParallel-24 | 3 | 349,605,952 | 559,422,440 | 7,379,837 | ≈ 1,048,817,856 |
| BenchmarkBranchGenerateReportLocalParallel-24 | 120,543 | 10,755 | 29,933 | 165 | ≈ 1,295,219,065 |
??
-
??? ?? ??:
-
BenchmarkGenerateReportILP-24 ? BenchmarkBranchGenerateReportLocal-24:
- ?? ? ??? ILP?? 99.29% ? ??? ?? ??? 1,694,029ns/op?? 12,106ns/op? ????. .
-
BenchmarkGenerateReportILP-24 ? BenchmarkBranchGenerateReportLocal-24:
-
BenchmarkGenerateReportILP-24 ? BenchmarkGenerateReportLocal-24:
- ILP? ???? 99.80% ? ??? ?? ??? 851,314,106ns/op?? 1,694,029ns/op.
-
BenchmarkGenerateReportILPParallel-24 ? BenchmarkBranchGenerateReportLocalParallel-24:
- ?? ? ??? ??? ILP ???? 94.28% ? ??? ?? ??? 187,871ns/op?? 10,755ns? ????. /op.
-
BenchmarkGenerateReportILPParallel-24 ? BenchmarkGenerateReportLocalParallel-24:
- ILP ??? ?? ???? 99.95% ? ??? ?? ??? 349,605,952ns/op?? 187,871ns/op? ????. .
-
??? ??:
- ILP ??: ?? ?? ? ??? ??? ? ??? ?? ?????.
- ?? ? ??? ??: A* ??? ?? ??? ??? ? ??? ????.
- A* ??: ??? ??? ?? ?? ??? ???? ???????.
-
???:
- ILP ?? ? ?? ? ?? ??? ???? ?? ? 21.74? ? ?? ??? ??? ? ????.
- A* ?? ??? ??? ?? ??? ??? ?? ??? ??? ????? ??? ?? ? ?? ?????.
ILP ? Branch ????? ??? ???
21.74? ? ?? ???? ????? ?? ???? ??? ???? ??? ? ????? ??? ???? ??? ????.
ILP ? ?? ????: ? ?? ???? ????? ? ?? ????? ????? ????. ? ?? ??? ????? ???? ? ?? ?? ??? ?????. ?? ????? ???? ?? ??? ???? ?? ?????? ????? ?? ?????.
?? ????: ???? ?? ?? ??? ?? ??? ? ????? ??? ?? ??? ???? ? ???? ?????. ILP ?? Branch? ??? ????? ???? ?? ??? ?? ??? ???? ?? ???? ???? ??? ?????.
????? ???? ??????? ? ?? ???? ????? ??? ? ?? ???? ?? ILP? Branch? ???? ??? ?????. ???, ????? ???? ?? ????? ILP ? Branch? ? ??? ??? ??? ? ??? ???? ???? ???? ??? ?? ??? ??? ???? ????.
???? ??
? ????? ?? ??? ??? ????? ? ???? ??? ? ??? ?? ????? ???? ?? ???? ??? ?????.
?? ?? ???(ILP)
??:
ILP? ????? ?? ??? ???? ??? ???? ??? ??(?: ?? ?? ?? ?? ??)? ?? ? ???? ??? ?????. ?? ?? ??? ?? ?? ??? ?? ??? ??? ?? ??????.
?? ?? ??:
?? ??:
??? ???? ???? ??? ?????.????:
?????? ????? ?? ?? ???? ??????.????:
???? ???? ?? ?? ??? ?? ??? ?????.?? ??:
ILP ??? ???? ?? ????? ????? ????? ??? ?? ????? ??????? ???? ????.
?? ??:
goos: linux goarch: amd64 pkg: github.com/sosalejandro/<my-project>/<my-package>/pkg cpu: 13th Gen Intel(R) Core(TM) i7-13700HX BenchmarkGenerateReportILP-24 724 1694029 ns/op 30332 B/op 181 allocs/op BenchmarkGenerateReportILPParallel-24 6512 187871 ns/op 34545 B/op 184 allocs/op BenchmarkGenerateReportLocal-24 2 851314106 ns/op 559466456 B/op 7379756 allocs/op BenchmarkBranchGenerateReportLocal-24 101449 12106 ns/op 29932 B/op 165 allocs/op BenchmarkGenerateReportLocalParallel-24 3 349605952 ns/op 559422440 B/op 7379837 allocs/op BenchmarkBranchGenerateReportLocalParallel-24 120543 10755 ns/op 29933 B/op 165 allocs/op PASS coverage: 81.4% of statements ok github.com/sosalejandro/<my-project>/<my-package>/pkg 11.121s
A* ????(?? ??)
??:
A*? ??? ????? ? ??? ? ?? ? ??? ?? ???????. ?? ?? ??? ?? ???? ?? ??? ???? ?? ? ?? ??? ????? ?????.
?? ?? ??:
???:
?? ??? ???? ???? ???? ?????.-
??:
- ???? ????? ?? ??? ?? ?? ??? ?????.
- ?? ???? ?????.
- ??? ??? ??? ???? ??? ?????.
- ? ??? ?? ??? ??? ???? ?? ?? ???? ???? ???????.
??:
?? ??? ????? ???? ?? ?? ???(??? ??? ???) ????? ?????.
?? ??:
goos: linux goarch: amd64 pkg: github.com/sosalejandro/<my-project>/<my-package>/pkg cpu: 13th Gen Intel(R) Core(TM) i7-13700HX BenchmarkGenerateReportILP-24 724 1694029 ns/op 30332 B/op 181 allocs/op BenchmarkGenerateReportILPParallel-24 6512 187871 ns/op 34545 B/op 184 allocs/op BenchmarkGenerateReportLocal-24 2 851314106 ns/op 559466456 B/op 7379756 allocs/op BenchmarkBranchGenerateReportLocal-24 101449 12106 ns/op 29932 B/op 165 allocs/op BenchmarkGenerateReportLocalParallel-24 3 349605952 ns/op 559422440 B/op 7379837 allocs/op BenchmarkBranchGenerateReportLocalParallel-24 120543 10755 ns/op 29933 B/op 165 allocs/op PASS coverage: 81.4% of statements ok github.com/sosalejandro/<my-project>/<my-package>/pkg 11.121s
?? ? ??? ????
??:
Branch and Bound? ??? ??? ????? ???? ??? ???????. ??? ? ?? ?? ??? ???(??) ??? ???? ?? ??? ??(??)?? ? ?? ???? ??? ? ?? ?? ??? ?????.
?? ?? ??:
???:
?? ????? ???? ?? ? ??? ???? ?????.??:
? ???? ??? ? ?? ?? ??? ????.??:
? ???? ??? ??? ???? ?? ??? ???(??)? ?????.????:
??? ?? ? ??? ????? ?? ??? ?????.??:
?? ?? ?? ?? ?? ??? ???? ??? ??? ????? ?????.??:
?? ??? ????? ??? ?? ?? ? ??? ???? ?????.
?? ??:
goos: linux goarch: amd64 pkg: github.com/sosalejandro/<my-project>/<my-package>/pkg cpu: 13th Gen Intel(R) Core(TM) i7-13700HX BenchmarkGenerateReportILP-24 724 1694029 ns/op 30332 B/op 181 allocs/op BenchmarkGenerateReportILPParallel-24 6512 187871 ns/op 34545 B/op 184 allocs/op BenchmarkGenerateReportLocal-24 2 851314106 ns/op 559466456 B/op 7379756 allocs/op BenchmarkBranchGenerateReportLocal-24 101449 12106 ns/op 29932 B/op 165 allocs/op BenchmarkGenerateReportLocalParallel-24 3 349605952 ns/op 559422440 B/op 7379837 allocs/op BenchmarkBranchGenerateReportLocalParallel-24 120543 10755 ns/op 29933 B/op 165 allocs/op PASS coverage: 81.4% of statements ok github.com/sosalejandro/<my-project>/<my-package>/pkg 11.121s
?? ??
| Feature | ILP Implementation | Local (A*) Implementation | Branch and Bound Implementation |
|---|---|---|---|
| Optimization Approach | Formulates the problem as a set of linear equations and inequalities to find the optimal solution. | Searches through possible states using heuristics to find the most promising path to the goal. | Systematically explores and prunes the solution space to find optimal solutions efficiently. |
| Scalability | Handles large-scale problems efficiently by leveraging optimized solvers. | Performance can degrade with increasing problem size due to the exhaustive nature of state exploration. | Efficient for combinatorial problems, with pruning reducing the search space significantly. |
| Development Time | Faster implementation as it relies on existing ILP solvers and libraries. | Requires more time to implement, especially when dealing with complex state management and heuristics. | Moderate development time, balancing complexity and optimization benefits. |
| Flexibility | Highly adaptable to various linear optimization problems with clear constraints and objectives. | Best suited for problems where pathfinding to a goal is essential, with heuristic guidance. | Effective for a wide range of optimization problems, especially combinatorial ones. |
| Performance | Demonstrates superior performance in handling a higher number of iterations with optimized memory usage. | While effective for certain scenarios, struggles with high memory allocations and longer execution times under heavy workloads. | Shows significant performance improvements over ILP and A* with optimized memory usage and faster execution times. |
| Developer Experience | Improves developer experience by reducing the need for extensive coding and optimization efforts. | May require significant debugging and optimization to achieve comparable performance levels. | Balances performance with manageable development effort, leveraging existing strategies for optimization. |
| Integration | Currently integrates a C ILP module with Golang, facilitating efficient computation despite cross-language usage. | Fully implemented within Golang, but may face limitations in performance and scalability without optimizations. | Implemented in Golang, avoiding cross-language integration complexities and enhancing performance. |
?? ??? ??? ??
-
???:
- ?? ? ??? ??? ??? ???? ???? ?? ??? ???? ?? ?? ?? ??? ????? ?????.
- ILP ?? ?? ?? ??? ???? ???? ?? ??? ???? ?? ?? ?? ??? ????? ?????.
- A* ??? ?? ???? ?? ??? ??? ???? ????.
-
?? ???:
- ?? ? ??? ?? ?? ??? ??? ?? ?? ???? ???? ????? ?????.
- ILP ??? ?? ?? CPU? ????? ???? ?? ??? ??? ??? ?? ???? ?????.
- A* ??? ??? ???? ???? ????? ??? ??? ??? ? ????.
????? ??? ??? ??
???? ??? ???? ??? ??? ????.
?? ? ??? ??? ILP ??? ??? ?? ??? ????? ???? ?? ?? ??? ?? ??? ???? ????? ??? ?????.
ILP ??? ???? ??? ?? ? ? ?? ??? ????? ?????.
A* ??? ?? ?? ??? ??? ????? ?? ??? ???? ????.
??
Branch and Bound ????? ???? ???? ???? ???? ?? ??? ?????, ?? ?? ? ??? ?? ???? ILP ? A* ????? ?? ??? ?? ?????? ?????. Branch and Bound ????? ???? ???? ILP ????? ?????.
Branch and Bound ?? BenchmarkBranchGenerateReportLocalParallel ??? ??? ?? ??? ?? ?? ???? ???? ??? ??? ???? ?? ??? ?? ?????.
?? ? ?? ?? ??? ??? ???? ?? ?? ??? ?? ????? ? ??? ?? ????? ??? ???? ???? ???? ??? ?? ??? ? ??? ? ? ????.
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??? ??????? ????? ??, ???, ??? ??? ??? ??? ?? ?????. ?? ? ??? ?? ??? ?? ???? ?? ???? ??? ?????? ???? ?? ???? ??? ?? ??? ?????.
? ???? ?? ??? ??? ????? ??????? ????? ?????? ???? ?? ???? ??? ???? ???? ??? ? ????.
? ??? ?? ????: ???? ?? ????? ILP, A*, ?? ? ??? ????? ?? ?????. ??? ??? PHP ??? ????? ?? ?? ??? ?????!
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Golang ???? ?? Python ???? ?????? ??
Jul 02, 2025 pm 04:39 PM
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Jun 23, 2025 pm 11:21 PM
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Jul 03, 2025 am 02:40 AM
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Jun 23, 2025 pm 08:37 PM
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