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? ??? ?? Golang ?? ????: ???? ?? ????? ILP, A*, ?? ? ??? ????

?? ????: ???? ?? ????? ILP, A*, ?? ? ??? ????

Nov 06, 2024 am 04:44 AM

Comparative Benchmarking: ILP, A*, and Branch and Bound Algorithms in High-Throughput Scenarios

?? ??? ?????? ?? ?? ????? ??? ? ?? ????? 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

??

  1. ??? ?? ??:
    • BenchmarkGenerateReportILP-24 ? BenchmarkBranchGenerateReportLocal-24:
      • ?? ? ??? ILP?? 99.29% ? ??? ?? ??? 1,694,029ns/op?? 12,106ns/op? ????. .

  • 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? ????. .

  1. ??? ??:

    • ILP ??: ?? ?? ? ??? ??? ? ??? ?? ?????.
    • ?? ? ??? ??: A* ??? ?? ??? ??? ? ??? ????.
    • A* ??: ??? ??? ?? ?? ??? ???? ???????.

  2. ???:

    • ILP ?? ? ?? ? ?? ??? ???? ?? ? 21.74? ? ?? ??? ??? ? ????.
    • A* ?? ??? ??? ?? ??? ??? ?? ??? ??? ????? ??? ?? ? ?? ?????.
??? ?? ??? ??? ??? ??

ILP ? Branch ????? ??? ???

21.74? ? ?? ???? ????? ?? ???? ??? ???? ??? ? ????? ??? ???? ??? ????.

  • ILP ? ?? ????: ? ?? ???? ????? ? ?? ????? ????? ????. ? ?? ??? ????? ???? ? ?? ?? ??? ?????. ?? ????? ???? ?? ??? ???? ?? ?????? ????? ?? ?????.

  • ?? ????: ???? ?? ?? ??? ?? ??? ? ????? ??? ?? ??? ???? ? ???? ?????. ILP ?? Branch? ??? ????? ???? ?? ??? ?? ??? ???? ?? ???? ???? ??? ?????.

????? ???? ??????? ? ?? ???? ????? ??? ? ?? ???? ?? ILP? Branch? ???? ??? ?????. ???, ????? ???? ?? ????? ILP ? Branch? ? ??? ??? ??? ? ??? ???? ???? ???? ??? ?? ??? ??? ???? ????.

???? ??

? ????? ?? ??? ??? ????? ? ???? ??? ? ??? ?? ????? ???? ?? ???? ??? ?????.

?? ?? ???(ILP)

??:

ILP? ????? ?? ??? ???? ??? ???? ??? ??(?: ?? ?? ?? ?? ??)? ?? ? ???? ??? ?????. ?? ?? ??? ?? ?? ??? ?? ??? ??? ?? ??????.

?? ?? ??:

  1. ?? ??:

    ??? ???? ???? ??? ?????.

  2. ????:

    ?????? ????? ?? ?? ???? ??????.

  3. ????:

    ???? ???? ?? ?? ??? ?? ??? ?????.

  4. ?? ??:

    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*? ??? ????? ? ??? ? ?? ? ??? ?? ???????. ?? ?? ??? ?? ???? ?? ??? ???? ?? ? ?? ??? ????? ?????.

?? ?? ??:

  1. ???:

    ?? ??? ???? ???? ???? ?????.

  2. ??:

    • ???? ????? ?? ??? ?? ?? ??? ?????.
    • ?? ???? ?????.
    • ??? ??? ??? ???? ??? ?????.
    • ? ??? ?? ??? ??? ???? ?? ?? ???? ???? ???????.

  3. ??:

    ?? ??? ????? ???? ?? ?? ???(??? ??? ???) ????? ?????.

?? ??:

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? ??? ??? ????? ???? ??? ???????. ??? ? ?? ?? ??? ???(??) ??? ???? ?? ??? ??(??)?? ? ?? ???? ??? ? ?? ?? ??? ?????.

?? ?? ??:

  1. ???:

    ?? ????? ???? ?? ? ??? ???? ?????.

  2. ??:

    ? ???? ??? ? ?? ?? ??? ????.

  3. ??:

    ? ???? ??? ??? ???? ?? ??? ???(??)? ?????.

  4. ????:

    ??? ?? ? ??? ????? ?? ??? ?????.

  5. ??:

    ?? ?? ?? ?? ?? ??? ???? ??? ??? ????? ?????.

  6. ??:

    ?? ??? ????? ??? ?? ?? ? ??? ???? ?????.

?? ??:

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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