A solver based on local search.
The goal of this repository is to provide a simple framework to quickly implement heuristic algorithms based on local search.
For complex and evolving problems, implementing and extending local search algorithms based on complex neighborhoods quickly becomes cumbersome and time consuming. This often makes them unsuitable for practical use. The algorithms of this repository are designed to get the best performances out of the simplest neighborhoods. Thus making them easier to implement and extend.
Still, more complex neighborhoods can be implemented if better performances are needed.
All algorithms require the Local Scheme to implement: GlobalCost, Solution, initial_solution, global_cost and local_search.
Implemented algorithms:
- Restarting Local Search
-a restarting_local_search- Most basic algorithm, can be used as a baseline
- Iterated Local Search
-a iterated_local_search- Single solution algorithm
- Low implementation cost
- Good for very large problems
- Additional requirements:
Perturbation,perturbations,apply_perturbation
- Best First Local Search
-a best_first_local_search- Multi-solution algorithm
- Higher implementation cost
- Higher quality solutions
- Additional requirements:
CompactSolution,compact_solution_hasher,solution2compact,compact2solution,Perturbation,perturbation_hasher,perturbations,apply_perturbation
- Genetic Local Search
-a genetic_local_search- Population-based algorithm
- Good when the ruggedness of the landscape is high
- Additional requirements:
crossoveranddistance
A specific implementation is also available for sequencing problems. The neighborhoods, perturbations and crossovers are already implemented. It is only required to provide a void append(SequenceData&, ElementId) const method to use them.
Following the framework described in "A unified solution framework for multi-attribute vehicle routing problems" (Vidal et al., 2014) DOI , more efficient neighborhood explorations can be obtained by providing either a void concatenate(SequenceData&, const SequenceData&) const method or a GlobalCost global_cost_concatenate(SequenceData&, const SequenceData&) const method (when it is possible).
In case the GlobalCost global_cost_concatenate(SequenceData&, const SequenceData&) const method is provided, the Swap and Reverse neighborhoods won't take much avantage of it. Therefore, it might be better to disable these neighborhoods, in particular when optimizing a single sequence.
- Local search neighborhoods:
- Intra:
- Shift a block of
kconsecutive elements - Shift and reverse a block of
kconsecutive elements - Swap a block of
k1consecutive elements with another block ofk2consecutive elements - Reverse a block of consecutive elements (2-opt)
- Shift a block of
- Inter:
- Swap the tails of two sequences (2-opt*)
- Replace the tail of sequence
i1with the reversed head of sequencei2and replace the head of sequencei2with the reversed tail of sequencei1(reversed 2-opt*) - Shift a block of
kconsecutive elements from one sequence to another - Shift and reverse a block of
kconsecutive elements from one sequence to another - Swap a block of
k1consecutive elements from a sequence with another block ofk2consecutive elements from another sequence - Swap the sequences of two elements
j1andj2and try to place them at promising positions in their new sequences (swap*)
- Sub-sequences:
- Add an element into the solution
- Remove an element from the solution
- Replace an element from the solution by an element outside of the solution
- Modes:
- Shift an element
jin the same sequence and change its mode - Swap the mode of element
j1with the mode of another elementj2from the same sequence - Swap an elemnt
j1with another elementj2from the same sequence and swap their modes
- Shift an element
- Intra:
- Perturbations:
- Swap two blocks of consecutive elements (double-bridge) (single sequence only)
- Remove
kelements and re-insert them (ruin-and-recreate) - Force an element into the solution
- Crossover algorithms:
- OX crossover
- SJOX crossover
- SBOX crossover
- SREX1 crossover (multiple sequences only)
- SREX2 crossover (multiple sequences only)
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/sequentialordering_main --csv ../ordata/sequentialordering/data.csv -f "row['Dataset'] == 'tsplib'" -l "${DATE}_sequentialordering" -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/sequentialordering/data.csv -f "row['Dataset'] == 'tsplib'" -l "${DATE}_sequentialordering" -b heuristiclong -t 62
Single machine scheduling problem with sequence-dependent setup times, Total weighted tardiness
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/schedulingwithsdsttwt_main --csv ../ordata/schedulingwithsdsttwt/data.csv -l "${DATE}_schedulingwithsdsttwt" -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/schedulingwithsdsttwt/data.csv -l "${DATE}_schedulingwithsdsttwt" -b heuristiclong -t 62
Permutation flow shop scheduling problem, Total completion time
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/permutationflowshopschedulingtct_main --csv ../ordata/flowshopscheduling/data_permutationflowshopschedulingtct.csv -l "${DATE}_permutationflowshopschedulingtct" --timelimitfield "Time limit"
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/flowshopscheduling/data_permutationflowshopschedulingtct.csv -l "${DATE}_permutationflowshopschedulingtct" -b heuristiclong -t 500
Permutation flow shop scheduling problem, Total tardiness
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/permutationflowshopschedulingtt_main --csv ../ordata/flowshopscheduling/data_permutationflowshopschedulingtt.csv -l "${DATE}_permutationflowshopschedulingtt" --timelimitfield "Time limit"
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/flowshopscheduling/data_permutationflowshopschedulingtt.csv -l "${DATE}_permutationflowshopschedulingtt" -b heuristiclong -t 2200
Benchmarks
python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/orderacceptanceandscheduling_main --csv ../ordata/orderacceptanceandscheduling/data.csv -l orderacceptanceandscheduling -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/orderacceptanceandscheduling/data.csv -l orderacceptanceandscheduling -b heuristiclong -t 61Time-dependent orienteering problem
Distributed permutation flow shop scheduling problem, Total completion time
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/permutationflowshopschedulingtct_main --csv ../ordata/flowshopscheduling/data_distributedpfsstct.csv -l "${DATE}_distributedpfsstct" --timelimitfield "Time limit"
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/flowshopscheduling/data_distributedpfsstct.csv -l "${DATE}_distributedpfsstct" -b heuristiclong -t 500Traveling salesman problem with release dates
Single machine batch scheduling problem, Total weighted tardiness
Capacitated vehicle routing problem
Vehicle routing problem with time windows
Data can be downloaded from fontanf/orproblems
Multidimensional Multiple-choice Knapsack Problem
- Straightforward example for a genetic local search: single neighborhood, basic operators
- Algorithm:
- Local search neighborhoods:
- Add item
jin the knapsack
- Add item
- Crossover algorithm
- Local search neighborhoods:
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/multidimensionalmultiplechoiceknapsack_main --csv ../ordata/multidimensionalmultiplechoiceknapsack/data.csv -l "${DATE}_multidimensionalmultiplechoiceknapsack" -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/multidimensionalmultiplechoiceknapsack/data.csv -l "${DATE}_multidimensionalmultiplechoiceknapsack" -b heuristiclong -t 62
- Example which implements a problem specific acceleration strategy to compute the move costs
- Algorithm:
- Local search neighborhood: swap two assignments
- Perturbation: ejection chain
- Crossover algorithm: UX crossover
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/quadraticassignment_main --csv ../ordata/quadraticassignment/data.csv -l "${DATE}_quadraticassignment" -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/quadraticassignment/data.csv -l "${DATE}_quadraticassignment" -b heuristiclong -t 62
Knapsack Problem with Conflicts
- Example with multiple neigborhoods
- Algorithm:
- Local search neighborhoods:
- Move item
jin/out of the solution (and remove conflicting items) - Swap two non-conflicting items
- Remove one item and add two non-conflicting items from its neighbors
- Move item
- Perturbation: force item
jin/out of the solution - Crossover algorithm: double backbone-based crossover
- Local search neighborhoods:
Benchmarks
DATE=$(date '+%Y-%m-%d--%H-%M-%S') && python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/knapsackwithconflicts_main --csv ../ordata/knapsackwithconflicts/data.csv -f "row['Dataset'] == 'hifi2006'" -l "${DATE}_knapsackwithconflicts_hifi2006" -t 60
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/knapsackwithconflicts/data.csv -f "row['Dataset'] == 'hifi2006'" -l "${DATE}_knapsackwithconflicts_hifi2006" -b heuristiclong -t 62
Generalized Assignment Problem from fontanf/generalizedassignmentsolver
- Example which implements a generic strategy for very large problems to avoid recomputing moves which have not change since the last neighborhood exploration
- Algorithm:
- Local search neighborhoods: shift item
jto agenti - Perturbation: shift 8 random jobs
- Local search neighborhoods: shift item
Permutation flow shop scheduling problem, Makespan
- This one is not considered as a sequencing problem since the dedicated acceleration strategy makes it possible to explore the neighborhoods more efficiently
- Algorithm:
- Local search neighborhood: move a block of
kconsecutive jobs,k = 1..4 - Perturbation: swap two blocks (double-bridge)
- Local search neighborhood: move a block of
Benchmarks
python3 ../optimizationtools/scripts/bench_run.py --main ./bazel-bin/examples/permutationflowshopschedulingmakespan_main --csv ../ordata/permutationflowshopscheduling/data_makespan.csv -f "row['Dataset'] == 'vallada2015_large'" -l permutationflowshopschedulingmakespan --timelimitfield "Time limit"
python3 ../optimizationtools/scripts/bench_process.py --csv ../ordata/permutationflowshopscheduling/data_makespan.csv -f "row['Dataset'] == 'vallada2015_large' and int(row['Job number']) <= 100" -l permutationflowshopschedulingmakespan -b heuristiclong -t 500ROADEF/EURO Challenge 2020: Maintenance Planning Problem
- Example of a problem with expensive move evaluations
- Algorithm:
- Local search neighborhood: shift intervention
jto timet_start - Perturbation: force intervention
jto start at timet_start
- Local search neighborhood: shift intervention
Benchmarks
python3 ../optimizationtools/scripts/bench_run.py --main "./bazel-bin/examples/roadef2020_main -w 0 -y 1 " --csv ../ordata/roadef2020/data/data.csv -l roadef2020 -t 900 -f "'A' not in row['Dataset']"
python3 ../optimizationtools/scripts/bench_process.py -b heuristiclong --csv ../ordata/roadef2020/data.csv -l roadef2020 -t 920 -f "'A' not in row['Dataset']"Maximum-Weight Independent Set Problem from fontanf/stablesolver
- Algorithm:
- Local search neighborhoods:
- Move vertex
vin/out of the solution (and remove conflicting vertices) - Remove one vertex and add two non-conflicting vertices from its neighbors
- Move vertex
- Perturbation: force vertex
vin/out of the solution
- Local search neighborhoods:
Compile:
bazel build -- //...Then, examples can be executed as follows:
./bazel-bin/examples/knapsackwithconflicts_main -v 1 -i ../ordata/knapsackwithconflicts/bettinelli2017/sparse_corr/test_1000_1000_r0.001-0.dat -f bettinelli2017 -t 5 -c sol.txt --print-solution 1=======================================
Local Search Solver
=======================================
Algorithm
---------
Best First Local Search
Parameters
----------
Maximum number of nodes: -1
Seed: 0
Maximum size of the pool: 1
Time limit: 5
Local scheme parameters
-----------------------
Swap: 1
(2,1)-swap: 1
Time Value Comment
---- ----- -------
0.001 -1310, 0 s0 (t0)
0.002 -1320, 0 n1 d1 c1 (t0)
0.005 -1330, 0 n4 d2 c3 (t0)
0.006 -1340, 0 n5 d3 c3 (t0)
0.007 -1350, 0 n7 d4 c4 (t0)
0.008 -1360, 0 n8 d5 c5 (t0)
0.009 -1370, 0 n9 d6 c2 (t0)
0.011 -1380, 0 n11 d7 c8 (t0)
0.013 -1390, 0 n15 d8 c12 (t0)
0.014 -1410, 0 n16 d9 c11 (t0)
0.015 -1420, 0 n17 d10 c12 (t0)
0.016 -1430, 0 n18 d11 c13 (t0)
0.017 -1440, 0 n19 d12 c13 (t0)
0.019 -1450, 0 n23 d13 c17 (t0)
0.021 -1460, 0 n24 d14 c18 (t0)
0.022 -1470, 0 n25 d15 c18 (t0)
0.028 -1480, 0 n31 d16 c26 (t0)
0.029 -1500, 0 n32 d17 c26 (t0)
0.029 -1510, 0 n33 d18 c26 (t0)
0.030 -1530, 0 n35 d19 c28 (t0)
0.032 -1540, 0 n36 d20 c27 (t0)
0.033 -1550, 0 n37 d21 c29 (t0)
0.034 -1560, 0 n38 d22 c26 (t0)
0.034 -1570, 0 n39 d23 c33 (t0)
0.053 -1580, 0 n54 d24 c48 (t0)
0.059 -1600, 0 n60 d25 c53 (t0)
0.068 -1610, 0 n68 d26 c62 (t0)
0.099 -1620, 0 n96 d27 c89 (t0)
0.113 -1640, 0 n110 d28 c-2 (t0)
0.116 -1650, 0 n113 d29 c12 (t0)
0.120 -1660, 0 n116 d30 c-2 (t0)
0.139 -1670, 0 n130 d31 c26 (t0)
0.140 -1680, 0 n131 d32 c28 (t0)
0.152 -1690, 0 n143 d33 c-2 (t0)
0.161 -1700, 0 n152 d34 c-2 (t0)
0.165 -1710, 0 n155 d35 c51 (t0)
0.169 -1720, 0 n159 d36 c54 (t0)
0.220 -1730, 0 n191 d37 c84 (t0)
0.232 -1750, 0 n202 d38 c-2 (t0)
0.235 -1760, 0 n204 d39 c93 (t0)
0.260 -1770, 0 n219 d40 c-2 (t0)
0.268 -1780, 0 n224 d41 c-2 (t0)
0.291 -1790, 0 n238 d42 c-2 (t0)
0.492 -1800, 0 n349 d44 c-2 (t0)
0.550 -1810, 0 n380 d45 c-2 (t0)
0.554 -1820, 0 n384 d46 c78 (t0)
0.560 -1830, 0 n389 d47 c83 (t0)
0.586 -1840, 0 n408 d48 c-2 (t0)
0.593 -1850, 0 n414 d49 c14 (t0)
0.677 -1860, 0 n464 d50 c-2 (t0)
0.688 -1870, 0 n470 d51 c67 (t0)
0.691 -1880, 0 n472 d52 c66 (t0)
0.696 -1890, 0 n477 d53 c-2 (t0)
0.702 -1900, 0 n482 d54 c-2 (t0)
0.707 -1910, 0 n486 d55 c-2 (t0)
0.742 -1920, 0 n512 d56 c-2 (t0)
0.761 -1930, 0 n526 d57 c-2 (t0)
0.764 -1940, 0 n530 d58 c91 (t0)
0.765 -1950, 0 n531 d59 c28 (t0)
0.777 -1960, 0 n540 d60 c37 (t0)
0.778 -1970, 0 n541 d61 c37 (t0)
0.862 -1980, 0 n591 d62 c-2 (t0)
0.882 -1990, 0 n601 d63 c96 (t0)
1.225 -2000, 0 n756 d65 c-2 (t0)
1.237 -2010, 0 n763 d66 c-2 (t0)
1.310 -2020, 0 n797 d67 c91 (t0)
1.516 -2030, 0 n883 d68 c-2 (t0)
1.629 -2040, 0 n936 d69 c-2 (t0)
1.679 -2050, 0 n963 d70 c-2 (t0)
1.689 -2060, 0 n968 d71 c66 (t0)
1.710 -2070, 0 n977 d72 c-2 (t0)
1.712 -2080, 0 n978 d73 c69 (t0)
1.719 -2090, 0 n982 d74 c-2 (t0)
1.726 -2100, 0 n984 d75 c74 (t0)
1.731 -2110, 0 n988 d76 c75 (t0)
1.741 -2120, 0 n996 d77 c85 (t0)
1.786 -2130, 0 n1017 d78 c115 (t0)
1.787 -2140, 0 n1018 d79 c114 (t0)
1.802 -2150, 0 n1026 d80 c124 (t0)
1.818 -2160, 0 n1035 d81 c133 (t0)
1.881 -2170, 0 n1065 d82 c165 (t0)
2.036 -2180, 0 n1149 d83 c247 (t0)
2.041 -2190, 0 n1152 d84 c248 (t0)
2.042 -2200, 0 n1153 d85 c246 (t0)
2.072 -2210, 0 n1171 d86 c268 (t0)
2.079 -2220, 0 n1175 d87 c265 (t0)
2.082 -2230, 0 n1177 d88 c271 (t0)
2.099 -2240, 0 n1187 d89 c280 (t0)
2.100 -2250, 0 n1188 d90 c279 (t0)
2.108 -2260, 0 n1192 d91 c284 (t0)
2.391 -2270, 0 n1328 d92 c424 (t0)
2.403 -2280, 0 n1336 d93 c429 (t0)
2.423 -2290, 0 n1348 d94 c444 (t0)
2.454 -2300, 0 n1367 d95 c462 (t0)
2.456 -2310, 0 n1368 d96 c457 (t0)
3.512 -2320, 0 n1811 d97 c-2 (t0)
3.584 -2330, 0 n1849 d98 c445 (t0)
Final statistics
----------------
Value: -2330, 0
Time: 5.00216
Local scheme statistics
-----------------------
Toggle: 0 / 0 / -nan%
Swap: 0 / 0 / -nan%
(2-1)-swap: 0 / 0 / -nan%
Solution
--------
Items: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 57 58 59 60 62 64 65 66 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 110 111 112 113 114 115 117 118 119 121 122 123 124 125 126 127 128 129 132 133 134 136 137 138 140 141 142 143 157 518
Weight: 1000 / 1000
Profit: 2330
Checker
-------
Number of Items: 133 / 1000
Number of duplicates: 0
Number of conflict violations: 0
Weight: 1000 / 1000
Feasible: 1
Profit: 2330
See examples.
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