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add integer programming solver and benchmark test
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simontao
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Sep 8, 2024
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47 changes: 47 additions & 0 deletions
47
algorithm/src/jmh/java/dev/carbonshow/algorithm/partition/MaxPartitionBenchmark.java
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| package dev.carbonshow.algorithm.partition; | ||
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| import org.openjdk.jmh.annotations.*; | ||
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| import java.util.ArrayList; | ||
| import java.util.Arrays; | ||
| import java.util.Map; | ||
| import java.util.concurrent.TimeUnit; | ||
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| @State(Scope.Benchmark) | ||
| public class MaxPartitionBenchmark { | ||
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| final private Map<Integer, Integer> ADDENDS = Map.of(1, 100, 2, 40, 5, 10); | ||
| final private int PARTITIONED = 10; | ||
| final private ArrayList<Map<Integer, Long>> PARTITION_PLANS = new ArrayList<>(Arrays.asList(Map.of(1, 6L, 2, 2L), | ||
| Map.of(1, 1L, 2, 2L, 5, 1L), | ||
| Map.of(5, 2L), | ||
| Map.of(1, 5L, 5, 1L) | ||
| )); | ||
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| final private DefaultMaxPartitions solver = new DefaultMaxPartitions(); | ||
| final private IntegerProgrammingMaxPartitions ipSolver = new IntegerProgrammingMaxPartitions(); | ||
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| @Fork(value = 1, warmups = 1) | ||
| @Benchmark | ||
| @OutputTimeUnit(TimeUnit.MILLISECONDS) | ||
| @BenchmarkMode(Mode.AverageTime) | ||
| public void solveTwoPhase() { | ||
| solver.solve(ADDENDS, PARTITIONED); | ||
| } | ||
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| @Fork(value = 1, warmups = 1) | ||
| @Benchmark | ||
| @OutputTimeUnit(TimeUnit.MILLISECONDS) | ||
| @BenchmarkMode(Mode.AverageTime) | ||
| public void solveWithPartitionsTwoPhase() { | ||
| solver.solveWithPartitionPlan(ADDENDS, PARTITIONED, PARTITION_PLANS); | ||
| } | ||
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| @Fork(value = 1, warmups = 1) | ||
| @Benchmark | ||
| @OutputTimeUnit(TimeUnit.MILLISECONDS) | ||
| @BenchmarkMode(Mode.AverageTime) | ||
| public void solveWithIntegerProgramming() { | ||
| ipSolver.solve(ADDENDS, PARTITIONED); | ||
| } | ||
| } |
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130
...thm/src/main/java/dev/carbonshow/algorithm/partition/IntegerProgrammingMaxPartitions.java
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| package dev.carbonshow.algorithm.partition; | ||
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| import com.google.ortools.Loader; | ||
| import com.google.ortools.linearsolver.MPObjective; | ||
| import com.google.ortools.linearsolver.MPSolver; | ||
| import com.google.ortools.linearsolver.MPVariable; | ||
| import org.apache.commons.lang3.StringUtils; | ||
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| import java.util.ArrayList; | ||
| import java.util.HashMap; | ||
| import java.util.Map; | ||
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| /** | ||
| * 基于整数线性规划实现的解决方案，具体是： | ||
| * <ul> | ||
| * <li>建立二维决策变量 Variables[MAX_ADDEND_KINDS][MAX_PARTITIONS_NUM]，表示各加数在各划分方案中使用次数 | ||
| * <ul> | ||
| * <li>MAX_ADDEND_KINDS，表示加数的不同种类的数量</li> | ||
| * <li>MAX_PLANS_NUM，表示划分的最大数量，可以划分可以重复，实际上不大于单个加数的最大数量</li> | ||
| * </ul> | ||
| * </li> | ||
| * <li>建立一维决策变量 Variables[MAX_PARTITIONS_NUM]，用于记录实际每个方案划分，要么存在是 1，要么不存在是 0</li> | ||
| * <li>约束条件有： | ||
| * <ul> | ||
| * <li>每个划分使用的加数之和必须等于被划分数</li> | ||
| * <li>每种加数在所有划分中的实际使用次数不能超过其总数</li> | ||
| * </ul> | ||
| * </li> | ||
| * <li>优化目标是：Variables[MAX_PARTITIONS_NUM] 中各变量之和最大化 </li> | ||
| * </ul> | ||
| */ | ||
| public class IntegerProgrammingMaxPartitions implements MaxPartitions { | ||
| // 基于 Google OR-Tools 的数学优化器 | ||
| final private MPSolver solver; | ||
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| IntegerProgrammingMaxPartitions() { | ||
| Loader.loadNativeLibraries(); | ||
| solver = MPSolver.createSolver("SCIP"); | ||
| if (solver == null) { | ||
| throw new RuntimeException("fail to create solver for IntegerProgramming"); | ||
| } | ||
| } | ||
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| /** | ||
| * 基于整数线性规划一步完成整个计算过程，不再区分划分方案和划分实例，而是直接评估划分实例： | ||
| * <ul> | ||
| * <li>决策变量：加数在不同划分中的出现次数；以及每个划分方案是否实际使用的标记 0 或 1</li> | ||
| * <li>约束条件：每个划分的加数之和等于被划分数；每种加数的使用次数不超过加数总数</li> | ||
| * <li>优化目标：每个划分方案的标记标记之和最大化，即有效划分的数量最大化</li> | ||
| * </ul> | ||
| * | ||
| * @param addends 加数集合，这是一个二维数组，一维表示不同的加数，二维应该具有两个元素，分别为加数的值，以及当前加数的数量 | ||
| * @param partitioned 对上面的加数集合进行划分，每个划分所含加数之和应该等于该值。 | ||
| * @return 返回最终划分结果的详细数据，将所有划分方案的组成以及实施数量罗列出来，不存在则返回 null | ||
| */ | ||
| @Override | ||
| public ArrayList<PartitionData> solve(Map<Integer, Integer> addends, int partitioned) { | ||
| // 清理求解器 | ||
| solver.clear(); | ||
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| // 确定加数种类的最大数量和划分的最大数量，划分最大数量一定不超过所有加数数量之和 | ||
| final int maxAddendKinds = addends.size(); | ||
| final int maxPartitions = addends.values().stream().mapToInt(i -> i).sum(); | ||
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| // 将加数和对应总数拆分到两个不同的数组中，并按加数大小升序排列 | ||
| var orderedAddends = new int[addends.size()]; | ||
| var orderedAddendCounts = new int[addends.size()]; | ||
| MaxPartitionsUtils.addendsToArray(addends, orderedAddends, orderedAddendCounts); | ||
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| // 定义加数决策变量， 即每个划分中该加数使用的数量，每个加数决策变量的上限必定不能超过当前加数的总数 | ||
| MPVariable[][] addendVariables = new MPVariable[maxAddendKinds][maxPartitions]; | ||
| for (int i = 0; i < maxAddendKinds; i++) { | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| addendVariables[i][j] = solver.makeIntVar(0, orderedAddendCounts[i], StringUtils.join("a", i, "_", j)); | ||
| } | ||
| } | ||
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| // 定义划分决策变量，每个划分要么存在为 1，要么不存在为 0 | ||
| MPVariable[] partitionVariables = new MPVariable[maxPartitions]; | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| partitionVariables[j] = solver.makeIntVar(0, 1, "p" + j); | ||
| } | ||
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| // 添加加数的约束条件，即加数使用总数不得超限 | ||
| for (int i = 0; i < maxAddendKinds; i++) { | ||
| var constraint = solver.makeConstraint(0, orderedAddendCounts[i], "ac" + i); | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| constraint.setCoefficient(addendVariables[i][j], 1); | ||
| } | ||
| } | ||
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| // 添加划分的约束条件，每个划分要么存在要么不存在，但不管怎样加数之和，划分标记与被划分数值乘积，两者必定相等 | ||
| // 换句话两者差值为 0 | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| var constraint = solver.makeConstraint(0, 0, "pc" + j); | ||
| constraint.setCoefficient(partitionVariables[j], -partitioned); | ||
| for (int i = 0; i < maxAddendKinds; i++) { | ||
| constraint.setCoefficient(addendVariables[i][j], orderedAddends[i]); | ||
| } | ||
| } | ||
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| // 设定优化目标，即方案总数最大化 | ||
| MPObjective objective = solver.objective(); | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| objective.setCoefficient(partitionVariables[j], 1); | ||
| } | ||
| objective.setMaximization(); | ||
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| // 求解 | ||
| final MPSolver.ResultStatus result = solver.solve(); | ||
| if (result == MPSolver.ResultStatus.OPTIMAL) { | ||
| ArrayList<PartitionData> partitionData = new ArrayList<>(); | ||
| for (int j = 0; j < maxPartitions; j++) { | ||
| if (partitionVariables[j].solutionValue() == 1) { | ||
| // 说明该划分实际存在，获取划分内容 | ||
| var partition = new HashMap<Integer, Long>(); | ||
| for (int i = 0; i < maxAddendKinds; i++) { | ||
| var addendCnt = (long) addendVariables[i][j].solutionValue(); | ||
| if (addendCnt > 0) { | ||
| partition.merge(orderedAddends[i], addendCnt, (k, v) -> v + addendCnt); | ||
| } | ||
| } | ||
| partitionData.add(new PartitionData(partition, 1)); | ||
| } | ||
| } | ||
| return partitionData; | ||
| } | ||
| return null; | ||
| } | ||
| } |
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25 changes: 25 additions & 0 deletions
25
algorithm/src/main/java/dev/carbonshow/algorithm/partition/MaxPartitionsUtils.java
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,25 @@ | ||
| package dev.carbonshow.algorithm.partition; | ||
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| import java.util.Map; | ||
| import java.util.TreeMap; | ||
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| public class MaxPartitionsUtils { | ||
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| /** | ||
| * 将 Map 类型的加数按照加数升序方式排列，并将加数和加数的数量分别保存在两个数组中 | ||
| * | ||
| * @param addends 加数集合 | ||
| * @param orderedAddends 输出的升序排列的加数 | ||
| * @param orderedAddendCounts 输出的加数数量，和 orderedAddends 一一对应 | ||
| */ | ||
| static void addendsToArray(Map<Integer, Integer> addends, int[] orderedAddends, int[] orderedAddendCounts) { | ||
| // 对加数进行升序排序 | ||
| var sortedAddendMap = new TreeMap<>(addends); | ||
| int i = 0; | ||
| for (Integer addend : sortedAddendMap.keySet()) { | ||
| orderedAddends[i] = addend; | ||
| orderedAddendCounts[i] = sortedAddendMap.get(addend); | ||
| i++; | ||
| } | ||
| } | ||
| } |
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