今天是：
带着程序的旅程，每一行代码都是你前进的一步，每个错误都是你成长的机会，最终，你将抵达你的目的地。
基于Apache math3 的遗传算法计算复杂函数在定义域内的最值（二）
上一节中主要写了遗传算法的定义，Apache math 提供的遗传算法接口实现求函数最大值的理论。这一节直接上代码。
EquationChromosome 该类主要为计算函数的适应度（函数值） 主要代码如下
@Override
public double fitness() {
return val;//返回在当前基因（解）的函数值，这里函数函数值计算我通过luaj框架来计算，具体百度
}
//在经过选择，交叉，突变后新的基因
@Override
public AbstractListChromosome<Integer> newFixedLengthChromosome(List<Integer> newReprs) {
EquationChromosome ecNew = new EquationChromosome(newReprs);
ecNew.setFunctionExpression(functionExpression);
ecNew.setFactorValues(binaryToDecimal(newReprs));
return ecNew;
}
private Map<String, Double> binaryToDecimal(List<Integer> newReprs) {
String [] name =new String[]{"x1","x2"};//测试用定死了两个变量
Map<String,Double> solution =new HashMap<>();
for(int i=0;i<newReprs.size()/64;i++){
List<Integer> one =newReprs.subList(i*64,(i+1)*64);
String binaryStr = one.stream().map(v->v+"").collect(Collectors.joining());
long longBit =Long.parseUnsignedLong(binaryStr,2);
//转换到定义域范围内，假定定义域为[0,4]
Double bd=Double.longBitsToDouble(longBit);
double max=4;
double min=0;
double value =((bd-Double.MIN_VALUE)/(Double.MAX_VALUE-Double.MIN_VALUE))*(max-min)+min;
solution.put(name[i],value);
}
return solution;
}
选择使用默认的选择类
TournamentSelection
EquationCrossover 该类继承了 NPointCrossover 重写主要是为了防止交叉后基因表现（二进制）超出Double范围 ，因为double 占8字节，二进制总共有64位，最高位位符号位，51-62 总共11位指数为，剩余的52位小数位
指数位的最大值为1204，如果指数位11位都为1，则此时将超出double范围，表示为NaN,故如下处理
for(int i=0;i<child1Rep.size()/64;i++){
List<Integer> sub =child1Rep.subList(i*64,(i+1)*64);
List<Integer> sub11 =sub.subList(1,12);
long sum = sub11.stream().filter(n->n==1).count();
if(sum==11)
child1Rep.set(i*64+11,0);
}
for(int i=0;i<child2Rep.size()/64;i++){
List<Integer> sub =child2Rep.subList(i*64,(i+1)*64);
List<Integer> sub11 =sub.subList(1,12);
long sum = sub11.stream().filter(n->n==1).count();
if(sum==11)
child2Rep.set(i*64+11,0);
}
EquationMutaion implements MutationPolicy 此类和上述EquationCrossover情况类似，不在叙述。
EquationStoppingCondition implements StoppingCondition 遗传算法的停止条件，这里给出集中方式。
- 在一段时间后停止
- 再执行N代后停止
- 基因在N次无变化后停止
- 函数值变化范围很小或不变化后停止
接下来执行GA运算
public class GATest {
public static final int POPULATION_SIZE = 60;
public static final double CROSSOVER_RATE = 0.9;
public static final double MUTATION_RATE = 0.03;
public static final double ELITISM_RATE = 0.1;
public static final int TOURNAMENT_ARITY = 2;
public static final int DIMENSION = TARGET_STRING.length();
public static final String exp="x1*x1+x2*x2";
// public static final String exp="21.5+x1*(math.sin(4*math.pi*x1)+x2*math.sin(20*math.pi*x2))";
public void getResult(){
long startTime = System.currentTimeMillis();
// initialize a new genetic algorithm
GeneticAlgorithm ga = new GeneticAlgorithm(new EquationCrossover<>(2), CROSSOVER_RATE,
new EquationMutaion(), MUTATION_RATE,
new TournamentSelection(TOURNAMENT_ARITY));
List<Map<String,Double>> init = new ArrayList<>();
Map<String,Double> initVal =new HashMap<>();
initVal.put("x1",1.2);
initVal.put("x2",1.5);
Map<String,Double> initVal2 =new HashMap<>();
initVal2.put("x1",3.1);
initVal2.put("x2",3.22);
init.add(initVal);
init.add(initVal2);
// initial population
Population initial = getInitialPopulation(init);
// stopping condition
StoppingCondition stoppingCondition = new EquationStoppingCondition(10000,200);
System.out.println("Starting evolution ...");
// run the algorithm
Population finalPopulation = ga.evolve(initial, stoppingCondition);
// Get the end time for the simulation.
long endTime = System.currentTimeMillis();
// best chromosome from the final population
EquationChromosome best = (EquationChromosome) finalPopulation.getFittestChromosome();
System.out.println("Generation " + ga.getGenerationsEvolved() + ": " + best.toString());
Map<String,Double> map= best.getFactorValues();
for(String key:map.keySet()){
double max= map.get(key);
System.out.println("Solution " + key+ " : "+map.get(key));
}
System.out.println("----------------------------Total execution time: " + (endTime - startTime) + "ms----------------------------");
}
private Population getInitialPopulation(List<Map<String,Double>> initValues) {
List<Chromosome> popList = new LinkedList<Chromosome>();
for(Map<String,Double> factors:initValues){
List<Double> geneList = factors.values().stream().collect(Collectors.toList());
for (int i = 0; i < POPULATION_SIZE; i++) {
EquationChromosome ec = new EquationChromosome(getGene(geneList));
ec.setFactorValues(factors);
ec.setFunctionExpression(exp);
popList.add(ec);
}
}
return new ElitisticListPopulation(popList, 2 * popList.size(), ELITISM_RATE);
}
public List<Integer> getGene(List<Double> values){
List<Integer> geneList =new ArrayList<>();
for(Double val:values){
String binStr = Long.toBinaryString(Double.doubleToLongBits(val));
//不足64位补0
if(binStr.length()==62){
StringBuilder sb = new StringBuilder(binStr);
sb.insert(0,"0");
sb.insert(1,"0");
binStr=sb.toString();
}
if(binStr.length()==63){
StringBuilder sb = new StringBuilder(binStr);
sb.insert(0,"0");
binStr=sb.toString();
}
for(int i=0;i<binStr.length();i++){
geneList.add(Integer.valueOf(binStr.charAt(i)-48));
}
}
return geneList;
}
public static String toBinary(long num,int digits){
String cover =Long.toBinaryString(1<<digits).substring(1);
String str =Long.toBinaryString(num);
return str.length()<digits?cover.substring(str.length())+str:str;
}
}
测试
@Test
public void test(){
for(int i=0;i<10;i++) {
GATest gat = new GATest();
gat.getResult();
}
}
执行10次之后的结果为：
Starting evolution ... Generation 530: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 6021ms---------------------------- Starting evolution ... Generation 627: (f=32.0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : -4.0 Solution x2 : 4.0 ----------------------------Total execution time: 2075ms---------------------------- Starting evolution ... Generation 544: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1383ms---------------------------- Starting evolution ... Generation 587: (f=32.0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : -4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1487ms---------------------------- Starting evolution ... Generation 586: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1454ms---------------------------- Starting evolution ... Generation 579: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1490ms---------------------------- Starting evolution ... Generation 527: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1272ms---------------------------- Starting evolution ... Generation 574: (f=32.0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : -4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1393ms---------------------------- Starting evolution ... Generation 595: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1486ms---------------------------- Starting evolution ... Generation 697: (f=32.0 [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) Solution x1 : 4.0 Solution x2 : 4.0 ----------------------------Total execution time: 1785ms----------------------------分享到：
