Basically I searched all methods that can be executed with a set of parameters. So, I sorted them by the distance between the parameterType to the methodParameterType. Doing this, I could get the most specific overloaded method.
To test:
@Test
public void test() throws Throwable {
    Object object = 1;
    Foo foo = new Foo();
    MethodExecutor.execute(foo, "foo", Void.class, object);
}
The Foo:
class Foo {
    public void foo(Integer integer) {
        System.out.println("integer");
    }
    public void foo(Number number) {
        System.out.println("number");
    }
    public void foo(Object object) {
        System.out.println("object");
    }
}
The MethodExecutor:
public class MethodExecutor{
    private static final Map<Class<?>, Class<?>> equivalentTypeMap = new HashMap<>(18);
    static{
        equivalentTypeMap.put(boolean.class, Boolean.class);
        equivalentTypeMap.put(byte.class, Byte.class);
        equivalentTypeMap.put(char.class, Character.class);
        equivalentTypeMap.put(float.class, Float.class);
        equivalentTypeMap.put(int.class, Integer.class);
        equivalentTypeMap.put(long.class, Long.class);
        equivalentTypeMap.put(short.class, Short.class);
        equivalentTypeMap.put(double.class, Double.class);
        equivalentTypeMap.put(void.class, Void.class);
        equivalentTypeMap.put(Boolean.class, boolean.class);
        equivalentTypeMap.put(Byte.class, byte.class);
        equivalentTypeMap.put(Character.class, char.class);
        equivalentTypeMap.put(Float.class, float.class);
        equivalentTypeMap.put(Integer.class, int.class);
        equivalentTypeMap.put(Long.class, long.class);
        equivalentTypeMap.put(Short.class, short.class);
        equivalentTypeMap.put(Double.class, double.class);
        equivalentTypeMap.put(Void.class, void.class);
    }
    public static <T> T execute(Object instance, String methodName, Class<T> returnType, Object ...parameters) throws InvocationTargetException, IllegalAccessException {
        List<Method> compatiblesMethods = getCompatiblesMethods(instance, methodName, returnType, parameters);
        Method mostSpecificOverloaded = getMostSpecificOverLoaded(compatiblesMethods, parameters);
        //noinspection unchecked
        return (T) mostSpecificOverloaded.invoke(instance, parameters);
    }
    private static List<Method> getCompatiblesMethods(Object instance, String methodName, Class<?> returnType, Object[] parameters) {
        Class<?> clazz = instance.getClass();
        Method[] methods = clazz.getMethods();
        List<Method> compatiblesMethods = new ArrayList<>();
        outerFor:
        for(Method method : methods){
            if(!method.getName().equals(methodName)){
                continue;
            }
            Class<?> methodReturnType = method.getReturnType();
            if(!canBeCast(returnType, methodReturnType)){
                continue;
            }
            Class<?>[] methodParametersType = method.getParameterTypes();
            if(methodParametersType.length != parameters.length){
                continue;
            }
            for(int i = 0; i < methodParametersType.length; i++){
                if(!canBeCast(parameters[i].getClass(), methodParametersType[i])){
                    continue outerFor;
                }
            }
            compatiblesMethods.add(method);
        }
        if(compatiblesMethods.size() == 0){
            throw new IllegalArgumentException("Cannot find method.");
        }
        return compatiblesMethods;
    }
    private static Method getMostSpecificOverLoaded(List<Method> compatiblesMethods, Object[] parameters) {
        Method mostSpecificOverloaded = compatiblesMethods.get(0);
        int lastMethodScore = calculateMethodScore(mostSpecificOverloaded, parameters);
        for(int i = 1; i < compatiblesMethods.size(); i++){
            Method method = compatiblesMethods.get(i);
            int currentMethodScore = calculateMethodScore(method, parameters);
            if(lastMethodScore > currentMethodScore){
                mostSpecificOverloaded = method;
                lastMethodScore = currentMethodScore;
            }
        }
        return mostSpecificOverloaded;
    }
    private static int calculateMethodScore(Method method, Object... parameters){
        int score = 0;
        Class<?>[] methodParametersType = method.getParameterTypes();
        for(int i = 0; i < parameters.length; i++){
            Class<?> methodParameterType = methodParametersType[i];
            if(methodParameterType.isPrimitive()){
                methodParameterType = getEquivalentType(methodParameterType);
            }
            Class<?> parameterType = parameters[i].getClass();
            score += distanceBetweenClasses(parameterType, methodParameterType);
        }
        return score;
    }
    private static int distanceBetweenClasses(Class<?> clazz, Class<?> superClazz){
        return distanceFromObjectClass(clazz) - distanceFromObjectClass(superClazz);
    }
    private static int distanceFromObjectClass(Class<?> clazz){
        int distance = 0;
        while(!clazz.equals(Object.class)){
            distance++;
            clazz = clazz.getSuperclass();
        }
        return distance;
    }
    private static boolean canBeCast(Class<?> fromClass, Class<?> toClass) {
        if (canBeRawCast(fromClass, toClass)) {
            return true;
        }
        Class<?> equivalentFromClass = getEquivalentType(fromClass);
        return equivalentFromClass != null && canBeRawCast(equivalentFromClass, toClass);
    }
    private static boolean canBeRawCast(Class<?> fromClass, Class<?> toClass) {
        return fromClass.equals(toClass) || !toClass.isPrimitive() && toClass.isAssignableFrom(fromClass);
    }
    private static Class<?> getEquivalentType(Class<?> type){
        return equivalentTypeMap.get(type);
    }
}
Ofcourse it can be improved with some refactoring and comments.