The designers of Optional explicitly warn against using it as method parameters (e.g. https://stackoverflow.com/a/26328555).

There are several ways to simulate optional parameters in Java.

Method overloading

Copyvoid foo(String a, Integer b) {
    //...
}

void foo(String a) {
    foo(a, 0); // here, 0 is a default value for b
}

foo("a", 2);
foo("a");

One of the limitations of this approach is that it doesn't work if you have two optional parameters of the same type and any of them can be omitted.

Varargs

a) All optional parameters are of the same type:

Copyvoid foo(String a, Integer... b) {
    Integer b1 = b.length > 0 ? b[0] : 0;
    Integer b2 = b.length > 1 ? b[1] : 0;
    //...
}

foo("a");
foo("a", 1, 2);

b) Types of optional parameters may be different:

Copyvoid foo(String a, Object... b) {
    Integer b1 = 0;
    String b2 = "";
    if (b.length > 0) {
      if (!(b[0] instanceof Integer)) { 
          throw new IllegalArgumentException("...");
      }
      b1 = (Integer)b[0];
    }
    if (b.length > 1) {
        if (!(b[1] instanceof String)) { 
            throw new IllegalArgumentException("...");
        }
        b2 = (String)b[1];
        //...
    }
    //...
}

foo("a");
foo("a", 1);
foo("a", 1, "b2");

The main drawback of this approach is that if optional parameters are of different types you lose static type checking. Furthermore, if each parameter has the different meaning you need some way to distinguish them.

Nulls

To address the limitations of the previous approaches you can allow null values and then analyze each parameter in a method body:

Copyvoid foo(String a, Integer b, Integer c) {
    b = b != null ? b : 0;
    c = c != null ? c : 0;
    //...
}

foo("a", null, 2);

Now all arguments values must be provided, but the default ones may be null.

Optional class

This approach is similar to nulls, but uses Java 8 Optional class for parameters that have a default value:

Copyvoid foo(String a, Optional<Integer> bOpt) {
    Integer b = bOpt.isPresent() ? bOpt.get() : 0;
    //...
}

foo("a", Optional.of(2));
foo("a", Optional.<Integer>absent());

Optional makes a method contract explicit for a caller, however, one may find such signature too verbose.

Update: Java 8 includes the class java.util.Optional out-of-the-box, so there is no need to use guava for this particular reason in Java 8. The method name is a bit different though.

Builder pattern

The builder pattern is used for constructors and is implemented by introducing a separate Builder class:

Copyclass Foo {
    private final String a; 
    private final Integer b;

    Foo(String a, Integer b) {
      this.a = a;
      this.b = b;
    }

    //...
}

class FooBuilder {
  private String a = ""; 
  private Integer b = 0;
  
  FooBuilder setA(String a) {
    this.a = a;
    return this;
  }

  FooBuilder setB(Integer b) {
    this.b = b;
    return this;
  }

  Foo build() {
    return new Foo(a, b);
  }
}

Foo foo = new FooBuilder().setA("a").build();

Maps

When the number of parameters is too large and for most of the default values are usually used, you can pass method arguments as a map of their names/values:

Copyvoid foo(Map<String, Object> parameters) {
    String a = ""; 
    Integer b = 0;
    if (parameters.containsKey("a")) { 
        if (!(parameters.get("a") instanceof Integer)) { 
            throw new IllegalArgumentException("...");
        }
        a = (Integer)parameters.get("a");
    }
    if (parameters.containsKey("b")) { 
        //... 
    }
    //...
}

foo(ImmutableMap.<String, Object>of(
    "a", "a",
    "b", 2, 
    "d", "value")); 

In Java 9, this approach became easier:

Copy@SuppressWarnings("unchecked")
static <T> T getParm(Map<String, Object> map, String key, T defaultValue) {
  return (map.containsKey(key)) ? (T) map.get(key) : defaultValue;
}

void foo(Map<String, Object> parameters) {
  String a = getParm(parameters, "a", "");
  int b = getParm(parameters, "b", 0);
  // d = ...
}

foo(Map.of("a","a",  "b",2,  "d","value"));

Please note that you can combine any of these approaches to achieve a desirable result.

If you have few parameters or very few sensible combinations of those parameters go for multiple overloads of the method with different parameter sets. If this generates a substantial number (more than 3-4), go for a config object instead

Why? The number of necessary overloads increases with quadratically with the number of parameters, therefore already even a reasonable set of parameters (like 5) will end up with tons of overloaded methods