Continuous

---

Continuous variables refer to decision variables whose values are a subset of real numbers.

In the current version of BQPhy, the continuous variable optimization solves problems whose all decision variables are continuous.

Bounds for the decision variables

For solving continuous variable problems, the decision variables must have bounds on its domain. Even if the problem might have unbounded decision variables, their bounds must be passed as a large positive or negative number, depending on upper or lower bound.

The bounds for the decision variables are passed during the run of an execution of the model file project. There are two ways to add the constraint

• General method: For a general set of bounds on the continuous variables of the form

  $$l_{i} \leq x_{i} \leq u_{i} \quad i \in \{1,2,...,n\}$$

  The upper bounds and lower bounds are to be passed as the following lists

  $$\text{Upper bound =} [u_{i}] \\ \text{Lower bound =} [i_{i}]$$

  For example, consider 3 continuous design variables with the bounds

    0   <= x[0] <= 10
    -5  <= x[1] <= 40
    6.8 <= x[2] <= 10.4

  The bounds are written as follows

    Lower bounds = [0,-5,6.8]
    Upper bounds = [10,40,10.4]

• Same bounds for all decision variables: If the bounds are of the following form

  $$l \leq x_{i} \leq u \quad i \in \{1,2,...,n\}$$

  This can be passed by clicking the Global checkbox near the text bar and then provide the values $l$ and $u$ at the respective places.

Examples

Ackley function and Rastrigin function

These are multimodal problems with continuous decision variables

You can check the problems and their implementation in the Examples section of the documentation.