Solution

$A^*$ algorithm uses the evaluation function:

$f(n)=g(n)+h(n)$

where,

$g(n)$ is the cost from start node to current node.

$h(n)$ is the estimated cost from current node to goal node.

$A^*$ is optimal when the heuristic function $h$ is admissible.

Admissible means:

$h(n)$ never overestimates the actual cost.

So, $A^*$ always finds the solution with the lowest total cost when $h$ is admissible.