Optimisation vs Decision Problem

Decision Problem 

There will be only one correct solution for each input. Or in other words, it is the one with yes/no answer.

Eg: Does a graph G has MST weight <= W

Optimisation Problem 

Finding the best/optimal solution from all the feasible solutions. 

Eg: Minimum Spanning Tree 

Discrete Optimisation 

Discrete - separate entity or detached from others. 

Some models only make sense if the variables take on values from a discrete set, often a subset of integers.  Models with discrete variables are discrete optimisation problems.

In discrete optimisation, some or all of the variables in a model required to belong to a discrete set. 

Combinatorial Optimisation 

Models contain variables that can take on any real value.  Models with continuous variable are continuous optimisation problems. 

In continuous optimisation, variables are allowed to take on any value within a range of values.