Chapter 3. Introduction to Red Hat build of OptaPlanner

OptaPlanner is a lightweight, embeddable planning engine that optimizes planning problems. It helps normal Java programmers solve planning problems efficiently, and it combines optimization heuristics and metaheuristics with very efficient score calculations.

For example, OptaPlanner helps solve various use cases:

  • Employee/Patient Rosters: It helps create time tables for nurses and keeps track of patient bed management.
  • Educational Timetables: It helps schedule lessons, courses, exams, and conference presentations.
  • Shop Schedules: It tracks car assembly lines, machine queue planning, and workforce task planning.
  • Cutting Stock: It minimizes waste by reducing the consumption of resources such as paper and steel.

Every organization faces planning problems; that is, they provide products and services with a limited set of constrained resources (employees, assets, time, and money).

OptaPlanner is open source software under the Apache Software License 2.0. It is 100% pure Java and runs on most Java virtual machines.

3.1. Planning problems

A planning problem has an optimal goal, based on limited resources and under specific constraints. Optimal goals can be any number of things, such as:

  • Maximized profits - the optimal goal results in the highest possible profit.
  • Minimized ecological footprint - the optimal goal has the least amount of environmental impact.
  • Maximized satisfaction for employees or customers - the optimal goal prioritizes the needs of employees or customers.

The ability to achieve these goals relies on the number of resources available. For example, the following resources might be limited:

  • The number of people
  • Amount of time
  • Budget
  • Physical assets, for example, machinery, vehicles, computers, buildings, and so on

You must also take into account the specific constraints related to these resources, such as the number of hours a person works, their ability to use certain machines, or compatibility between pieces of equipment.

Red Hat build of OptaPlanner helps Java programmers solve constraint satisfaction problems efficiently. It combines optimization heuristics and metaheuristics with efficient score calculation.

3.2. NP-completeness in planning problems

The provided use cases are probably NP-complete or NP-hard, which means the following statements apply:

  • It is easy to verify a given solution to a problem in reasonable time.
  • There is no simple way to find the optimal solution of a problem in reasonable time.

The implication is that solving your problem is probably harder than you anticipated, because the two common techniques do not suffice:

  • A brute force algorithm (even a more advanced variant) takes too long.
  • A quick algorithm, for example in the bin packing problem, putting in the largest items first returns a solution that is far from optimal.

By using advanced optimization algorithms, OptaPlanner finds a good solution in reasonable time for such planning problems.

3.3. Solutions to planning problems

A planning problem has a number of solutions.

Several categories of solutions are:

Possible solution
A possible solution is any solution, whether or not it breaks any number of constraints. Planning problems often have an incredibly large number of possible solutions. Many of those solutions are not useful.
Feasible solution
A feasible solution is a solution that does not break any (negative) hard constraints. The number of feasible solutions are relative to the number of possible solutions. Sometimes there are no feasible solutions. Every feasible solution is a possible solution.
Optimal solution
An optimal solution is a solution with the highest score. Planning problems usually have a few optimal solutions. They always have at least one optimal solution, even in the case that there are no feasible solutions and the optimal solution is not feasible.
Best solution found
The best solution is the solution with the highest score found by an implementation in a given amount of time. The best solution found is likely to be feasible and, given enough time, it’s an optimal solution.

Counterintuitively, the number of possible solutions is huge (if calculated correctly), even with a small data set.

In the examples provided in the planner-engine distribution folder, most instances have a large number of possible solutions. As there is no guaranteed way to find the optimal solution, any implementation is forced to evaluate at least a subset of all those possible solutions.

OptaPlanner supports several optimization algorithms to efficiently wade through that incredibly large number of possible solutions.

Depending on the use case, some optimization algorithms perform better than others, but it is impossible to know in advance. Using OptaPlanner, you can switch the optimization algorithm by changing the solver configuration in a few lines of XML or code.

3.4. Constraints on planning problems

Usually, a planning problem has minimum two levels of constraints:

  • A (negative) hard constraint must not be broken.

    For example, one teacher can not teach two different lessons at the same time.

  • A (negative) soft constraint should not be broken if it can be avoided.

    For example, Teacher A does not like to teach on Friday afternoons.

Some problems also have positive constraints:

  • A positive soft constraint (or reward) should be fulfilled if possible.

    For example, Teacher B likes to teach on Monday mornings.

Some basic problems only have hard constraints. Some problems have three or more levels of constraints, for example, hard, medium, and soft constraints.

These constraints define the score calculation (otherwise known as the fitness function) of a planning problem. Each solution of a planning problem is graded with a score. With OptaPlanner, score constraints are written in an object oriented language such as Java, or in Drools rules.

This type of code is flexible and scalable.