New to Optimization
A better decision begins with a better question
Schedules, delivery plans, rosters and quantum circuits share one challenge: making choices under constraints. Start here with the fundamentals.
Six short lessons, from your first question to a model you build yourself.
What an optimizer does
An optimizer searches the possible plans for one that keeps every rule and scores best on your goal. Switch between the three plans to see the difference.
One van leaves the depot, serves all seven stops and returns.
Stops served6 of 7
Distance driven81 km
Illustrative example, not customer data.
Every optimization problem has three parts
The van in the example above has all three. So does a production schedule, a delivery plan or a staff roster.
Decisions
What you can choose
The order of the stops, which machine runs which job, who works which shift.
Constraints
The rules every plan keeps
Every stop served, every vehicle within its capacity, every shift covered.
Objective
The goal you measure
Fewer kilometers, earlier delivery or lower cost: the score that makes one feasible plan better than another.
Follow the learning path
Six short lessons lead from everyday decisions to the ideas behind optimization software. No mathematical background is required: read in order, or start with the question that interests you.
Part 1
What is mathematical optimization?
Start with jobs, resources, constraints and objectives. Discover the difference between choosing a plan and predicting what happens.
Part 2
Do I have an optimization problem?
Recognize the telltale signs: competing priorities, scarce resources, many possible combinations and outcomes you can measure. Learn when simpler methods may be enough.
Part 3
Why can optimization be difficult?
A small change in the number of jobs or assignments can create an enormous increase in the number of possible plans. Understand why it is hard to search effectively.
Part 4
What makes a mathematical model?
Explore decision variables, constraints and objectives using a manageable example. See what an algorithm needs to know before it can search.
Part 5
How do algorithms search?
See how different methods construct feasible answers, improve them and explore alternatives without checking every possibility.
Part 6
Can I build a small model myself?
Turn a modest decision into a model, test the result and see how changing the constraints affects the answer.
Where can this take you?
Operational decisions
See optimization at work in scheduling, routing, packing and planning.
Practical modeling
Turn a real decision into a model, step by step.
The ideas behind the algorithms
Articles on search, benchmarks and what better algorithms change.
What 4colors offers
Software, planning applications and projects for classical optimization.
Ready for the first lesson?
Begin with the fundamentals, or bring a real decision and talk it through with us.
Start with the fundamentalsDiscuss an optimization challenge