Balancing different optimization goals

Planning problems often involve multiple optimization goals. In real-world scenarios, there is not a single "best plan". Instead, optimization must balance different objectives, requiring a normalizing function to weigh the goals against each other.

This challenge is well illustrated in employee rostering, where multiple goals must be optimized simultaneously:

In Timefold models, each of these goals is implemented through one or more constraints. Some constraints naturally optimize for multiple goals — such as matching the preferred skills of employees with tasks, which can enhance both service quality and employee satisfaction. Others might work adversarially — reducing employee costs might lead to more stringent scheduling, negatively impacting employee satisfaction.

In this article we will explain how you can use Timefold to align multiple optimization goals with your business goals, and how to do “goal alignment”.

Timefold plans include output metrics that reflect the real-world impact of different optimization goals. If minimizing overtime is an objective, the system will track “total overtime hours”. When comparing different plans in the Timefold Platform, these metrics provide transparency into how well each plan aligns with the optimization goal.

Learn more about Run metrics.

Multi-objective optimization (or Pareto optimization) involves balancing trade-offs between competing goals. There is no single “best plan”, only different trade-offs depending on business priorities. A plan that is better in each of the aspects is always better then a previously found plan, but more often than not what might be better in one aspect, might be worse in another aspect. To compare plans, a weighted function translates multiple optimization goals into a common scale.

In Timefold, the scoring function serves as this normalizing function. It evaluates each plan based on:

Learn more about constraints.

Each constraint contributes to the final score of a plan. A constraint minimizing the travel distance will take into account the total distance required to execute a plan, a constraint minimizing the amount of overtime could use both the total minutes of overtime required to execute a plan and the number of affected employees with overtime. Other constraints might be even more complex and take multiple non-linear approaches. As such, the scoring function will sum different units (e.g. kilometers, minutes, affected employees) to come to a final score. But how does one balance an extra kilometer driven to an extra minute of overtime? Only you as a business know.

In the Timefold Platform, the score graph shows you the evolution of the hard/medium/soft scores, and the score analysis shows you the impact of each constraint on those scores.

Timefold implements its constraints so that multiple optimization goals are balanced as much as possible by default. But of course, every business, and every business case is different, so what we see as good defaults might not be the best defaults for your business.

Read on to understand how our features help with this.

To allow customization, Timefold supports giving each soft constraint a different weight via Configuration Profiles. By default, all constraints have an equal weight (1), but users can adjust this:

For example, if reducing overtime is more important than minimizing travel distance, users can increase the weight of the “minimize overtime” constraint while leaving “minimize travel distance” unchanged. Timefold will then prioritize plans that better align with this preference.

Read more on how to change configuration parameters.

By running similar datasets with different constraint weights, plans will be different. By analyzing the metrics across these different plans, users can make informed decisions about which plan best meets their needs.

If you’re interested in balancing the different optimization goals differently, we recommend taking the following approach in the Timefold Platform:

This process of gradual adjustment — running multiple experiments, tweaking constraint weights, and analyzing the trade-offs — is what we call goal alignment.

What if we could just assign a dollar value to each time a constraint is broken? While the cost of an extra kilometer might be easy to express in a currency, the impact on employee satisfaction of that extra kilometer is already harder to quantify. We’re convinced that trying to express every optimization goal in a currency will not greatly improve the experience. Not only because certain constraints (like fairness or employee well-being) are very hard to quantify in monetary terms, but because to do this you need to again define values before seeing their impact, resulting in a process that would still require iterative adjustments, not unlike constraint weighting today. Expressing each constraint in a currency is actually a very similar exercise to figuring out the constraint weights.

While today, tuning optimization goals is a manual and iterative process, we are working on making this easier with:

With these improvements, which we plan to tackle in the order above, we think we can gradually make the finetuning process smarter and easier.

Timefold helps businesses navigate the complexity of multi-objective optimization in planning problems. By providing balanced scoring functions and configurable constraint weights, we empower users to find plans that best align with their unique goals — balancing efficiency, cost, and employee satisfaction in a way that fits their needs. By offering a UI that helps to compare the metrics of different plans, you can make more informed decisions.