Interactive multiobjective optimization allows to find the most preferred compromise between the conflicting objectives

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What is optimization?

Optimization means finding the best performance for the system (or product) that satisfies the existing constraints. The goodness of the performance is measured with an objective function which can be for example cost, profit, quality, safety or environmental impact. The performance of the system can be changed by giving different values for decision variables that describe the actual implementation of the system. Feasible values for the decision variables are determined by constraint functions that can constrain either the decision variable values directly or indirectly through constraints for some properties of the system like for example resources or capacities.
Only one objective function is considered in single objective optimization. In that case, the aim is to find such feasible decision variable values that either produce the minimum (e.g. for cost) or maximum value for the objective function depending on the objective function used. In single objective optimization, comparing different solutions (i.e. different values for the decision variables) is easy because the single objective function used directly measures which solution has better performance (or in some cases the performance can be the same).

Multiobjective optimization

Typical for real world optimization problems is that multiple objective functions need to be considered simultaneously and, in that case, multiobjective optimization is needed. The objective functions considered can be conflicting which means that the solutions giving the best performance to each of them individually are not the same (if e.g. at the same time cost is minimized and quality is maximized). In that case, there does not exist a feasible solution that gives the best performance for all of them simultaneously and a compromise between them is required. In multiobjective optimization these compromise solutions are called Pareto optimal solutions where none of the objective function values can be improved without impairing some of the others.

Typically, there exist several Pareto optimal solutions for a multiobjective optimization problem and picking the best among them can’t be made without some additional information about the application considered. The overall goal in solving real world multiobjective optimization problems is to identify the most preferred compromise (Pareto optimal solution) between the conflicting objective functions. What is “most preferred” is defined with the help of a human decision maker (e.g. a designer or an operator) who is an expert in the application area and is able to express preferences among the conflicting objectives.

Interactive Multiobjective Optimization – What FINNOPT is all about

The ultimate goal in solving real world multiobjective optimization problem is to identify the most preferred compromise (i.e. Pareto optimal solution) between the conflicting objectives in practice. Interactive multiobjective optimization is an approach to multiobjective optimization, where a human decision maker (e.g. a designer or an operator) searches for the most preferred compromise by providing their preferences in terms of the objective function values iteratively. This iterative approach allows the decision maker to guide the solution process towards preferred compromise solutions, instead of using resources in computing uninteresting ones.

To be more precise, some compromise solution is computed to start with and it is shown to the decision maker. Then, they can express how the solution should be improved if it is not desirable in their current situation. Based on decision maker’s preferences, new compromise solution(s) are computed and shown to them. This iterative process continues until the decision maker is satisfied, that is, they have found the most preferred compromise. During the iterative solution process, the decision maker can learn about the interdependencies between the conflicting objectives since they get feedback about what kind of compromise solutions there exist based on the solutions computed reflecting the given preference information.