What are the best practices for developing a robust multicriteria optimization solution?

2 Generate the solution

The second step in developing a robust multicriteria optimization solution is to generate the solution using the chosen optimization method and algorithm. You need to ensure that the algorithm can explore the feasible region efficiently and effectively, and that it can produce a diverse and representative set of Pareto-optimal solutions. Pareto-optimal solutions are those that cannot be improved in any objective without worsening another. You also need to monitor the convergence and stability of the algorithm, and adjust the parameters if necessary to improve the performance.

3 Evaluate the solution

The third step in developing a robust multicriteria optimization solution is to evaluate the solution using the performance indicators and statistical tests. You need to assess how well the solution satisfies the constraints, how close it is to the true Pareto front, how diverse and uniform it is, and how sensitive it is to changes in the problem parameters. You also need to compare the solution with other alternative solutions or benchmarks, and test the significance and robustness of the differences.

4 Incorporate uncertainty

The fourth step in developing a robust multicriteria optimization solution is to incorporate uncertainty into the problem and the solution. Uncertainty can arise from various sources, such as measurement errors, model errors, parameter variations, or environmental changes. You need to identify and quantify the sources and types of uncertainty, and use appropriate methods to propagate them through the optimization process. You also need to use robust optimization techniques to handle uncertainty, such as worst-case analysis, stochastic optimization, or interval analysis.

5 Elicit preference

The fifth step in developing a robust multicriteria optimization solution is to elicit preference from the decision maker or the stakeholders. Preference can be expressed in various ways, such as weights, goals, thresholds, or rankings. You need to use suitable methods to elicit preference, such as surveys, interviews, or interactive optimization. You also need to use preference-based optimization techniques to incorporate preference into the optimization process, such as weighted sum, goal programming, or outranking methods.

6 Implement and validate

The final step in developing a robust multicriteria optimization solution is to implement and validate the solution in the real-world context. You need to select one or more solutions from the Pareto-optimal set based on the preference and the performance indicators, and test them in the actual engineering system or environment. You also need to validate the solution using relevant criteria, such as feasibility, reliability, efficiency, or sustainability. You need to monitor and update the solution if the problem or the preference changes over time.