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JYU subproject

Enhanced multiobjective optimization algorithms for computationally expensive problems


Multiple conflicting objectives for optimisation typically arise in engineering design problems. In such problems, there does not usually exist a single optimal solution, but a set of solutions called Pareto optimal solutions, which cannot be mathematically ordered. Considering multiple objectives provides a higher in-depth insight into the design problem and interdependencies involved. In practice, objective and constraint functions are often computationally expensive, which hinders the wide-spread use of multiobjective optimization. Several methods have been proposed in the literature for solving computationally expensive multiobjective optimisation problems, including heuristics based methods such as nature inspired algorithms with several enhancements. Applicability of such heuristics based methods to practical multiobjective optimisation problems involving computationally expensive functions was the main focus of this research.

In the project, several demands were identified to be addressed to promote the use of multiobjective optimization in industry:

  • It became apparent at the beginning of the project that awareness of the advantages and potential of using multiobjective optimization was not very strong and more information and understanding was to be given to all associated project partners.
  • A practitioner or a researcher when faced with a real-life computationally expensive multiobjective optimization problem has several challenges, such as choosing a suitable method even though extensive literature exists.
  • When solving a multiobjective optimization problem, a decision maker is often looking for a solution which (s)he wishes to implement. However, decision support systems that can help her/him to find such a solution are rare in the literature for computationally expensive problems.

Thus, this subproject aimed at being a platform for empowerment of practitioners, who have a computationally expensive multiobjective optimisation problem to solve.


We addressed the above-mentioned demands and documented them as articles, reports etc. besides giving talks. We had four main types of outputs.

  1. Knowledge aggregation through literature surveys: Three survey articles were written to summarize the state of the art in the literature in solving computationally expensive multiobjective optimization problems:
    1. A survey on handling computationally expensive multiobjective optimization problems using surrogates in non-nature inspired methods.
    2. A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms.
    3. A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms and parallel computing.
  2. Novel methods to find preferred Pareto optimal solutions: To utilize and exploit the preference information from the decision maker, the following two methods were developed and corresponding articles written.
    1. An interactive simple indicator-based evolutionary algorithm (I-SIBEA) for multiobjective optimization problems. In this method, hypervolume is used as the quality indicator to be maximised.
    2. Synchronous R-NSGA-II: an extended preference-based evolutionary algorithm for multi-objective optimization. The main idea of this method is to use multiple functions, all using the same preference information of the decision maker in different ways and generate a subset of Pareto optimal solutions desirable to her/him.
  3. Novel decision support system:
    1. E-NAUTILUS: A decision support system for complex multiobjective op-timization problems based on the NAUTILUS method. In this method, the decision maker iteratively proceeds to the most preferred Pareto optimal solution. The method starts from the worst solution called nadir point, and takes one step closer to the Pareto optimal set at each iteration guided by the preferences of the decision maker. It effectively handles computationally expensive multiobjective optimisation problems.
  4. Spread understanding of the potential of multiobjective optimization among researchers and practitioners:
    1. Design of a permanent magnet synchronous generator using interactive multiobjective optimization. The multiobjective optimisation problem considered consisted of six objective functions, four inequality constraints and fourteen design variables. The interactive multiobjective optimization method was NIMBUS (developed earlier at the University of Jyväskylä).

Benefits and use cases

  1. Knowledge aggregation through literature surveys: The literature surveys written provide practitioners knowledge about the methods available so that one can choose a method based on recorded past experiences of other researchers and practitioners and relevant selection criteria.
  2. Novel methods to generate preferred Pareto optimal solutions: The methods developed deal with alternative ways of effectivele handling decision maker’s preference information and generating desirable Pareto optimal solutions.
  3. Novel decision support system: A decision support system that overcomes some cognitive biases and helps a decision maker to find her/his preferred Pareto optimal solution in an interactive fashion. The method offers a new way of solving computationally expensive problems. This method can also be used to find the most preferred solution among the population of solutions generated by nature inspired methods like evolutionary multiobjective optimization methods.
  4. Spread the idea of multiobjective optimization among researchers and practitioners: The permanent magnet synchronous generator design problem solved provided an opportunity for the decision maker to consider the design problem as a whole, understand all the relevant trade-offs and ultimately find her preferred solutions. At the end of the decision making process, the decision maker involved was extremely satisfied both with respect to the solution process and with the solution she selected finally as her most preferred solution.

Overall, the challenges involved in solving computationally expensive multiobjective optimization problems were tackled in different ways and the awareness of the potential was increased. The outcomes of the JYU subproject are given in the figure below.


Subproject deliverables