Abstract-In this paper, we propose a metric for evaluating the performance of user-preference based evolutionary multiobjective algorithms by defining a preferred region based on the location of a user-supplied reference point. This metric uses a composite front which is a type of reference set and is used as a replacement for the Pareto-optimal front. This composite front is constructed by extracting the non-dominated solutions from the merged solution sets of all algorithms that are to be compared. A preferred region is then defined on the composite front based on the location of a reference point. Once the preferred region is defined, existing evolutionary multi-objective performance metrics can be applied with respect to the preferred region. In this paper the performance of a cardinality-based metric, a distance-based metric, and a volume-based metric are compared against a baseline which relies on knowledge of the Pareto-optimal front. The experimental results show that the distance-based and the volume-based metrics are consistent with the baseline, showing meaningful comparisons. However, the cardinality-based approach shows some inconsistencies and is not suitable for comparing the algorithms.

Abstract-Evolutionary algorithms that rely on dominance ranking often suffer from a low selection pressure problem when dealing with many-objective problems. Decomposition and userpreference based methods can help to alleviate this problem to a great extent. In this paper, a user-preference based evolutionary multi-objective algorithm is proposed that uses decomposition methods for solving many-objective problems. Decomposition techniques that are widely used in multi-objective evolutionary optimization require a set of evenly distributed weight vectors to generate a diverse set of solutions on the Pareto-optimal front. The newly proposed algorithm, R-MEAD2, improves the scalability of its previous version, R-MEAD, which uses a simplexlattice design method for generating weight vectors. This makes the population size is dependent on the dimension size of the objective space. R-MEAD2 uses a uniform random number generator to remove the coupling between dimension and the population size. This paper shows that a uniform random number generator is simple and able to generate evenly distributed points in a high dimensional space. Our comparative study shows that R-MEAD2 outperforms the dominance-based method R-NSGA-II on many-objective problems.

In this paper we propose a user-preference based evolutionary algorithm that relies on decomposition strategies to convert a multi-objective problem into a set of single-objective problems. The use of a reference point allows the algorithm to focus the search on more preferred regions which can potentially save considerable amount of computational resources. The algorithm that we proposed, dynamically adapts the weight vectors and is able to converge close to the preferred regions. Combining decomposition strategies with reference point ap proaches paves the way for more effective optimization of many objective problems. The use of a decomposition method alleviates the selection pressure problem associated with dominance-based approaches while a reference point allows a more focused search. The experimental results show that the proposed algorithm is capable of finding solutions close to the reference points specified by a decision maker. Moreover, our results show that high quality solutions can be obtained using less computational effort as compared to a state-of-the-art decomposition based evolutionary multi-objective algorithm.

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