Abstract
Nadir point, constructed by the worst Pareto optimal objective values, plays an important role in multi-objective optimization and decision making. For example, the nadir point is often a pre-requisite in many multi-criterion decision making approaches. Along with the ideal point, the nadir point can be applied to normalize solutions so as to facilitate a comparison and aggregation of objectives. Moreover, nadir point is useful in visualization software catered for multi-objective optimization. However, the estimation of nadir point is still a challenging problem, particularly, for optimization and/or decision-making problems with many objectives. In this paper, a modified preference-inspired coevolutionary algorithm using goal vectors (PICEA-g) called extremized PICEA-g is proposed to estimate the nadir point. The extremized PICEA-g, denoted as e-PICEA-g, is an \( \left( {N + N} \right) \) elitist algorithm and employs a two-phase selection strategy. In the first-phase \( \left( {N + K} \right) \) solutions are selected out from the overall \( 2N \) solutions based on the dominance-level and an angle based closeness indicator. In the second-phase the selected \( \left( {N + K} \right) \) solutions are further filtered by removing \( K \) poor ones in terms of their fitness calculated by a slightly modified PICEA-g fitness scheme. By the two-phase selection strategy, the e-PICEA-g skillfully harnesses the advantages of edge-point-to-nadir and extreme-to-nadir principles. Experimental results demonstrate the efficiency and effectiveness of the e-PICEA-g on many-objective optimization benchmarks with up to 13 objectives.
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Acknowledgment
This work was supported by the National key research and development plan (2016YFB0901900), the National Natural Science Foundation of China (Nos. 61773390), National Natural Science Fund for Distinguished Young Scholars of China (61525304) and Natural Science Fund for Distinguished Young Scholars of Hunan Province (2017JJ1001).
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Wang, R., Ming, Mj., Xing, Ln., Gong, Wy., Wang, L. (2018). Extremized PICEA-g for Nadir Point Estimation in Many-Objective Optimization. In: Huang, DS., Gromiha, M., Han, K., Hussain, A. (eds) Intelligent Computing Methodologies. ICIC 2018. Lecture Notes in Computer Science(), vol 10956. Springer, Cham. https://doi.org/10.1007/978-3-319-95957-3_85
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