Dynamic Multiobjective Optimization Problems (DMOPs) challenge Multiobjective Evolutionary Algorithms (MOEAs) because those problems change rapidly over time. The class of DMOPs whose objective functions change over time steps, in ways that exhibit some hidden patterns has gained much attention. Their predictability indicates that the problem exhibits some correlations between solutions obtained in sequential time periods. Most of current approaches use linear models or similar strategies to describe the correlations between historical solutions obtained, and predict the new solutions in the following time period as an initial population from which the MOEA can begin searching in order to improve its efficiency. However, nonlinear correlations between historical solutions and current solutions are more common in practice, and a linear model may not be suitable for the nonlinear case. In this paper, we present a Support Vector Regression-based predictor to generate the initial population for the MOEA in the new environment. The basic idea of this predictor is to map the historical solutions into a high-dimensional feature space via a nonlinear mapping, and to do linear regression in this space. Support Vector Regression is used to implement this process. We incorporate this predictor into the Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) to construct a novel algorithm for solving the aforementioned class of DMOPs. Comprehensive experiments have shown the effectiveness and competitiveness of our proposed predictor, comparing with the state-of-the-art methods.

Within the 21st century, in the Maritime Silk Road, wave energy, a clean renewable source, is drawing more interest, especially in areas with power shortages. This paper investigates wave energy in ships, particularly in a hybrid electric bulk carrier, by designing a system that supplements the existing power setup with oscillating buoy wave energy converters. The system includes diesel generators (DGs), a wave energy generation system, heterogeneous energy storage (consisting of battery storage (BS) and thermal storage (TS)), a combined cooling heat and power (CCHP) unit, and a power-to-thermal conversion (PtC) unit. To ensure safe and reliable navigation despite uncertainties in wave energy output, onboard power loads, and outdoor temperature, a robust coordination method is adopted. This method employs a two-stage robust optimization (RO) strategy to coordinate the various onboard units across different time scales, minimizing operational costs while satisfying all operational constraints, even in the worst-case scenarios. By applying constraint linearization, the robust coordination model is formulated as a mixed-integer linear programming (MILP) problem and solved using an efficient solver. Finally, the effectiveness of the proposed method is validated through case studies and comparisons with existing ship operation benchmarks, demonstrating significant reductions in operational costs and robust performance under various uncertain conditions. Notably, the simulation results for the Singapore–Trincomalee route show an 18.4% reduction in carbon emissions compared to conventional systems.