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• A multi-objective IES planning model with DR and uncertainty is constructed. • A novel multi-objective optimization framework (MOOF) for IES planning is proposed. • A constrained multi-objective coevolutionary algorithm is developed and verified. • The effectiveness of the proposed MOOF is verified by case studies. The planning of integrated energy systems (IES) faces significant challenges due to the presence of multiple uncertainties caused by stochastic demands and renewable energy generation. Particularly, how to balance different conflicted objectives in IES planning under multiple uncertainties is a major obstacle with few studies. Thus, this paper proposes a novel multi-objective optimization framework (MOOF) for uncertain IES planning with demand response to achieve the synergistic enhancement of multiple performance indicators of the system while ensuring its flexibility and safety. The proposed MOOF encompasses several key steps. Firstly, a multi-objective optimization model under various uncertainties is constructed, with the minimization of investment and operating costs, maximization of exergy efficiency, and minimization of carbon emissions as optimization objectives. Secondly, the chance constraint approach is used to convert the constraint conditions into deterministic ones. Subsequently, the Pareto dominance concept is incorporated into robust, interval, and opportunistic optimization techniques to obtain three deterministic transformation methods for multi-objective optimization with uncertainty. Further, a high-efficiency constrained multi-objective coevolutionary algorithm (CMCA) is developed to solve the proposed planning model, which has the characteristics of nonlinearity, and high-dimensional complexity. Finally, the effectiveness of the proposed MOOF and CMCA is verified through numerous case studies. [ABSTRACT FROM AUTHOR]

• An iterative optimization framework is proposed to control the effect of outliers. • An iterative algorithm is designed to solve the general L p -norm optimization problem. • The iterative algorithm converges to a local optimum by rigorous theoretical analysis. • We can adjust the parameters of the GEPSVM Lp to balance the accuracy and training time. The proximal support vector machine via generalized eigenvalues (GEPSVM) is a well-known pattern classification method. GEPSVM, however, is prone to outliers due to its use of the squared L 2 -norm distance criterion. A robust GEPSVM version is proposed to tackle this problem using L 1 -norm distance optimization technique (GEPSVM L1). As optimizing a GEPSVM L1 with L 1 -norm terms can be challenging, we have developed an iterative algorithm to address the L 1 -norm ratio problem associated with GEPSVM L1. Furthermore, an efficient iterative optimization framework has been developed to conveniently address related optimization problems. The research contribution of this paper lies in providing a theoretical analysis of the algorithm's convergence. Besides, we find that the L 1 -norm distance-based methods in real-world applications, especially for handling samples with outliers, sometimes provides an unsatisfactory recognition result. Thus, a generalized version of GEPSVM L1 is proposed. The L 1 -norm distance is replaced with a L p -norm distance in GEPSVM L1 (GEPSVM Lp). It is the robust counterpart of GEPSVM L1 and GEPSVM. It is worth noting that we fine-tune GEPSVM Lp 's parameters to strike a balance between training time and classification accuracy, an especially crucial step for larger datasets. Our experiments indicate that the proposed GEPSVM Lp is more efficient and robust than the competitors in numerous experimental settings. Overall, our work demonstrates the importance of developing robust pattern classification methods in the presence of outliers and provides a practical solution for handling such cases in real-world applications. [ABSTRACT FROM AUTHOR]