## 1 Introduction
[11] presented an energy management framework with a dual focus on reducing generation costs and optimizing battery usage. This solution also integrates load-shifting mechanisms and adapts to varying grid tariffs. Moreover, various approaches have been proposed to address the critical presence of uncertain data in energy management optimization problems. [PERSON] et al. [12] proposed to combine Machine Learning and Robust Optimization for optimally scheduling energy generation, consumption, and buy/sell actions in a microgrid, taking into account the uncertainty of photovoltaic power generation and user consumption. [PERSON] et al. [13] adopted chance-constrained programming for modeling and solving an uncertain multi-objective microgrid scheduling problem, addressing the uncertainty of renewable energy generation. [PERSON] et al. [14] combined Mixed Integer Programming and Stackelberg games for defining an optimal energy scheduling in a microgrid context. [PERSON] et al. [15] proposed a computationally efficient Robust Optimization method for tackling energy price data uncertainty while optimally managing production and battery storage actions. However, it should be noted that existing single-objective optimization methods for energy management rarely consider the control of controllable loads, and most of them only utilize existing optimization methods without designing proprietary methods for the complex and high-dimensional constraints present in energy management problems. Consequently, the convergence capability of these methods may be limited. Various objectives such as cost, emissions, and battery lifespan should be considered when supplying the load. Consequently, the necessity of multi-objective optimization algorithms becomes apparent. In this context, [PERSON] and [PERSON] [16] introduced the Non-dominated Sorting Genetic Algorithm II (NSGA-II) method as an effective means to address multiple objectives within microgrid management, with a particular emphasis on reducing operating costs and mitigating air pollutants. Incorporating grid power consumption cost and battery degradation cost, [PERSON] et al. [17] developed a multi-objective genetic algorithm similar to NSGA-II to optimize the energy management strategy in microgrids. [PERSON] and [PERSON] [18] presented a multi-objective optimization framework to obtain the optimal energy dispatch strategy for grid-connected and standalone microgrids integrated with photovoltaic cells, wind turbines, fuel cells, micro turbines, diesel generators, and battery energy storage system. This method aims to minimize the costs of main grid energy, fuel costs, emissions, and other objectives. A multi-objective grey wolf method is proposed in [19] to obtain the Pareto front considering the opposing objectives of energy system cost and battery lifespan. In this work, sizing optimization and energy management strategy are both analyzed. [PERSON] and [PERSON] [20] proposed a multi-objective modified personal best particle swarm optimization method for multi-microgrids energy management. This work aims to find the Pareto front of minimizing both operation costs and power losses. [PERSON] et al. [21] addressed a wide spectrum of objectives, including power quality, security, and financial considerations, in their quest to optimize energy scheduling within microgrids. [PERSON] et al. [22] considered a variant of nature-inspired metaheuristics for multi-objective power generation scheduling. Other multi-objective methods [23; 24; 25] have also been proposed for energy management of microgrids considering various objectives and microgrid properties. However, most existing works directly used off-the-shelf multi-objective algorithms, which might perform poorly on energy management problems with hard constraints. Given the substantial number of controllable loads, each with specific on/off timings and power demand constraints, the optimization problem becomes challenging to converge.