## 1 Introduction  
Microgrids (MGs) are small-scale, independent power systems widely used in communities, industrial parks, remote regions, and post-disaster recovery. Microgrids reduce carbon emissions by integrating renewable energy resources, increasing generation-sufficiency, and enabling flexible scheduling  
Integrated combined heat and power (CHP) configurations simultaneously produce electrical power and thermal energy, typically employing fuel sources, including biomass, natural gas, coal, and petroleum derivatives. Biomass combined heat and power (BCHP) facilities have gained significant traction as dual-purpose energy providers worldwide, delivering both power generation and district-heating services through cogeneration processes. Introducing biomass gasification equipment in microgrids enables generated gas to fuel internal combustion engines, microturbines, or other generators, while also powering heating furnaces or boilers, thus reducing the utility's demand for natural gas [1]. In the future, solar and wind power, along with BCHP, are expected to be the primary sources of electricity and heat in microgrids. However, determining the optimal configuration and operation duration of various devices in different scenarios to meet electricity and heat demands while minimizing economic and environmental costs is challenging. Previous studies have typically developed single- or multi-objective optimization models for microgrid design, aiming to minimize investment costs, maximize renewable energy self-consumption, and reduce CO\({}_{2}\) emissions [2; 3; 4; 5]. Researchers assessed the environmental effects of modifications in energy production within coal-fired cogeneration boilers following the introduction of low-percentage wood pellet co-firing [6]. [PERSON] et al. conducted a comparison of the environmental impacts associated with Willow biomass power generation and those of other renewable and non-renewable energy sources [2]. These studies aimed to design the microgrid configuration model with the lowest economic costs by quantifying expenses. However, few studies have performed bi-objective optimization. Most current research on microgrid configuration and scheduling is electricity load following, which indicates the process of adjusting power generation to match fluctuating electricity demand, ensuring a continuous and reliable supply while optimizing the use of renewable energy sources. [PERSON] et al. proposed an economic linear programming model to evaluate the planning and operation of BCHP systems that simultaneously meet electricity and heat demands [7]. With the emergence of carbon taxes, the cost of using high carbon-emitting energy has increased, potentially prompting microgrids to favor renewable energy sources. Carbon taxes influence the scheduling methods of different capacity devices within microgrids, prioritizing low-carbon energy capacity devices to optimize operational costs. [PERSON] et al. methodologically examines the incorporation of renewable energy systems within power generation infrastructures, conducting comprehensive assessments of operational reliability and carbon footprint across diversified generation portfolios in contemporary power systems [8]. However, the impact of carbon tax rates on UC decisions has not yet been studied, nor has there been explicit constraint modeling of TGR's greenhouse gas emissions in the formulation of the UC problem. [PERSON] et al. proposed a stochastic operation-scheduling scheme to optimize carbon emissions and generation fuel costs. Two different stochastic approaches based on sample average approximation and probabilistic-constrained stochastic programming are formulated and solved by CPLEX 12.5.1 [9]. In the optimization problem of configuration and generation scheduling in microgrids, scholars typically employ heuristic algorithms, including such as Particle Swarm Optimization [10], Fuzzy Logic [11], and Genetic Algorithms [12]. [PERSON] et al.