# A New Multi-Objective Unit Commitment Model
## 1 Introduction  
With the depletion of fossil resources and the growing awareness of environmental protection, higher requirements have been put forward for energy efficiency and clean use. As one of the biggest production systems, it is essential to improve operational strategies to take the economy as well as the environmental protection targets into account at the same time. In this paper, the economic objective is to reduce the CO\({}_{2}\) emission, and the economic objective is to reduce the fuel cost. MOUC provides an operation schedule considering both objectives, hence it is of great value and practical significance. Currently, a great number of scholars have conducted in-depth research on the unit commitment (UC) problem and have achieved great performance. UC is a mixed integer, non-convex, non-linear problem, and with the scale of the system grows, the computation time increases almost linearly [1,2]. The objective of UC is to determine the optimal or near optimal operating schedule of the power system in a feasible time, and the schedule must minimize the operating and commitment cost of a giving forecasted system load, considering the unit and system constraints as well as the tie-line limitation between any pairs of regions. A lot of work has been done on the literature of UC, which could be mainly grouped as numerical optimization and heuristics methods. Numerical optimization methods such as priority list [3] gives a high cost schedule, and dynamic programming may suffer from 'curse of dimension' [4]. In considering the dual problem, LR involves decomposition of the problem into a sequence of master problem and multiple independent subproblems, and the subproblems could be solved separately. One of the most obvious advantages of the LR method is its quantitative measure of the solution quality since the cost of the dual function is a lower bound on the cost of the primal problem [5]. Some papers improve LR by finding an advanced technique to update the Largrangian multiplier. [PERSON] [5] presents a better search direction by combining the concepts of augmented LR and surrogate subgradient. In [6], a tight and compact reformulation of the thermal unit commitment is presented, which reduces the search space and increases the searching speed by exploring that reduced space. Presently, researchers tend to use optimizers like GUROBI or CPLEX optimizer to deal with mixed integer problems, which use the branch and bound algorithm, and models based on these optimizers have been proposed [7; 8; 9; 10; 11]. Numerical optimization methods are simple and fast but most of them may suffer from numerical convergence and solution quality problems [12]. Hence heuristics methods such as a genetic algorithm [13], particle swarm optimization [14], or memetic algorithm have been proposed for the UC problem. In [15], a hybrid evolutionary framework based on hybridization of genetic algorithm and differential evolution is proposed to solve UC. The binary variables (such as \(u_{i,t}\) in (1)) in UC is solved using the genetic algorithm while the continuous variables (such as \(p_{i,t}\) in (1)) are solved using differential evolution. Genetic algorithm is more capable of handling binary variables and differential evolution is better in real parameter optimization, hence the performance is enhanced by combining the two algorithms. [PERSON] [14] uses a three stages approach to get the optimum solution of UC. In the first two stages, operating status of units are obtained by predefined priority while the generation of each unit is obtained by a weight-improved crazy particle swarm optimization algorithm. Finally, total operating cost and reserve are minimized using a solution restructuring process. For the above literature about UC, most of the research failed to consider the emission or other environmental indicators, but considered the thermal cost only.