# A Review: Machine Learning for Combinatorial Optimization Problems in Energy Areas
With the development of relevant game theory and ML methods, more and more individuals and institutes have started to integrate both of them on industrial issues, such as device-to-device (D2D) communication using the Stackelberg game and MARL method [42], anti-jamming for internet of satellites through the deep RL approach and Stackelberg game [43], moving target defense using MARL in Bayesian Stackelberg Markov games [40], etc. In this work, we mainly survey the COPs in energy areas, using a series of modern ML approaches, i.e., the interdisciplinary areas of COPs, ML and energy areas. We first list the categories of the classical COPs, such as the traveling salesman problem (TSP), maximum independent set (MIS) and minimum spanning tree (MST), etc., then investigate the ML techniques that can effectively address the above COPs, where the SL, DL and RL, as well as game-theoretic approaches, are mainly concerned due to their unique abilities. The research works of COPs in energy areas with ML methods are specifically studied afterwards. We mainly survey the petroleum supply chain, steel-making, electric power system, and wind power, which are currently popular applications in energy fields since the resource consumption is fairly high and even a little optimization can help save numerous costs. Finally, we also find some important deficiencies when investigating the above materials, and the challenges of this cross area are also summarized. On the one hand, we hopefully notice that game theory can be appropriately integrated into ML, DL and RL methods for handling the COPs in consideration of the typical issues, such as accuracy, efficiency, and scalability. On the other hand, the applications in energy areas are frequently represented in a complicated manner since the objective functions are often formulated as NP-hard problems with a great many constraints. The learning methods above can probably be a category of promising technique in dealing with these issues. In addition, the contents are analyzed as follows. The search identified 274 documents containing the theoretical conclusions of various algorithms and the results of applicable approaches. Background information contains relevant knowledge in COPs [44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54], deep learning [55; 56; 57; 58; 59; 60; 61] and reinforcement learning [62; 63; 64; 65; 66; 67; 68]. Supervised learning, reinforcement learning and game theoretic methods are introduced in learning methods, where supervised learning includes methods of B&B [69; 70; 71; 72; 73; 74], sequence to vector [57; 75; 76; 77], GNN [78; 79; 80; 81; 82] and end-to-end architecture [83; 84]. A few sources are relevant to reinforcement learning [85; 86; 87; 88], and different types of games were demonstrated [89; 90; 91; 92]. Another aspect mentioned was classic COPs [71; 72; 84; 85; 93; 94; 95; 96; 97], where ILP, MIS, MC, MVC and TSP were introduced. The rest of the literature references demonstrate application. The aspects contain petroleum supply chain [10; 11; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107], steel-making [108; 109; 110; 111], electric power system [112; 113; 114; 115; 116; 117; 118; 119], and wind power [1120; 121; 122; 123]. The aforementioned references were mostly searched from Google Scholar with related key words, such as \"optimization\", \"combinatorial optimization problem\", \"machine learning\", \"supervised learning\", \"reinforcement learning\", \"game theory\", \"refinery scheduling\", \"steel-making\", \"electric power system\", \"wind power\", etc. The rest of this review is organized as follows. In Section 2, we introduce the background of combinatorial optimization problems and several popular approaches of ML in addressing this kind of issue over the past years. The sub-fields of combinatorial optimization problems and more details of these ML methods are further discussed in Section 3. In Section 4, we concentrate on some specific applications in energy field and investigate how the ML algorithms are applied to these issues.