## 1 Introduction  
As one of the most environmentally friendly renewable energies, the wind is an ideal resource for meeting the greatly increasing electricity demand while reducing the impacts on the environment [1]. According to the statistics of the European Wind Energy Association, 15.6% of total power capacity was from wind energy in 2015, which has a 13.2% increased share of the market compared to the data in 2000 [2]. Offshore wind energy has unique advantages [3] such as higher energy density, stable wind distribution as well as reduced impacts on residents. Consequently, the penetration of offshore wind energy is expected to continuously increase [4]. However, the huge investment an offshore wind farm represents makes the economic operation infeasible without subsidies at an earlier time. Therefore technological innovation and development to lower the levelised cost of energy (\(LCoE\)) of the wind farm are attracting attention globally. As introduced in [5], up to 30% of the capital expenditure (CAPEX) of the offshore wind farm is related to its electrical system, of which the internal array cables and their associated costs make up a large proportion. As a result, a good deal of research has been conducted on the optimization of the cable connection layout to make a cost-effective wind farm. When bigger cables are applied to transmit the energy, the overall energy losses will be reduced, which contributes to a large amount of revenue increase within the wind farm's operating lifetime. However, more CAPEX is paid out. Hence, in the offshore wind farm cable connection layout problem (OWFCCLP), the cable connection layout, as well as the sectional area of each cable, should be optimized simultaneously considering the cable's current carrying capacity [6]. As mentioned in [7], the OWFCCLP is a highly non-convex combinatory optimization problem where the combination of the electrical equipment is required to be optimized under the power system constraints. Deterministic algorithms may fail to resolve this kind of problem [8]. In comparison, the heuristic algorithm can find a sub-optimal solution in an acceptable time. Hence, this has been widely used in solving OWFCCLP [8; 9; 10; 11; 12; 13; 14; 15]. Different sea cable connection layouts--the string structure, ring structure, and multiloop structure--on a three-dimensional seabed were analyzed in [8], wherein a multiple loop cable connection structure was proposed and the overall length of cables was minimized by the particle swarm optimization algorithm (PSO). In [9], the common electrical system schemes of the offshore wind farm and electrical component costs are analyzed. Based on that, the optimization model for OWFCCLP was proposed and solved by a genetic algorithm (GA). The above works only considered one type of cable and thus could only minimize the length of cables in each branch instead of minimizing the overall cost. To further reduce the cost, a mixed integer linear programming method was proposed in [10] which considered the cable section area's impact on the cable connection scheme. The authors in [11] proposed an adaptive particle swarm optimization minimum spanning tree method to solve the OWFCCLP using cables with different sectional areas. In [12], in addition to different sectional areas, the collection system and transmission system were both considered in the OWFCCLP. It encoded the topology to a binary string and solved the problem via standard GA. However, the power losses are not taken into account in [10; 11; 12]. In [13], the power losses were considered in the optimization model, and the proposed model was solved by a hybrid immune GA algorithm. Similarly, a dynamic minimum spanning tree algorithm was proposed in [14] to solve the OWFCCLP, which considered the power loss. Besides this, considering both the power losses and cable sectional area selection, the open multiple travelling salesman problem (OMMSP) was compared with OWFCCLP in [15]; based on their common properties, a new optimization model was established and solved by GA.