# Multi-Stage Dynamic Transmission Network Expansion Planning Using LSHADE-SPACMA
###### Abstract
Mathematical optimization methods effectively solve linear and straightforward optimization problems with a relatively small search area; however, mathematical methods require high computational efforts combined with explosion problems and large search space. Furthermore, mathematical optimization techniques cannot guarantee the global optimum if non-convexities are contained within the search space [11; 12; 13]. In heuristic methods, simple step-by-step search processes are used to analyze possible options to choose quality solutions. While heuristic methods can produce feasible solutions with low computational burden, they cannot guarantee high-quality or optimum solutions [14; 15]. Meta-heuristic methods involve the iteration of heuristic techniques to produce high-quality solutions using \"smart\" criteria. These methods require a high computational effort but lead to better solutions compared to basic heuristics. In contrast to mathematical optimization approaches, meta-heuristics aims to find high-quality solutions with less computational burden, but they cannot guarantee the global optimum. Recently, meta-heuristic approaches have been applied to address TNEP. A genetic algorithm (GA) was introduced by [PERSON] et al. [16] to solve STNEP problems. The expansion cost of the new lines and the loss of load were included in the objective function. An extended GA (EGA) solution to the DTNEP problem was proposed by [PERSON] et al. [17]. This GA has a set of advanced genetic operators and an efficient mode of generation of the initial population that finds high-quality sub-optimal topologies for large-scale and complex systems. [PERSON] et al. [18] proposed a tabu search (TS)-based method to reduce the investment cost in TNEP. The TS approach is feasible and powerful enough to solve the STNEP problem. [PERSON] et al. [19] optimized the cost of transmission expansion and reliability concerning the value of the lost load of busses, using the greedy adaptive search method (GRASP). GRASP is a meta-heuristic method that uses iterative sampling to solve non-linear optimization problems. A discrete particle swarm optimization (DPSO) approach was proposed by [PERSON] et al. [20] to optimize transmission line loading in STNEP. The DPSO is a useful tool for optimizing engineering problems using swarm intelligence; nevertheless, it may fail to reach global optimums. An improved DPSO with mutations based on the similarity (IDPSOMS) method was presented by [PERSON] et al. [21] to resolve this shortcoming and optimize the fitness function of the DPSO. [PERSON] and [PERSON] [22] implemented an improved local PSO (LPSO) algorithm to solve the STNEP problem. Moreover, [PERSON] and [PERSON] [23] presented the multi-group PSO (MGPSO) algorithm to solve the DSTNEP problem. The MGPSO is based on the DPSO framework with many improvements, including an initialization method, a multi-group co-evolution strategy, and a mutation mechanism. The integer-based particle swarm optimization (IBPSO) technique [24] and multiverse optimization (MVO) technique [25] were recently applied to solve TNEP; however, these techniques cannot guarantee the global optimum. The present study employed a meta-heuristic algorithm called LSHADE-SPACMA to solve a MSDTNEP for the West Delta Network (WDN) up to year 2040 with an embedded N-1 security constraint. The semi-adaptive nature of LSHADE-SPACMA improved the exploration capability and exploitation tendency of the algorithm's ability to avoid local optima stagnation [26]. Moreover, the hybridization between LSHADE and CMA-ES is powerful in solving complex optimization problems [26]. The planning period (2016 to 2040) was divided into five stages, and two scenarios were suggested and solved to guarantee N-1 security and decrease the amount of energy not supplied based on the DCTNEP model. The load forecasting up to year 2040 was calculated based on adaptive neuro-fuzzy inference system (ANFIS), because it is efficient for long-term load forecasting based on a set of statistical tests [24].