A new Benders decomposition approach to solve power transmission network design problems

Optimal transmission switching

“…Voltage angle limits are imposed by (1). 3 Constraint (2) limits the output of generator g at node n to its physical capabilities, and (3) limit the power flow across line k at node n. 4 Power balance at each node is enforced by (4), and Kirchhoff's laws are incorporated in constraint (5). P nk represents the power flow from line k to node n, and therefore can be positive or negative depending on whether power is flowing into or out of the node.…”

“…Electric transmission planning has long been an important field in power system engineering, and many planning techniques have been developed and studied [3] [4] [5]. By necessity, these techniques focus on long-term decisions about investments and uncertainty, not operational decisions based on short-term system conditions.…”

Benders decomposition and an IP-based heuristic for selecting IMRT treatment beam angles

“…Convergence is finite but may require many iterations. Cordeau et al (2001) applied Benders to simultaneously solve the aircraft routing and crew scheduling problems, while Binato et al (2001) used it to solve power transmission network design problems. Costa (2005) gives an extensive survey on applications to fixed-charge network design problems.…”

Time‐horizons in the planning and operation of transmission networks: an overview

“…In the recent period, Lattore et al [13] [32][33][34], disjunctive mixed integer programming [35], branch and bound algorithm [36], implicit enumeration [37,38], Benders decomposition [12, 39,40], maximum flow [12], hierarchical decomposition [41], sensitivity analysis [42,43], genetic algorithm (GA) [44][45][46][47][48][49], object-oriented programming [50], game-theory [51][52][53][54], simulated annealing [55,56], expert systems [57,58], fuzzy set [49,59,60], greedy randomised adaptive search [61], non-convex optimisation [62], tabu search [63], ant-colony [64], data-mining [65], particle swarm optimisation (PSO) [66][67][68][69], harmony search [70,71], artificial neural network (ANN) [72], game theory [73], and robust optimisation techniques [74][75]…”