A Projection-Adapted Cross Entropy (PACE) method for transmission network planning

Abstract

In this paper, we propose an adaptation of the Cross Entropy (CE) method called Projection-Adapted CE (PACE) to solve a transmission expansion problem that arises in management of national and provincial electricity grids. The aim of the problem is to find an expansion policy that is both economical and operational from the technical perspective. Often, the transmission network expansion problem is mathematically formulated as a mixed integer nonlinear program that is very challenging algorithmically. The challenge originates from the fact that a global optimum should be found despite the presence, of possibly a huge number, of local optima. The PACE method shows promise in solving global optimization problems regardless of continuity or other assumptions. In our approach, we sample the integer variables using the CE mechanism, and solve LPs to obtain matching continuous variables. Numerical results, on selected test systems, demonstrate the potential of this approach.

Tactical supply chain planning under a carbon tax policy scheme: A case study

“…We initially tried to adopt the Projection Adaptive Cross-Entropy (PACE) method proposed by Eshragh et al (2011) to solve this model. According to PACE, to solve a nonlinear binary programming model, a sample of 0-1 variables is randomly generated at each iteration from which only those that result in feasible solutions are considered.…”

A heuristic algorithm for optimal fleet composition with vehicle routing considerations

“…It was soon realized that cross entropy can be adapted to solve difficult combinatorial optimization problems. This is done by transforming the deterministic optimization problem into a related stochastic optimization problem and then applying the rare event simulation techniques developed by Rubinstein and others [6,14,15,17]. A typical iteration of the cross entropy method involves the following two steps [15]:…”

Transmission expansion planning considering energy storage

“…A procedure for calculating minimum values of M ij is given in [3]. Power flow limits are enforced on existing and candidate circuits by (5) and (6).…”

“…Modern commercial solvers, such as IBM ILOG CPLEX, solve small, linear TEP instances to optimality quickly. However, numerous specialist solution methods have been developed including branch and bound with a GRASP metaheuristic [2], Projection-Adapted Cross Entropy [6], heuristic methods [12], and various evolutionary algorithms [4,18].…”