We discuss the almost-sure convergence of a broad class of sampling algorithms for multi-stage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cut coefficients. This differs from existing published proofs in that it does not require a restrictive assumption.
Electricity market designs that decentralize decision making for participants can lead to inefficiencies in the presence of nonconvexity or missing markets. This has been shown in the case of unit-commitment problems that can make a decentralized market equilibrium less efficient than a centrally-planned solution. Less attention has been focused on systems with large amounts of hydro-electric generation. We describe the results of an empirical study of the New Zealand wholesale electricity market that attempts to quantify production efficiency losses by comparing market outcomes with a counterfactual central plan.
This paper innovatively introduces particle swarm optimization (PSO) and neural network (NN) to solve the job-shop scheduling problem (JSP). Each particle in the swarm was treated as a connection in the NN. Then, the connection weight was iteratively updated according to the latest position of the corresponding particle. In this way, the NN no longer falls into the local optimum trap. Then, the PSOoptimized NN was applied to solve the JSP with a single objective: minimizing the maximum makespan. Through experiments on benchmark problems, it is confirmed that the proposed strategy outperforms the other scheduling methods in fulfilling the optimization objective.
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