A column generation algorithm for solving energy system planning problems

Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation (CG) is a classical tool to generate feasible solutions of sub-models, defining columns of global master problems, which are used to steer the search for a global solution. In this paper, we present a new inner approximation method for solving energy system MINLP models. The approach is based on combining CG and the Frank Wolfe algorithm for generating an inner approximation of a convex relaxation and a primal heuristic for computing solution candidates. The features of this approach are: (i) no global branch-and-bound tree is used, (ii) sub-problems can be solved in parallel to generate columns, which do not have to be optimal, nor become available at the same time to synchronize the solution, (iii) an arbitrary solver can be used to solve sub-models, (iv) the approach (and the implementation) is generic and can be used to solve other nonconvex MINLP models. We perform experiments with decentralized energy supply system models with more than 3000 variables. The numerical results show that the new decomposition method is able to compute high-quality solutions and has the potential to outperform state-of-the-art MINLP solvers.

Contrastive Losses and Solution Caching for Predict-and-Optimize

Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning approaches, which rely on solving one optimization problem for each training instance at every epoch. In this context, we provide two distinct contributions. First, we use a Noise Contrastive approach to motivate a family of surrogate loss functions, based on viewing non-optimal solutions as negative examples. Second, we address a major bottleneck of all predict-and-optimize approaches, i.e. the need to frequently recompute optimal solutions at training time. This is done via a solver-agnostic solution caching scheme, and by replacing optimization calls with a lookup in the solution cache. The method is formally based on an inner approximation of the feasible space and, combined with a cache lookup strategy, provides a controllable trade-off between training time and accuracy of the loss approximation. We empirically show that even a very slow growth rate is enough to match the quality of state-of-the-art methods, at a fraction of the computational cost.

Outer and inner approximations in quantum spaces

The present paper introduces and studies the concepts of K-outer approximation and K-inner approximation for a monotone function μ defined on a D-poset P, by a subfamily K of P. Some desirable properties of K-approximable functions are established and it is shown that the family of all elements of P that possess K-approximation, forms a lattice and is closed under orthosupplementation. We have proved that a submodular measure on a suitable subfamily of P having K-outer approximation can be extended to a function that has K-outer approximation, and a tight function that has K-inner approximation can be extended to a function having K-inner approximation.

A Model for Demand Planning in Supply Chains with Congestion Effects

This paper is concerned with demand planning for internal supply chains consisting of workstations, production facilities, warehouses, and transportation links. We address the issue of how to help a supplier firmly accept orders and subsequently plan to fulfill demand. We first formulate a linear aggregate planning model for demand management that incorporates elements of order promising, recipe run constraints, and capacity limitations. Using several scenarios, we discuss the use of the model in demand planning and capacity planning to help a supplier firmly respond to requests for quotations. We extend the model to incorporate congestion effects at assembly and blending nodes using clearing functions; the resulting model is nonlinear. We develop and test two algorithms to solve the nonlinear model: one based on inner approximation and the other on outer approximation.

Rate Fairness and Power Consumption Optimization for NOMA-Assisted Downlink Networks

This paper considers a non-orthogonal multiple access (NOMA) downlink network, where a hybrid of NOMA and beamforming designs is developed to enhance the channel capacity. We aim to improve the system performance in terms of rate fairness and power consumption. Hence, a multi-objective problem with a joint optimization of user equipment pairing, power control, and quality-of-service requirements is addressed. To efficiently solve the problem, we propose two low-complexity algorithms based on the inner-approximation method, with the first algorithm using the relaxation method and the second one using graph theory. Numerical results are provided to demonstrate the effectiveness of the two proposed algorithms in comparison with the exhaustive search and existing methods.

Max-Min Fairness and Sum Throughput Maximization for In-Band Full-Duplex IoT Networks: User Grouping, Bandwidth and Power Allocation

The skyrocketing growth in the number of Internet of Things (IoT) devices has posed a huge traffic demand for fifth-generation (5G) wireless networks and beyond. In-band full-duplex (IBFD), which is theoretically expected to double the spectral efficiency of a half-duplex wireless channel and connect more devices, has been considered as a promising technology in order to accelerate the development of IoT. In order to exploit the full potential of IBFD, the key challenge is how to handle network interference (including self-interference, co-channel interference, and multiuser interference) more effectively. In this paper, we propose a simple yet efficient user grouping method, where a base station (BS) serves strong downlink users and weak uplink users and vice versa in different frequency bands, mitigating severe network interference. First, we aim to maximize a minimum rate among all of the users subject to bandwidth and power constraints, which is formulated as a nonconvex optimization problem. By leveraging the inner approximation framework, we develop a very efficient iterative algorithm for solving this problem, which guarantees at least a local optimal solution. The proposed iterative algorithm solves a simple convex program at each iteration, which can be further cast to a conic quadratic program. We then formulate the optimization problem of sum throughput maximization, which can be solved by the proposed algorithm after some slight modifications. Extensive numerical results are provided to show not only the benefit of using full-duplex radio at BS, but also the advantage of the proposed user grouping method.

Max-Min Rate Fairness Optimization for In-Band Full-Duplex IoT Networks: User Grouping and Power Control

The skyrocketing growth in the number of Internet of Things (IoT) devices will certainly pose a huge traffic demand for fifth-generation (5G) wireless networks and beyond. In-band full-duplex (IBFD), which is theoretically expected to double the spectral efficiency of a half-duplex (HD) wireless channel and to connect more devices, has been considered as a promising technology to accelerate the development of IoT. To exploit the full potential of IBFD, the key challenge is how to handle network interference (including self-interference, co-channel interference and multiuser interference) more effectively. In this paper, we propose a simple yet efficient user grouping method, where a base station (BS) serves strong downlink users and weak uplink users and vice versa in different frequency bands, mitigating severe network interference. We aim to maximize a minimum rate among all users subject to bandwidth and power constraints, which is formulated as a highly nonconvex optimization problem. By leveraging inner approximation framework, we develop a very efficient iterative algorithm to solve this problem, which guarantees at least a local optimal solution. Numerical results are provided to show not only the benefit of using full-duplex raido at BS, but also the advantage of the proposed user grouping method.