Comments on “Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques”

Real-time power optimization for application server clusters based on Mixed-Integer Programming

In this paper, we consider simultaneous wireless information and energy transfer in an orthogonal-frequency-division-multiple-access decode-and-forward relay network, in which an energy-constrained relay node harvests energy from a source node and uses the harvested energy to forward information to multiple destination nodes. Our objective is to maximize the end-to-end sum rate by resource allocation, subject to transmit power constraint at the source and energy-harvesting (EH) constraint at the relay. A non-convex and mixed-integer programming (MIP) problem is formulated to optimize time-switching (TS) ratios of EH and information decoding at the relay, TS ratio of information transmission from relay to destinations, subcarrier allocation as well as power allocation (PA) over all subcarriers at source and relay. We propose to decouple this problem into a convex problem and an MIP problem in fractional form. To solve the MIP problem, we transform it into an equivalent optimization problem in subtractive form which has a tractable solution. As a result, we propose a novel scheme to achieve jointly optimal TS ratios, subcarrier allocation and PA. Simulation results verify the optimality of our proposed resource allocation scheme.

In this paper a general framework is discussed within which a municipal authority can assess future needs for certain public services within its area and can develop a programme for land purchase within a fixed budget. Concentration is on developing an optimising model, using mixed integer programming techniques, to identify available plots of land and to earmark them for specific land uses. A range of constraints is discussed, and a set of subsidies and penalties arising out of a solution method due to Balas, explained with reference to the local municipality of Coimbra in central Portugal, is presented.

An Application of Interior Point Method to 0-1 Mixed Integer Programing Problems

Future wireless communication systems are expected to provide a broad range of multimedia services that have a significant traffic asymmetry between uplink and downlink. The code division multiple access‐time division duplex (CDMA‐TDD) system is a promising solution to cope with the problem of traffic asymmetry. However, the TDD system is subject to inter‐cell interference compared to frequency division duplex (FDD) system. Since both uplink and downlink share the same frequency in TDD, uplink and downlink may interfere each other especially when neighboring cells require different rates of traffic load. Thus, the resource allocation among cells is an important issue in TDD. In this paper, the resource allocation in the CDMA‐TDD is formulated as a mixed integer programming (MIP) problem. A dynamic resource allocation algorithm (DRAA) is provided that effectively solves the traffic asymmetry problem. The MIP problem is also solved by a well‐known branch and bound procedure. Both the crossed slot and non‐crossed slot allocation are examined and compared to the DRAA. Computational result shows that proposed DRAA gives a good performance as the traffic asymmetry increases between the uplink and downlink. Copyright © 2003 John Wiley & Sons, Ltd.

Mixed-integer nonlinear programming techniques for process systems engineering

We provide the methods for searching for the unique Nash equilibrium using mixed integer programming techniques. We also simulate the model parameters using this technique and derive the numerical solution to show the characteristics of a key player providing both public goods as suggested by Bergstrom et al. (1986). We present two key results. First, when the number of players decreases, the appearance rate of the unique equilibrium accompanying a key player increases. Second, when the variance of the preference or price parameters decreases, the appearance rate of the unique equilibrium accompanying a key player increases.

This paper proposes a real time price based optimal scheduling mechanism for centralized air conditioning load. In residential context, air conditioners are the main reason for peak load in summers. The proposed mechanism aims to determine optimal operation of air conditioner such that it results in reduction in consumer's electricity bills. Mixed Integer Programming technique is used for obtaining optimal schedule. The results obtained are compared with a previously established Linear Sequential Algorithm for evaluating the effectiveness of the scheme. The results show that Mixed Integer Programming technique provides higher reduction in electricity bill as compared to Linear Sequential technique.

In this paper, we consider an optimization problem solving for model predictive control (MPC) of a modular multilevel converter (MMC). An MMC consists of a large number of submodules. The objective of the MPC is to determine the best switching sequences for the submodules in the MMC to track the phase current references for T time horizons. The MPC is formulated as a nonlinear mixed-integer programming (MIP) problem with the on/off status of submodules as binary decision variables and MMC dynamic states such as phase currents, circulating currents and submodule capacitor voltages as continuous decision variables. With a large number of submodules and a large number of time horizons, the dimension of the nonlinear MIP problem becomes difficult to handle. Our contribution is to formulate this problem and solve this problem using Bender's decomposition. An example 5-level single-phase MMC is demonstrated for the proposed algorithm.

A feasibility pump heuristic for general mixed-integer problems

This article presents an overview and a flavour of almost two decades of MARKAL model developments and selected applications. The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s. Under the auspices of the International Energy Agency’s (IEA) Energy Technology Systems Analysis Programme (ETSAP) the model started as a linear programming (LP) application focused strictly on the integrated assessment of energy systems. It was followed by a non-linear programming (NLP) formulation which combines the ‘bottom-up’ technology model with a ‘top-down’ simplified macro-economic model. In recent years, the family was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, to model endogenous technology learning using mixed integer programming (MIP) techniques, and to model multiple regions (NLP/LP).

Network virtualization, as a fundamental technology of Future Internet Architecture, has been used to overcome the ossification of the current Internet. This paper focuses on virtual nodes splitting for aggregating the diverse physical resources in the issue of virtual network embedding (VNE), which is used for the resource allocation in network virtualization. A mixed integer programming (MIP) problem has been proposed by taking both path-splitting and node-splitting into considerations. The feasibility of virtual node splitting is analyzed and a corresponding formal expression is formulated. The VNE performance is evaluated using by a generic MIP solver over a NSFNET topology. The numerical evaluations in this paper show that, comparing with the approaches for VNE without node-splitting, the proposed algorithm is beneficial to reduce VNE cost, as well as to increase VN acceptance ratio.

Centralized algorithms are widely used for optimization and control in power system applications. These algorithms require all the measurements and data to be accumulated at central location and hence suffer from single-point-of-failure. Additionally, these algorithms lack scalability with an increasing number of sensors and actuators, specially with the increasing integration of distributed energy resources (DERs). As the power system becomes a confluence of a diverse set of decision-making entities with a multitude of objectives, the preservation of privacy and operation of the system with limited information has been a growing concern. Distributed optimization techniques solve these challenges while also ensuring resilient computational solutions for the power system operation in the presence of both natural and man-made adversaries. A detailed discussion of possible applications of distributed optimization in power systems is provided in this work. However, there exist multiple challenges for accurate and computationally efficient distributed solutions. Commonly-used distributed optimization approaches include Lagrange relaxation, augmented Lagrangian, approximate network directions in conjunction with standard Lagrangian, auxiliary problem principle, alternating directions method of multipliers, optimality condition decomposition, proximal atomic coordination, and optimal feedback-based voltage control. A comprehensive classification of the distributed optimization problems has been discussed and detailed in this work. All of these algorithms have displayed efficient identification of global optimum solutions for convex continuous distributed optimization problems. The algorithms discussed so far are predominantly used to manage continuous state variables. Inclusion of integer variables in the decision support are needed for specific power system problems. Mixed integer programming (MIP) problem arises in a power system operation and control due to tap changing transformers, capacitors and switches. The global optimization techniques for MIPs are Branch and Bound, Branch and Cut, Cutting planes, Adaptive coordinate search, Nelder-Mead, Genetic algorithm etc. Although the above optimization techniques are able to solve NP-hard convexified MIP problems centrally, but are time consuming and do not scale well for large scale distributed problems. Decomposition and solution approach of distributed coordination can resolve the scalability issue. Despite the fact that a large body of work is present on the centralized solution methods for convexified MIP problems, the literature on distributed MIPs is relatively limited. The distributed optimization algorithms applied in power network to solve MIPs are reported here. ML based solutions can help to get faster convergence for distributed optimization or can replace optimization techniques depending on the problem as discussed in this work. Finally, a summary and path forward are provided, and the advancement needed in distributed optimization for the power grid is also presented.

The sugarcane transport system is very complex and uses a daily schedule, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Producing efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. In this paper, the sugarcane rail operations are formulated as a blocking job shop scheduling problem. A mixed integer programming approach is used to formulate the shop job scheduling problem. Mixed integer programming and constraint programming search techniques are integrated for solving the problem. A case study is solved to test the approach.

Mixed-integer programming and multi-objective optimization techniques for the design of control augmented structures