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To satisfy the rapidly growing demands of wireless communications, new structures have been proposed for the fifth-generation (5G) mobile communication networks, such as cloud radio access networks (C-RANs), which have advantages including high energy efficiency, large network capacity, and high flexibility. This paper concentrates on the problem of remote radio head (RRH) activation, user association, and power allocation in C-RANs. To tackle the problem with $l_{0}$ norm, we transform it into a mixed-integer nonlinear programming (MINLP) problem. Instead of solving it by centralized solvers, we propose a novel algorithm based on Benders decomposition, which can obtain the optimal solution of the MINLP problem. To solve the primal problem in Benders decomposition efficiently, we adopt the alternating direction method of multipliers (ADMM) to achieve a parallel implementation. To further reduce the complexity of solving the MINLP problem, a distributed two-stage iterative algorithm combining the ADMM and the max-sum algorithm is also proposed. The simulation results demonstrate that the first proposed algorithm can obtain the optimal solution, and the second proposed algorithm outperforms conventional algorithms significantly. [ABSTRACT FROM AUTHOR]

This paper deals with day-ahead power systems security planning under uncertainties by posing an optimization problem over a set of power injection scenarios that could show up the next day and modeling the next day's real-time control strategies aiming at ensuring security with respect to contingencies by a combination of preventive and corrective controls. We seek to determine whether and which day-ahead decisions must be taken so that, for scenarios over the next day, there still exists an acceptable combination of preventive and corrective controls ensuring system security for any postulated contingency. We formulate this task as a three-stage feasibility checking problem, where the first stage corresponds to day-ahead decisions, the second stage to preventive control actions, and the third stage to corrective post-contingency controls. We propose a solution approach based on the problem decomposition into successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. Our approach is illustrated on the Nordic32 system and on a 1203-bus model of a real-life system. [ABSTRACT FROM PUBLISHER]

Deregulation of the electric power industry has introduced new uncertainties for market participants and made planning of transmission expansion more difficult. More flexible transmission expansion plans are needed, to cope with the increased risks. In this paper, a novel planning approach is proposed to meet the above challenge. In our approach, the planning process is modeled as a mixed integer nonlinear programming (MINLP) problem, so that conflicting objectives can be optimized simultaneously. To minimize planning risks, our method identifies several scenarios based on statistics and expert knowledge; the most flexible expansion plan is selected as the plan that has least adaptation cost. The proposed method is tested with the IEEE 14-bus system. Promising results are obtained to demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, a generalized projection quasi-Newton method with inexact line search is proposed for the nonlinear optimization problem with linear constraints. The projection and quasi-Newton technique are used to determine the search direction at each iteration. It is proved that the method has properties of global convergence and superlinear convergence rate under some suitable assumptions. [ABSTRACT FROM AUTHOR]

Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point. [ABSTRACT FROM AUTHOR]

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a new method for VAr planning under multiple operating scenarios, optimizing sizes and locations of new reactive compensation equipment to ensure that both the system voltage profile and voltage stability requirements are met. The approach is based on \mbi L1-norm regularization for finding a solution with minimum VAr installation sites and on the \mbi L2-norm penalty function for satisfying the multiple state constraints. The \mbi L2-norm penalty function is exact in the sense that a finite penalty parameter is required to establish equivalence with the VAr planning problem, thus avoiding numerical ill-conditioning. The solution is obtained from a successive conic programming algorithm which makes use of adaptive trust-region control. The results of the new method are compared with those of an optimal power flow-based program for VAr planning. [ABSTRACT FROM PUBLISHER]

Abstract: This paper is concerned with the constrained optimization problem. A detailed discussion of surrogate constraints with zero duality gaps is presented. Readily available surrogate multipliers are considered that close the duality gaps where constraints are rational-valued. Through illustrative examples, the sources of duality gaps are examined in detail. While in the published literature, in many situations conclusions have been made about the existence of non-zero duality gaps, we show that taking advantage of full problem information can close the duality gaps. Overlooking such information can produce shortcomings in the research in which a non-zero duality gap is observed. We propose theorems to address the shortcomings and report results regarding implementation issues. [Copyright &y& Elsevier]

Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R optimization infrastructure ROI which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.

The Paper concentrates upon a modified maximum-entropy method of solution of linear and non-linear programming problem transforming it by an equivalent surrogate program. [ABSTRACT FROM AUTHOR]

Abstract: Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations. [Copyright &y& Elsevier]

This paper provides a new methodology to solve bilinear, non-convex mathematical programming problems by a suitable transformation of variables. Schur's decomposition and special ordered sets (SOS) type 2 constraints are used resulting in a mixed integer linear or quadratic program in the two applications shown. While Beale, Tomlin and others developed the use of SOS type 2 variables to handle non-convexities, our approach is novel in two aspects. First, the use of Schur's decomposition as an integral part of the approximation step is new and leads to a numerically viable method to separate the variables. Second, the combination of our approach for handling bilinear side constraints in a complementarity or equilibrium problem setting is also new and opens the way to many interesting and realistic modifications to such models. We contrast our approach with other methods for solving bilinear problems also known as indefinite quadratic programs. From a practical point of view our methodology is helpful since no specialized procedures need to be created so that existing solvers can be used. The approach is illustrated with two engineering examples and the mathematical analysis appears in the Appendices. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a line search sequential quadratic programming (SQP) approach to a system of nonlinear equations (SNE) is taken. In this method, the system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved using SQP algorithms with a line search strategy. Furthermore, at each step, some equations, which are satisfied at the current point, are treated as constraints and the others act as objective functions. In essence, constrained optimization strategies are utilized to cope with the system of nonlinear equations. [Copyright &y& Elsevier]

The interconnection of vehicles in the future fifth generation (5G) wireless ecosystem forms the so-called Internet of Vehicles (IoV). IoV offers new kinds of applications requiring delay-sensitive, compute-intensive, and bandwidth-hungry services. Mobile edge computing (MEC) and network slicing are two of the key enabler technologies in 5G networks that can be used to optimize the allocation of the network resources and guarantee the diverse requirements of IoV applications. As traditional model-based optimization techniques generally end up with NP-hard and strongly non-convex and nonlinear mathematical programming formulations, in this article, we introduce a model-free approach based on deep reinforcement learning (DRL) to solve the resource allocation problem in MEC-enabled IoV networks based on network slicing. Furthermore, the solution uses non-orthogonal multiple access (NOMA) to enable better exploitation of the scarce channel resources. The considered problem addresses jointly the channel and power allocation, the slice selection, and the vehicle selection (vehicle grouping). We model the problem as a single-agent Markov decision process. Then we solve it using DRL with the well-known deep Q learning (DQL) algorithm. We show that our approach is robust and effective under different network conditions compared to benchmark solutions. [ABSTRACT FROM AUTHOR]

Marine debris pollution is becoming an increasingly serious problem, affecting not only navigational safety but also the health of marine ecosystems. Carbon emission causes ocean acidification, which greatly harms marine lives. In order to respond to these environmental issues, this paper studies marine debris collection with consideration of carbon cap using logistics network. To the most of our knowledge, this is first work to study marine debris removal from logistics way. We proposed a three-phase marine debris collection framework: (1) identifying initial locations of the debris; (2) utilizing GNOME software to predict the drifting trajectory of the debris; and (3) formulating vessel routing as a mixed integer nonlinear programming with consideration of carbon emission. The model seeks to minimize the total costs including fuel cost, berth cost, unloading cost in the harbor, vessel rent, vessel insurance, and labor cost, with respect to the constraints of carbon cap, vessel capacities, and time windows. After the linearization process, a Branch-and-Cut (B&C) algorithm with multiple variable fixing techniques and valid inequalities is used to solve the proposed model. The debris dispersion located in Boston vicinity is used as a case study to validate the proposed model and algorithm. The results reveal that the farther away the debris location is from the shore, the higher the collection cost and the more the carbon emission would be. The daily collection cost in the closest location and in the farthest location is $140 lower and $210 higher than that in the initial location. The carbon emission in the farthest location is 21% and 32% higher than that in the initial location and in the closest location. Sensitivity analysis is also carried out for the fuel price and carbon cap to test their impact on total costs These results show that proposed model and algorithm can significantly improve the efficiency of marine debris collection process, reduce carbon emission and total costs. • A three-phase structured framework for marine debris cleanup is firstly proposed. • Vessel velocity has been used as a variable to trade off carbon emission and cost. • A mixed integer nonlinear programming vessel routing problem is firstly formulated. • Α Branch-and-Cut algorithm combined with linearization is used to solve the model. • The vicinity of Boston case study is used to validate the model and algorithm. [ABSTRACT FROM AUTHOR]

• New framework for work and heat exchange networks synthesis and optimization. • Work and heat integration by means of superstructure-based mathematical programming. • Mixed-integer nonlinear programming model with reduced number of decision variables. • Two-level meta-heuristic optimization approach. • Non-intuitive work and heat exchange networks resulted cost reduction up to 7.2% Integrating the energy available in industrial processes in the form of heat and work is fundamental to achieve higher energy efficiencies as well as to reduce process costs and environmental impacts. To perform this integration, a new framework for the optimal synthesis of work and heat exchange networks (WHEN) aiming to reduce capital and operating costs is presented. The main contribution of this paper is the elaboration of a new WHEN superstructure and mixed-integer nonlinear programming (MINLP) derived model. Strategies of changing variables are applied to reduce the number of decision variables from the model. The MINLP problem with a reduced number of decision variables is solved with a two-level meta-heuristic optimization approach, using Simulated Annealing in the combinatorial problem and Particle Swarm Optimization in the nonlinear programming problem. For the sake of validation, this methodology is applied to three case studies comprising two, five, and six process streams. Economic savings achieved outperform results reported in the literature from 1.0 to 7.2%. Also, the solutions obtained present non-intuitive WHENs that shows the importance of using superstructure-based mathematical programming for such a difficult decision-making task. [ABSTRACT FROM AUTHOR]

This study introduces the weed optimization algorithm (WOA) to optimal reservoir operation. The WOA is a metaheuristic optimization method inspired by weeds' life cycle. The effectiveness of the WOA is demonstrated with the optimization of mathematical functions and reservoir systems. The WOA is applied in continuous-time and discrete-time formulations of reservoir-operation optimization and its results are compared with global optimal solutions obtained with nonlinear programming (NLP), linear programming (LP), and the genetic algorithm (GA). The results show the WOA's fast convergence to solutions that are very near the global optimal solutions of the reservoir optimization problems. [ABSTRACT FROM AUTHOR]

This paper resolves four previous software reliability optimization models published in this journal. It is shown that a recent optimization software, LINGO, makes it unnecessary to develop special branch and bound or dynamic programming schemes to solve nonlinear reliability optimization models with binary decision variables. [ABSTRACT FROM AUTHOR]

In this correspondence, we present a new and fast design algorithm for perfect-reconstruction (PR), maximally decimated, uniform, cosine-modulated filter banks. Perfect reconstruction is obtained within arithmetic machine precision. The new design does not need numerical optimization routines and is significantly faster than a competing method based on second-order cone programming (SOCP). The proposed design algorithm finds the optimum solution by iteratively solving a quadratic programming problem with linear equality constraints. By a special modification of the basic algorithm, we obtain PR filter banks with high stopband attenuations. In addition, fast convergence is verified by designing PR filter banks with up to 128 channels. [ABSTRACT FROM PUBLISHER]

Classic bilevel programming deals with two level hierarchical optimization problems in which the leader attempts to optimize his/her objective, subject to a set of constraints and his/her follower’s solution. In modelling a real-world bilevel decision problem, some uncertain coefficients often appear in the objective functions and/or constraints of the leader and/or the follower. Also, the leader and the follower may have multiple conflicting objectives that should be optimized simultaneously. Furthermore, multiple followers may be involved in a decision problem and work cooperatively according to each of the possible decisions made by the leader, but with different objectives and/or constraints. Following our previous work, this study proposes a set of models to describe such fuzzy multi-objective, multi-follower (cooperative) bilevel programming problems. We then develop an approximation Kth-best algorithm to solve the problems. [ABSTRACT FROM AUTHOR]

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Nonsharp distillation sequences are widely used in industrial separation processes; however, most current research has not discussed this topic, except in sequences with heat integration under special operating conditions, including complex columns. The sequence with nonsharp separation has the features of general distillation sequences, which are usually optimized by adjusting the separation sequence and the design/operation parameters of each column in the sequence, making the optimization a mixed integer nonlinear programming (MINLP) problem, which is usually hard to solve. With inclusion of nonsharp separation columns, the sequence optimization becomes even more complicated and computationally intensive. This work aimed to optimize the distillation sequence, including nonsharp distillation alongside simple columns and dividing wall columns. Inspired by the dynamic programing method for sharp distillation sequence, a framework for automatic optimization is proposed to decompose the MINLP problem into integer programming (IP) and nonlinear programming (NLP) problems. The optimization processes of sharp and nonsharp distillation sequences are compared and the solution space in terms of the possible number of distillation sequences with nonsharp separation is discussed. Two optimization cases, including an industrial one, are included to validate the proposed framework. [ABSTRACT FROM AUTHOR]