Fixed point optimization algorithm and its application to power control in CDMA data networks

We discuss the variational inequality problem for a continuous operator over the fixed point set of a nonexpansive mapping. One application of this problem is a power control for a direct-sequence code-division multiple-access data network. For such a power control, each user terminal has to be able to quickly transmit at an ideal power level such that it can get a sufficient signal-to-interference-plus-noise ratio and achieve the required quality of service. Iterative algorithms to solve this problem should not involve auxiliary optimization problems and complicated computations. To ensure this, we devise a fixed point optimization algorithm for the variational inequality problem and perform a convergence analysis on it. We give numerical examples of the algorithm as a power control.     

A new two‐stage algorithm for solving power flow tracing

This article proposed a new hybrid algorithm for solving power flow tracing (PFT) through the comparison by other techniques. This proposed hybrid strategy in detail discuses over the achieved results. Both methods use the active and reactive power balance equations at each bus to solve the tracing problem, where the first method considers the proportional sharing assumption and the second one considers the circuit laws to find the relationship between power inflows and outflows through each line, generator, and load connected to each bus of the network. Both algorithms are able to handle loop flow and loss issues in tracing the problem. A mathematical formulation is also introduced to find the share of each unit in provision of each load. These algorithms are employed to find the producer and consumer's shares on the cost of transmission for each line in different case studies. As the results of these studies show, both algorithms can effectively solve the PFT problem. © 2014 Wiley Periodicals, Inc. Complexity 21: 187–194, 2015     

The Efficient Allocation of Private Contractors to Public Works

A large, publicly owned corporation has a yearly problem of allocating work to private contractors. The current heuristic procedure used to do this economically on a minicomputer is described. This quick procedure generally does not lead to an optimal solution. The formulation and solution of the problem as an optimization model (an integer programme) is then described. It is then pointed out that this model can be regarded as a minimum cost network flow model showing the optimization problem to be much easier than it at first appeared. Regarding the problem in this manner has the advantage of (i) showing it is possible to optimize very quickly on a minicomputer; (ii) demonstrating that meaningful shadow prices can be derived.     

Robust placement and tuning of UPFC via a new multiobjective scheme‐based fuzzy theory

This article addresses a new modified honey bee mating optimization namely multiobjective honey bee mating optimization (MOIHBMO) based fuzzy multiobjective methodology for optimal locating and parameter setting of unified power flow controller (UPFC) in a power system for a long‐term period. One of the profits obtained by UPFC placement in a transmission network is the reduction in total generation cost due to its ability to change the power flow pattern in the network. Considering this potential, UPFC can be also used to remove or at least mitigate the congestion in transmission networks. The other issue in a power system is voltage violation which could even render the optimal power flow problem infeasible to be solved. Voltage violation could be also mitigated by proper application of UPFC in a transmission system. These objectives are considered simultaneously in a unified objective function for the proposed optimization algorithm. At first, these objectives are fuzzified and designed to be comparable against each other and then they are integrated and introduced to a MOIHBMO method to find the solution which maximizes the value of integrated objective function in a 3‐year planning horizon, considering the load growth. A power injection model is adopted for UPFC. Unlike, the most previous works in this field the parameters of UPFC are set for each load level to avoid inconvenient rejection of more optimal solutions. IEEE reliability test system is used as an illustrative example to show the effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 126–137, 2015     

Decentralized Dual-Based Algorithm for Computing Optimal Flows in a General Supply Chain

This paper addresses the issue of the optimal flow allocation in general supply chains. Our basic observation is that a distribution channel involving several reselling steps for a particular product can be viewed as a route in a supply chain network. The flow of goods or services along each route is influenced by the customer's demand, described by the corresponding utility functions, and prices charged at each node. We develop an optimization algorithm based on the primal-dual framework and the Newton's step that computes optimal prices at each node (dual problem) and then computes the optimal flow allocation (primal problem) based on these prices. Our main contribution is a discovery that the Newton's step leads to a partially decentralized algorithm which is a first step toward a decentralization schema for computing optimal prices.     

Balancing modular transfer lines with serial-parallel activation of spindle heads at stations

The paper deals with an as yet unexplored combinatorial optimization problem concerning balancing complex transfer lines in the machining/process environment. In contrast to similar problems for assembly lines, in transfer line balancing, tasks are grouped into blocks. All tasks of each block are executed simultaneously (in parallel) by one piece of equipment (spindle head). For the transfer lines considered in this paper, spindle heads at each station are activated in serial-parallel order. The set of all available spindle heads is known beforehand. Precedence, cycle time, compatibility, and parallelism constraints for the blocks and tasks are given. The line investment cost is estimated by the sum of block and station costs. The problem is to assign all tasks (using the available blocks) such that all constraints are respected and line investment cost is at a minimum. This paper focuses on solving the problem via a branch-and-bound algorithm. An approach for obtaining an efficient lower bound is offered, based on a reduction of the initial problem to a set partitioning problem. Computational experiments reveal that the proposed approach is efficient mathematically and can be used to solve practical transfer line design problems of a medium size.     

Efficient contraflow algorithms for quickest evacuation planning

The optimization models and algorithms with their implementations on flow over time problems have been an emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and Efficiently as possible, contraflow configuration is one of the highly applicable operations research (OR) models. It increases the outbound road capacities by reversing the direction of arcs towards the safe destinations that not only minimize the congestion and increase the flow but also decrease the evacuation time significantly. In this paper, we sketch the state of quickest flow solutions and solve the quickest contraflow problem with constant transit times on arcs proving that the problem can be solved in strongly polynomial time O(nm²(log n)²), where n and m are number of nodes and number of arcs, respectively in the network. This contraflow solution has the same computational time bound as that of the best min-cost flow solution. Moreover, we also introduce the contraflow approach with load dependent transit times on arcs and present an Efficient algorithm to solve the quickest contraflow problem approximately. Supporting the claim, our computational experiments on Kathmandu road network and on randomly generated instances perform very well matching the theoretical results. For sufficiently large number of evacuees, about double flow can be shifted with the same evacuation time and about half time is sufficient to push the given flow value with contraflow reconfiguration.     

Application of chaos-based chaotic invasive weed optimization techniques for environmental OPF problems in the power system

This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems.     

Optimal Configurations of General Job Shops

In this paper we study the problem of minimizing the expected number of jobs in a single class general open queueing network model of a job shop. This problem was originally posed by Buzacott and Shanthikumar [2] and solved by them for a special case. We extend their work in this paper. We derive feasibility conditions that simplify the analysis of the problem. We show that the optimal configuration can be completely characterized when both the utilizations of the machine centers are high and there are a large number of servers at each machine center. We also derive conditions under which the optimization problem reduces to solving a concave or a convex program and provide conditions under which the uniform flow line and the symmetric job shop (or variants of these) are optimal configurations for the job shop.     

Optimal abort landing trajectories in the presence of windshear

This paper is concerned with optimal flight trajectories in the presence of windshear. The abort landing problem is considered with reference to flight in a vertical plane. It is assumed that, upon sensing that the airplane is in a windshear, the pilot increases the power setting at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.The performance index being minimized is the peak value of the altitude drop. The resulting optimization problem is a minimax problem or Chebyshev problem of optimal control, which can be converted into a Bolza problem through suitable transformations. The Bolza problem is then solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. Numerical results are obtained for several combinations of windshear intensities, initial altitudes, and power setting rates.For strong-to-severe windshears, the following conclusions are reached: (i) the optimal trajectory includes three branches: a descending flight branch, followed by a nearly horizontal flight branch, followed by an ascending flight branch after the aircraft has passed through the shear region; (ii) along an optimal trajectory, the point of minimum velocity is reached at about the time when the shear ends; (iii) the peak altitude drop depends on the windshear intensity, the initial altitude, and the power setting rate; it increases as the windshear intensity increases and the initial altitude increases; and it decreases as the power setting rate increases; (iv) the peak altitude drop of the optimal abort landing trajectory is less than the peak altitude drop of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory; (v) the survival capability of the optimal abort landing trajectory in a severe windshear is superior to that of comparison trajectories, for example, the constant pitch guidance trajectory and the maximum angle of attack guidance trajectory.Portions of this paper were presented at the IFAC 10th World Congress, Munich, Germany, July 27–31, 1987 (Paper No. IFAC-87-9221).This research was supported by NASA Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company (BCAC), and by Air Line Pilots Association (ALPA). Discussions with Dr. R. L. Bowles (NASA-LRC) and Mr. C. R. Higgins (BCAC) are acknowledged.     

Scope of stationary multi-objective evolutionary optimization: a case study on a hydro-thermal power dispatch problem

Many engineering design and developmental activities finally resort to an optimization task which must be solved to get an efficient and often an intelligent solution. Due to various complexities involved with objective functions, constraints, and decision variables, optimization problems are often not adequately suitable to be solved using classical point-by-point methodologies. Evolutionary optimization procedures use a population of solutions and stochastic update operators in an iteration in a manner so as to constitute a flexible search procedure thereby demonstrating promise to such difficult and practical problem-solving tasks. In this paper, we illustrate the power of evolutionary optimization algorithms in handling different kinds of optimization tasks on a hydro-thermal power dispatch optimization problem: (i) dealing with non-linear, non-differentiable objectives and constraints, (ii) dealing with more than one objectives and constraints, (iii) dealing with uncertainties in decision variables and other problem parameters, and (iv) dealing with a large number (more than 1,000) variables. The results on the static power dispatch optimization problem are compared with that reported in an existing simulated annealing based optimization procedure on a 24-variable version of the problem and new solutions are found to dominate the solutions of the existing study. Importantly, solutions found by our approach are found to satisfy theoretical Kuhn–Tucker optimality conditions by using the subdifferentials to handle non-differentiable objectives. This systematic and detail study demonstrates that evolutionary optimization procedures are not only flexible and scalable to large-scale optimization problems, but are also potentially efficient in finding theoretical optimal solutions for difficult real-world optimization problems. Kalyanmoy Deb, Deva Raj Chair Professor. Currently a Finland Distinguished Professor, Department of Business Technology, Helsinki School of Economics, 00101 Helsinki, Finland.     

A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.     

基于物理规划的工程项目综合均衡优化

质量、工期和成本是工程项目三大主要控制目标,对于工程项目中质量-工期-成本综合均衡优化问题,传统的基于权重的决策方法存在各目标权重难以合理确定的问题.为此引入物理规划方法建立工程项目质量-工期-成本综合均衡优化模型.决策者只需设定各目标的偏好,即可通过该均衡优化模型获得符合决策者偏好的优化方案,使决策过程更加符合工程实际,避免了确定无实际物理意义的各目标权重的问题.通过桥梁工程实例验证了该方法的有效性和实用性.     

Solution to Global Minimization of Polynomials by Backward Differential Flow

This paper presents a study on solutions to the global minimization of polynomials. The backward differential flow by the K–T equation with respect to the optimization problem is introduced to deal with a ball-constrained optimization problem. The unconstrained optimization is reduced to a constrained optimization problem which can be solved by a backward differential flow. Some examples are illustrated with an algorithm for computing the backward flow.     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

A method based on Rayleigh quotient gradient flow for extreme and interior eigenvalue problems

Recently, a continuous method has been proposed by Golub and Liao as an alternative way to solve the minimum and interior eigenvalue problems. According to their numerical results, their method seems promising. This article is an extension along this line. In this article, firstly, we convert an eigenvalue problem to an equivalent constrained optimization problem. Secondly, using the Karush-Kuhn-Tucker conditions of this equivalent optimization problem, we obtain a variant of the Rayleigh quotient gradient flow, which is formulated by a system of differential-algebraic equations. Thirdly, based on the Rayleigh quotient gradient flow, we give a practical numerical method for the minimum and interior eigenvalue problems. Finally, we also give some numerical experiments of our method, the Golub and Liao method, and EIGS (a Matlab implementation for computing eigenvalues using restarted Arnoldi’s method) for some typical eigenvalue problems. Our numerical experiments indicate that our method seems promising for most test problems.     

Equipment Location in Machining Transfer Lines with Multi-spindle Heads

The considered problem appears when a machining line must be configured. It is necessary to define the number of workstations and the number of spindle heads at each workstation to be put in the line in order to produce a given part. This problem is known to be $\mathcal{NP}$ -hard and, as a consequence, the solution time increases exponentially with the size of the problem. A number of pre-processing procedures are suggested in this article in order to decrease the initial problem size and thus shorten the solution time. A new algorithm for calculating a lower bound on the number of required equipment is also presented. A numerical example is given.     

A robust and informative method for solving large-scale power flow problems

Solving power flow problems is essential for the reliable and efficient operation of an electric power network. However, current software for solving these problems have questionable robustness due to the limitations of the solution methods used. These methods are typically based on the Newton–Raphson method combined with switching heuristics for handling generator reactive power limits and voltage regulation. Among the limitations are the requirement of a good initial solution estimate, the inability to handle near rank-deficient Jacobian matrices, and the convergence issues that may arise due to conflicts between the switching heuristics and the Newton–Raphson process. These limitations are addressed by reformulating the power flow problem and using robust optimization techniques. In particular, the problem is formulated as a constrained optimization problem in which the objective function incorporates prior knowledge about power flow solutions, and solved using an augmented Lagrangian algorithm. The prior information included in the objective adds convexity to the problem, guiding iterates towards physically meaningful solutions, and helps the algorithm handle near rank-deficient Jacobian matrices as well as poor initial solution estimates. To eliminate the negative effects of using switching heuristics, generator reactive power limits and voltage regulation are modeled with complementarity constraints, and these are handled using smooth approximations of the Fischer–Burmeister function. Furthermore, when no solution exists, the new method is able to provide sensitivity information that aids an operator on how best to alter the system. The proposed method has been extensively tested on real power flow networks of up to 58k buses.     

A fast heuristic algorithm for the maximum concurrent <Emphasis Type="Italic">k</Emphasis>-splittable flow problem

In this paper, we propose a fast heuristic algorithm for the maximum concurrent k-splittable flow problem. In such an optimization problem, one is concerned with maximizing the routable demand fraction across a capacitated network, given a set of commodities and a constant k expressing the number of paths that can be used at most to route flows for each commodity. Starting from known results on the k-splittable flow problem, we design an algorithm based on a multistart randomized scheme which exploits an adapted extension of the augmenting path algorithm to produce starting solutions for our problem, which are then enhanced by means of an iterative improvement routine. The proposed algorithm has been tested on several sets of instances, and the results of an extensive experimental analysis are provided in association with a comparison to the results obtained by a different heuristic approach and an exact algorithm based on branch and bound rules.     

On computational complexity of the electric power flow optimization problem in market environment

Under consideration is the electric power flow optimization problem for an electric power system which typically arises in calculation of electrical power auctions in the “day-ahead” and balancing markets. It was established that the problem of finding a feasible flow in the balancing market is NP-hard in the strong sense even in case of one generator. The problem of finding an optimal flow in the day-ahead market is proved to be NP-hard even with one generator and without controlled cuts.