Optimization of control setting and size of shunt capacitors on distribution feeders

Loads on electric utility systems have two components: active power (measured in kilowatts) and reactive power (measured in kilovars). Active power has to be generated at the power plant, whereas reactive power can be provided by either power plants or capacitors. It is a well-known fact that shunt power capacitors are the most economical source to meet the reactive power requirements of inductive loads and transmission lines operating at a lagging power factor.This paper describes new contributions to the problem of optimization of size and control setting of shunt capacitors on distribution feeders, so that the losses along the feeder are minimized. The variation of the KVAR of the load on the feeder with the distance from the substation is assumed to be linear. The parameters of this function are estimated from the available KVAR loading on the feeder first by using least-square techniques and then by using least-absolute-value parameter estimation techniques. The results obtained are compared with that obtained if the current profile is assumed to be uniformly distributed on the feeder. Our results show that the optimum size of the capacitor bank as well as its optimum location depend on the parameters of the model used for the load. Also, our results show a large saving in the size of the capacitor banks used with a considerable per-unit-loss reduction along the feeder.This work was supported by the National Science and Engineering Research Council of Canada, Grant No. A4146. The first author acknowledges the help received from Engineer Samy Soliman for reviewing all the mathematical expressions in this paper.     

Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal dali alignments for the very first time.     

Ranking in quadratic integer programming problems

The present paper develops an algorithm for ranking the integer feasible solutions of a quadratic integer programming (QIP) problem. A linear integer programming (LIP) problem is constructed which provides bounds on the values of the objective function of the quadratic problem. The integer feasible solutions of this related integer linear programming problem are systematically scanned to rank the integer feasible solutions of the quadratic problem in non-decreasing order of the objective function values. The ranking in the QIP problem is useful in solving a nonlinear integer programming problem in which some other complicated nonlinear restrictions are imposed which cannot be included in the simple linear constraints of QIP, the objective function being still quadratic.     

Regulation of Overlaps in Technology Development Activities

In this paper, we present an algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems involving (i) 0-1 integer variables, and, (ii) more than one parameter, bounded between lower and upper bounds, present on the right hand side (RHS) of constraints. The solution is approached by decomposing the mp-MILP into two subproblems and then iterating between them. The first subproblem is obtained by fixing integer variables, resulting in a multiparametric linear programming (mp-LP) problem, whereas the second subproblem is formulated as a mixed integer linear programming (MILP) problem by relaxing the parameters as variables.     

A decomposition approach to the two-stage stochastic unit commitment problem

The unit commitment problem has been a very important problem in the power system operations, because it is aimed at reducing the power production cost by optimally scheduling the commitments of generation units. Meanwhile, it is a challenging problem because it involves a large amount of integer variables. With the increasing penetration of renewable energy sources in power systems, power system operations and control have been more affected by uncertainties than before. This paper discusses a stochastic unit commitment model which takes into account various uncertainties affecting thermal energy demand and two types of power generators, i.e., quick-start and non-quick-start generators. This problem is a stochastic mixed integer program with discrete decision variables in both first and second stages. In order to solve this difficult problem, a method based on Benders decomposition is applied. Numerical experiments show that the proposed algorithm can solve the stochastic unit commitment problem efficiently, especially those with large numbers of scenarios.     

A Branch and Bound Algorithm for a Class of Asymmetrical Vehicle Routeing Problems

This paper describes a branch and bound algorithm for a general class of asymmetrical vehicle routeing problems. Vehicle routes start and end at a central depot. Visits are made to nodes grouped into clusters: every cluster must receive a minimum number of visits. But not all nodes must be visited: there are specified nodes and non-specified nodes. Vehicle routes are also constrained by capacity and distance restrictions. The problem is formulated as an integer linear program. It is then solved by a branch and bound algorithm which exploits the unimodular structure of the subproblems. Computational results are reported.     

Polynomial Algorithms for a Class of Discrete Minmax Linear Programming Problems

We consider the problem of obtaining integer solutions to a minmax linear programming problem. Although this general problem is NP-complete, it is shown that a restricted version of this problem can be solved in polynomial time. For this restricted class of problems two polynomial time algorithms are suggested, one of which is strongly polynomial whenever its continuous analogue and an associated linear programming problem can be solved by a strongly polynomial algorithm. Our algorithms can also be used to obtain integer solutions for the minmax transportation problem with an inequality budget constraint. The equality constrained version of this problem is shown to be NP-complete. We also provide some new insights into the solution procedures for the continuous minmax linear programming problem.     

A method for solving the general parametric linear complementarity problem

This paper presents a solution method for the general (mixed integer) parametric linear complementarity problem pLCP(q(θ),M), where the matrix M has a general structure and integrality restriction can be enforced on the solution. Based on the equivalence between the linear complementarity problem and mixed integer feasibility problem, we propose a mixed integer programming formulation with an objective of finding the minimum 1-norm solution for the original linear complementarity problem. The parametric linear complementarity problem is then formulated as multiparametric mixed integer programming problem, which is solved using a multiparametric programming algorithm. The proposed method is illustrated through a number of examples.     

Zero-one integer programs with few constraints —Lower bounding theory

The zero-one integer programming problem and its special case, the multiconstraint knapsack problem frequently appear as subproblems in many combinatorial optimization problems. We present several methods for computing lower bounds on the optimal solution of the zero-one integer programming problem. They include Lagrangean, surrogate and composite relaxations. New heuristic procedures are suggested for determining good surrogate multipliers. Based on theoretical results and extensive computational testing, it is shown that for zero-one integer problems with few constraints surrogate relaxation is a viable alternative to the commonly used Lagrangean and linear programming relaxations. These results are used in a follow up paper to develop an efficient branch and bound algorithm for solving zero-one integer programming problems.     

Minimum power multicasting in wireless networks under probabilistic node failures

In this paper we deal with a probabilistic extension of the minimum power multicast (MPM) problem for wireless networks. The deterministic MPM problem consists in assigning transmission powers to the nodes, so that a multihop connection can be established between a source and a given set of destination nodes and the total power required is minimized. We present an extension to the basic problem, where node failure probabilities for the transmission are explicitly considered. This model reflects the necessity of taking uncertainty into account in the availability of the hosts. The novelty of the probabilistic minimum power multicast (PMPM) problem treated in this paper consists in the minimization of the assigned transmission powers, imposing at the same time a global reliability level to the solution network. An integer linear programming formulation for the PMPM problem is presented. Furthermore, an exact algorithm based on an iterative row and column generation procedure, as well as a heuristic method are proposed. Computational experiments are finally presented.     

基于可变航速的支线集装箱船舶调度优化模型与算法

随着航运市场的竞争不断加剧和集装箱船舶大型化的发展,越来越多的航运企业选择轴-辐式航运网络模式。支线船舶调度问题作为轴-辐式航运网络的重要组成部分受到研究者的高度关注。本文研究了可变航速和经济航速两种情境下的支线船舶调度问题,同时考虑枢纽港和喂给港的取送箱时间窗限制,以航运企业运营成本最小化为目标函数建立非线性混合整数规划模型。首先使用专业的规划求解器进行小规模算例的求解,验证了模型的准确性。同时运用改进的遗传算法对大规模支线船舶优化调度模型进行求解。为了提高求解效果,进一步设计了多智能体进化算法进行求解。数值结果表明,可变航速的运营成本低于经济航速的运营成本;在算法效率方面,改进遗传算法收敛速度较快,多智能体进化算法则可以提高求解精度。     

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

The paper is devoted to solving the two‐stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

A column generation based decomposition algorithm for a parallel machine just-in-time scheduling problem

We propose a column generation based exact decomposition algorithm for the problem of scheduling n jobs with an unrestrictively large common due date on m identical parallel machines to minimize total weighted earliness and tardiness. We first formulate the problem as an integer program, then reformulate it, using Dantzig–Wolfe decomposition, as a set partitioning problem with side constraints. Based on this set partitioning formulation, a branch and bound exact solution algorithm is developed for the problem. In the branch and bound tree, each node is the linear relaxation problem of a set partitioning problem with side constraints. This linear relaxation problem is solved by column generation approach where columns represent partial schedules on single machines and are generated by solving two single machine subproblems. Our computational results show that this decomposition algorithm is capable of solving problems with up to 60 jobs in reasonable cpu time.     

考虑占位决策的围堵嫌犯模型

研究了2011年中国大学生数学建模竞赛B题的突发事件中交巡警对在逃嫌犯的围堵问题。不同于对该问题的以往的研究,本文考虑了交巡警在包围圈中可以占据某些路口,使得嫌犯不能通过这些被交巡警占据的路口,从而为形成包围圈的交巡警赢得更多时间。利用两篇相关文献的关于点截集判断的结论和考虑占位决策的建模方法,以不同的目标函数建立了考虑占位决策的围堵嫌犯问题的三个混合0-1非线性整数规划模型。通过选取部分线性约束和目标函数一起组合成混合0-1线性整数规划模型,设计了基于混合0-1线性整数规划方法的算法,并给出了算例。     

Mixed-integer quadratic programming

This paper considers mixed-integer quadratic programs in which the objective function is quadratic in the integer and in the continuous variables, and the constraints are linear in the variables of both types. The generalized Benders' decomposition is a suitable approach for solving such programs. However, the program does not become more tractable if this method is used, since Benders' cuts are quadratic in the integer variables. A new equivalent formulation that renders the program tractable is developed, under which the dual objective function is linear in the integer variables and the dual constraint set is independent of these variables. Benders' cuts that are derived from the new formulation are linear in the integer variables, and the original problem is decomposed into a series of integer linear master problems and standard quadratic subproblems. The new formulation does not introduce new primary variables or new constraints into the computational steps of the decomposition algorithm.The author wishes to thank two anonymous referees for their helpful comments and suggestions for revising the paper.     

Two commodity network flows and linear programming

This paper shows that the linear programming formulation of the two-commodity network flow problem leads to a direct derivation of the known results concerning this problem. An algorithm for solving the problem is given which essentially consists of two applications of the Ford—Fulkerson max flow computation. Moreover, the algorithm provides constructive proofs for the results. Some new facts concerning feasible integer flows are also given.     

Column enumeration based decomposition techniques for a class of non-convex MINLP problems

We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are computed via subproblems. These problems can be linear, mixed integer linear, (non-)convex nonlinear, or mixed integer nonlinear. However, the important property of the subproblems is that we can compute their exact global optimum quickly. The proposed technique will be illustrated solving a cutting problem with optimum nonlinear programming subproblems.     

Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching

The airline crew scheduling problem is the problem of assigning crew itineraries to flights. We develop a new approach for solving the problem that is based on enumerating hundreds of millions random pairings. The linear programming relaxation is solved first and then millions of columns with best reduced cost are selected for the integer program. The number of columns is further reduced by a linear programming based heuristic. Finally an integer solution is obtained with a commercial integer programming solver. The branching rule of the solver is enhanced with a combination of strong branching and a specialized branching rule. The algorithm produces solutions that are significantly better than ones found by current practice.     

Solving a minimum-power covering problem with overlap constraint for cellular network design

We consider a type of covering problem in cellular networks. Given the locations of base stations, the problem amounts to determining cell coverage at minimum cost in terms of the power usage. Overlap between adjacent cells is required in order to support handover. The problem we consider is NP-hard. We present integer linear models and study the strengths of their continuous relaxations. Preprocessing is used to reduce problem size and tighten the models. Moreover, we design a tabu search algorithm for finding near-optimal solutions effectively and time-efficiently. We report computational results for both synthesized instances and networks originating from real planning scenarios. The results show that one of the integer models leads to tight bounds, and the tabu search algorithm generates high-quality solutions for large instances in short computing time.     

Structural properties and tractability results for linear synteny

The syntenic distance between two species is the minimum number of fusions, fissions, and translocations required to transform one genome into the other. The linear syntenic distance, a restricted form of this model, has been shown to be close to the syntenic distance. Both models are computationally difficult to compute and have resisted efficient approximation algorithms with non-trivial performance guarantees. In this paper, we prove that many useful properties of syntenic distance carry over to linear syntenic distance. We also give a reduction from the general linear synteny problem to the question of whether a given instance can be solved using the maximum possible number of translocations. Our main contribution is an algorithm exactly computing linear syntenic distance in nested instances of the problem. This is the first polynomial time algorithm exactly solving linear synteny for a non-trivial class of instances. It is based on a novel connection between the syntenic distance and a scheduling problem that has been studied in the operations research literature.