Discrete optimization in public rail transport

Many problems arising in traffic planning can be modelled and solved using discrete optimization. We will focus on recent developments which were applied to large scale real world instances. Most railroad companies apply a hierarchically structured planning process. Starting with the definition of the underlying network used for transport one has to decide which infrastructural improvements are necessary. Usually, the rail system is periodically scheduled. A fundamental base of the schedule are the lines connecting several stations with a fixed frequency. Possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of the passengers’s comfort satisfying certain regulations. After the lines of the system are fixed, the train schedule can be determined. A criterion for the quality of a schedule is the total transit time of the passengers including the waiting time which should be minimized satisfying some operational constraints. For each trip of the schedule a train consisting of a locomotive and some carriages is needed for service. The assignment of rolling stock to schedule trips has to satisfy operational requirements. A comprehensible objective is to minimize the total cost. After all strategic and tactical planning the schedule has to be realized. Several external influences, for example delayed trains, force the dispatcher to recompute parts of the schedule on-line. A Web page with examples quoted in this survey can be found at http://www.math.tu-bs.de/mo/ismp.html.     

A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem

Multilevel programming is characterized as mathematical programming to solve decentralized planning problems. The models partition control over decision variables among ordered levels within a hierarchical planning structure of which the linear bilevel form is a special case of a multilevel programming problem. In a system with such a hierarchical structure, the high-level decision making situations generally require inclusion of zero-one variables representing ‘yes-no’ decisions. We provide a mixed-integer linear bilevel programming formulation in which zero-one decision variables are controlled by a high-level decision maker and real-value decision variables are controlled by a low-level decision maker. An algorithm based on the short term memory component of Tabu Search, called Simple Tabu Search, is developed to solve the problem, and two supplementary procedures are proposed that provide variations of the algorithm. Computational results disclose that our approach is effective in terms of both solution quality and efficiency.     

Optimization models for the single delay management problem in public transportation

Passengers travelling in public transportation networks often have to use different lines to cover the trip from their origin to the desired destination. As a consequence, the reliability of connections between vehicles is a key issue for the attractiveness of the intermodal transportation network and it is strongly affected by some unpredictable events like breakdowns or vehicle delays. In such cases, a decision is required to determine if the connected vehicles should wait for the delayed ones or keep their schedule. The delay management problem (DMP) consists in defining the wait/depart policy which minimizes the total delay on the network. In this work, we present two equivalent mixed integer linear programming models for the DMP with a single initial delay, able to reduce the number of variables with respect to the formulations proposed by the literature. The two models are solved by a branch and cut procedure and by a constraint generation approach respectively, and preliminary computational results are presented.     

小批量随机块坐标下降算法

针对机器学习中广泛存在的一类问题：结构化随机优化问题（其中“结构化”是指问题的可行域具有块状结构,且目标函数的非光滑正则化部分在变量块之间是可分离的）,我们研究了小批量随机块坐标下降算法（mSBD）。按照求解非复合问题和复合问题分别给出了基本的mSBD和它的变体,对于非复合问题,分析了算法在没有一致有界梯度方差假设情况下的收敛性质。而对于复合问题,在不需要通常的Lipschitz梯度连续性假设条件下得到了算法的收敛性。最后通过数值实验验证了mSBD的有效性。     

Cutting plane algorithms for the inverse mixed integer linear programming problem

We present cutting plane algorithms for the inverse mixed integer linear programming problem (InvMILP), which is to minimally perturb the objective function of a mixed integer linear program in order to make a given feasible solution optimal.     

A new linear programming approach and genetic algorithm for solving airline boarding problem

The airline industry is under intense competition to simultaneously increase efficiency and satisfaction for passengers and profitability and internal system benefit for itself. The boarding process is one way to achieve these objectives as it tends itself to adaptive changes. In order to increase the flying time of a plane, commercial airlines try to minimize the boarding time, which is one of the most lengthy parts of a plane’s turn time. To reduce boarding time, it is thus necessary to minimize the number of interferences between passengers by controlling the order in which they get onto the plane through a boarding policy. Here, we determine the passenger boarding problem and examine the different kinds of passenger boarding strategies and boarding interferences in a single aisle aircraft. We offer a new integer linear programming approach to reduce the passenger boarding time. A genetic algorithm is used to solve this problem. Numerical results show effectiveness of the proposed algorithm.     

Recent advances in optimization techniques for statistical tabular data protection

One of the main services of National Statistical Agencies (NSAs) for the current Information Society is the dissemination of large amounts of tabular data, which is obtained from microdata by crossing one or more categorical variables. NSAs must guarantee that no confidential individual information can be obtained from the released tabular data. Several statistical disclosure control methods are available for this purpose. These methods result in large linear, mixed integer linear, or quadratic mixed integer linear optimization problems. This paper reviews some of the existing approaches, with an emphasis on two of them: cell suppression problem (CSP) and controlled tabular adjustment (CTA). CSP and CTA have concentrated most of the recent research in the tabular data protection field. The particular focus of this work is on methods and results of practical interest for end-users (mostly, NSAs). Therefore, in addition to the resulting optimization models and solution approaches, computational results comparing the main optimization techniques - both optimal and heuristic - using real-world instances are also presented.     

Optimality-based clustering: An inverse optimization approach

We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who (approximately) solves an optimization problem and cluster the data points by identifying a common objective function of the optimization problems for each cluster such that the worst-case optimality error is minimized. We propose three different clustering models and test them in the diet recommendation application.     

A note on “A new local and global optimization method for mixed integer quadratic programming problems” by G.Q. Li et al.

In this comment, we preset a minor mistake in typing which is made in “A new local and global optimization method for mixed integer quadratic programming problems” by G.Q. Li et al.     

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn.     

天然气稳态运行优化的混合整数模型及其算法

天然气稳态运行优化问题的难点在于网络结构复杂、规模大、目标函数及约束高度非线性.针对其混合整数非线性规划模型,基于网络约简和线性化技术,建立了线性近似模型,并提出一种新的求解算法.将新算法用于优化我国西部天然气管网系统,结果表明所提算法是有效的.     

Robust ranking and portfolio optimization

The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.     

A new approach based on the surrogating method in the project time compression problems

This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.     

A new approach to tactical and strategic planning in production-distribution networks

Today the most important concern of the managers is to make their firms viable in the competitive trade world. Managers are looking for effective tools for decision making in the complex business world. This paper presents a new mathematical model for strategic and tactical planning in a multiple-echelon, multiple-commodity production-distribution network. In the proposed model, different time resolutions are considered for strategic and tactical decisions. Also expansion of the network is planned based on cumulative net incomes. To illustrate applications of the proposed model as well as its performance based on the solution times, some hypothetical numerical examples have been generated and solved by CPLEX. Results show that in small and medium scale of instances, high quality solutions can be obtained using this solver, but for larger instances, some heuristics has to be designed to reduce solution time.     

An evolutionary programming approach to mixed-variable optimization problems

Many engineering optimization problems frequently encounter discrete variables as well as continuous variables and the presence of nonlinear discrete variables considerably adds to the solution complexity. Very few of the existing methods can find a globally optimal solution when the objective functions are non-convex and non-differentiable. In this paper, we present a mixed-variable evolutionary programming (MVEP) technique for solving these nonlinear optimization problems which contain integer, discrete, zero-one and continuous variables. The MVEP provides an improvement in global search reliability in a mixed-variable space and converges steadily to a good solution. An approach to handle various kinds of variables and constraints is discussed. Some examples of mixed-variable optimization problems in the literature are tested, which demonstrate that the proposed approach is superior to current methods for finding the best solution, in terms of both solution quality and algorithm robustness.     

Checking solvability of systems of interval linear equations and inequalities via mixed integer programming

This paper deals with the problems of checking strong solvability and feasibility of linear interval equations, checking weak solvability of linear interval equations and inequalities, and finding control solutions of linear interval equations. These problems are known to be NP$\mathit{NP}$-hard. We use some recently developed characterizations in combination with classical arguments to show that these problems can be equivalently stated as optimization tasks and provide the corresponding linear mixed 0–1 programming formulations.     

Transportation problem with nonlinear side constraints a branch and bound approach

In a container terminal management, we are often confronted with the following problem: how to assign a reasonable depositing position for an arriving container, so that the efficiency of searching for and loading of a container later can be increased. In this paper, the problem is modeled as a transportation problem with nonlinear side constraints (TPNSC). The reason of nonlinear side constraints arising is that some kinds of containers cannot be stacked in the same row (the space of storage yard is properly divided into several rows). A branch and bound algorithm is designed to solve this problem. The algorithm is based on the idea of using disjunctive arcs (branches) for resolving conflicts that are created whenever some conflicting kinds of containers are deposited in the same row. During the branch and bound, the candidate problems are transformed into classical transportation problems, so that the efficient transportation algorithm can be applied, at the same time the reoptimization technique is employed during the branch and bound. Further, we design a heuristic to obtain a feasible initial solution for TPNSC in order to prune some candidates as early and/or as much as possible. We report computational results on randomly generated problems.     

Hybrid flexible flowshop problems: Models and solution methods

This paper considers the problem of hybrid flowshop scheduling. First, we review the shortcoming of the available model in the literature. Then, four different mathematical models are developed in form of mixed integer linear programming models. A complete experiment is conducted to compare the models for performance based on the size and computational complexities. Besides the models, the paper proposes a novel hybrid particle swarm optimization algorithm equipped with an acceptance criterion and a local search heuristic. The features provide a fine balance of diversification and intensification capabilities for the algorithm. Using Taguchi method, the algorithm is fine tuned. Then, two numerical experiments are performed to evaluate the performance of the proposed algorithm with three particle swarm optimization algorithms available in the scheduling literature and one well-known iterated local search algorithm in the hybrid flowshop literature. All the results show the high performance of the proposed algorithm.     

Designing Least-Cost Survivable Wireless Backhaul Networks

This paper presents a new heuristic algorithm for designing least-cost telecommunications networks to carry cell site traffic to wireless switches while meeting survivability, capacity, and technical compatibility constraints. This requires solving the following combinatorial optimization problems simultaneously: (1) Select a least-cost subset of locations (network nodes) as hubs where traffic is to be aggregated and switched, and choose the type of hub (high-capacity DS3 vs. lower-capacity DS1 hub) for each location; (2) Optimally assign traffic from other nodes to these hubs, so that the traffic entering the network at these nodes is routed to the assigned hubs while respecting capacity constraints on the links and routing-diversity constraints on the hubs to assure survivability; and (3) Optimally choose the types of links to be used in interconnecting the nodes and hubs based on the capacities and costs associated with each link type. Each of these optimization problems must be solved while accounting for its impacts on the other two. This paper introduces a short term Tabu Search (STTS) meta-heuristic, with embedded knapsack and network flow sub-problems, that has proved highly effective in designing such backhaul networks for carrying personal communications services (PCS) traffic. It solves problems that are challenging for conventional branch-and-bound solvers in minutes instead of hours and finds lower-cost solutions. Applied to real-world network design problems, the heuristic has successfully identified designs that save over 20% compared to the best previously known designs.     

Improving the robustness in railway station areas

In order to improve the robustness of a railway system in station areas, this paper introduces an iterative approach to successively optimize the train routing through station areas and to enhance this solution by applying some changes to the timetable in a tabu search environment. We present our vision on robustness and describe how this vision can be used in practice. By introducing the spread of the trains in the objective function for the route choice and timetabling module, we improve the robustness of a railway system. Using a discrete event simulation model, the performance of our algorithms is evaluated based on a case study for the Brussels’ area. The computational results indicate an average improvement in robustness of 6.2% together with a decrease in delay propagation of about 25%. Furthermore, the effect of some measures like changing the train offer to further increase the robustness is evaluated and compared.