General Cost Functions Research Articles

The path-specific traffic equilibrium problem with generalized cost functions

The traffic equilibrium problem (TEP) is an essential module in transportation planning. This paper studies an extended TEP version, i.e. the path-specific traffic equilibrium problem (PS-TEP), which has many applications in the real world. Due to inherent path interactions, the PS-TEP cannot be formulated as an optimization model but can be formulated as a variational inequality model. The corresponding user equilibrium conditions are characterized by the equal and minimum generalized path cost, which in turn can be expressed as a function of actual path costs and path-specific disutility. To interpret the PS-TEP as an extension of the TEP, an augmented network representation that includes a basic network (incurred actual path costs) and an additional virtual network (incurred path-specific disutility) is proposed. A path-based solution algorithm, called the gradient projection method, is modified for demonstration. Four path-specific cost schemes of the path-specific disutility are used for elaboration using the same framework. The numerical examples show that the user equilibrium conditions are fully satisfied. Future research should address the corresponding efficient solution algorithms.

Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model

In this paper, we propose a novel approach to model route choice behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume further that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indifference curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least negative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi-objective user equilibrium (TSmaxBUE) condition. That is, for each O–D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O–D pair.We show that the TSmaxBUE condition is a proper generalisation of user equilibrium with generalised cost function, and that it is equivalent to bi-objective user equilibrium. We also present a multi-user class version of the TSmaxBUE condition and demonstrate our concepts with illustrative examples.

Stochastic unit commitment problem considering risk constraints and its improved GA‐based solution method

AbstractThis paper proposes a model of the stochastic unit commitment (SUC) problem, which takes account of the uncertainty of electric power demand and its resulting risk, and its solution method based on an improved genetic algorithm (IGA). The uncertainty of electric power demand is modeled using a set of scenarios which are introduced by scenario analysis. The variance, which measures the dispersion of generation costs of unit commitment schedule under each scenario around the expected generation cost, is used as a measure of risk. Based on the expected returns–variance of returns (E–V) rule in the theory of portfolio analysis, a utility function is devised by appending the variance of the expected generation cost into the original expected generation cost function, with consideration of the risk attitude of the generation companies and power exchange centers. The objective of this optimization problem is to minimize the utility function. The proposed IGA is used to solve this NP‐hard optimization problem. Based on numerical examples, the superiority of the IGA‐based solution method is verified through comparison with a traditional GA‐based solution method. Optimal schedules of SUC, as well as the expected costs and variances, are compared with/without risk constraints, and with different risk attitudes. Test results show that, in solving the SUC problem, it is necessary to consider the electric power demand uncertainty and its resulting risk, as well as the risk attitude of the decision maker. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Optimizing Cloud Resources for Delivering IPTV Services Through Virtualization

Virtualized cloud-based services can take advantage of statistical multiplexing across applications to yield significant cost savings. However, achieving similar savings with real-time services can be a challenge. In this paper, we seek to lower a provider's costs for real-time IPTV services through a virtualized IPTV architecture and through intelligent time-shifting of selected services. Using Live TV and Video-on-Demand (VoD) as examples, we show that we can take advantage of the different deadlines associated with each service to effectively multiplex these services. We provide a generalized framework for computing the amount of resources needed to support multiple services, without missing the deadline for any service. We construct the problem as an optimization formulation that uses a generic cost function. We consider multiple forms for the cost function (e.g., maximum, convex and concave functions) reflecting the cost of providing the service. The solution to this formulation gives the number of servers needed at different time instants to support these services. We implement a simple mechanism for time-shifting scheduled jobs in a simulator and study the reduction in server load using real traces from an operational IPTV network. Our results show that we are able to reduce the load by ~24%(compared to a possible ~31.3% as predicted by the optimization framework).

Modelling Route Choice Behaviour in a Tolled Road Network with a Time Surplus Maximisation Bi-objective User Equilibrium Model

In this paper, we propose a novel approach to model route choice behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume further that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indifference curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least negative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi-objective user equilibrium (TSmaxBUE) condition. That is, for each O-D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O-D pair.We show that the TSmaxBUE condition is a proper generalisation of user equilibrium with generalised cost function, and that it is equivalent to bi-objective user equilibrium. We also present a multi-user class version of the TSmaxBUE condition and demonstrate our concepts with illustrative examples.

Bicriterion Shortest Path Problem with a General Nonadditive Cost

A bicriterion shortest path problem with a general nonadditive cost seeks to optimize a combination of two path costs, one of which is evaluated by a nonlinear function. This paper first identifies a number of emerging transportation applications for which such a shortest path problem might be considered a core subproblem. We propose to first approximate the general nonlinear cost function with a piecewise linear counterpart, and then solve each linear subproblem sequentially. A specialized algorithm is developed to solve the subproblems, which makes use of the efficient path set (or the convex hull) to update upper and lower bounds of the original problem. Conditions under which the solution to a subproblem must belong to the efficient path set are specified. Accordingly, we show that the optimal path must be efficient if the nonlinear cost function is concave. If the optimal path to a subproblem is not efficient, partial path enumeration, implemented using a simple K-shortest path ranking procedure, is conducted to close the gap. The proposed algorithm includes strategies aiming to expedite path enumeration by using upper bounds derived from the efficient path set. Numerical experiments are conducted to demonstrate correctness and effectiveness of the proposed algorithm.

Optimal design of multi‐server Markovian queues with polynomial waiting and service costs

This paper is concerned with the optimal design of queueing systems. The main decisions in the design of such systems are the number of servers, the appropriate control to have on the arrival rates, and the appropriate service rate these servers should possess. In the formulation of the objective function to this problem, most publications use only linear cost rates. The linear rates, especially for the waiting cost, do not accurately reflect reality. Although there are papers involving nonlinear cost functions, no paper has ever considered using polynomial cost functions of degree higher than two. This is because simple formulas for computing the higher moments are not available in the literature. This paper is an attempt to fill this gap in the literature. Thus, the main contributions of our work are as follows: (i) the derivation of a very simple formula for the higher moments of the waiting time for the M/M/s queueing system, which requires only the knowledge of the expected waiting time; (ii) proving their convexity with respect to the design variables; and (iii) modeling and solving more realistic design problems involving general polynomial cost functions. We also focus on simultaneous optimization of the staffing level, arrival rate and service rate. Copyright © 2013 John Wiley & Sons, Ltd.

A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing

This paper studies the dynamic lot sizing problem with product returns and remanufacturing (DLRR). Given demands and returns over a planning horizon, DLRR is to determine a production schedule of manufacturing new products and/or remanufacturing returns such that demand in each period is satisfied and the total cost (set-up cost plus holding cost of inventory) is minimized.Since DLRR with general cost functions for set-ups of manufacturing and remanufacturing is NP-hard, we develop a tabu search to produce high-quality solutions. To generate a good initial solution, we use a block-chain based method where the planning horizon is split into a chain of blocks. A block may contain either a string of manufacturing set-ups, a string of remanufacturing set-ups, or both. Given the cost of each block, an initial solution corresponding to a best combination of blocks is found by solving a shortest-path problem. Neighboring operators aim at shifting integer variables for manufacturing and remanufacturing set-ups.We evaluate our algorithm on 6480 benchmark problems and compare it with other available algorithms. Computational results demonstrate that our algorithm produces an optimal solution in 96.60% of benchmark problems, with an average deviation of 0.00082% from optimality and it is a state-of-the-art method for DLRR.

Basis Paths and a Polynomial Algorithm for the Multistage Production-Capacitated Lot-Sizing Problem

We consider the multilevel lot-sizing problem with production capacities (MLSP-PC), in which production and transportation decisions are made for a serial supply chain with capacitated production and concave cost functions. Existing approaches to the multistage version of this problem are limited to nonspeculative cost functions—up to now, no algorithm for the multistage version of this model with general concave cost functions has been developed. In this paper, we develop the first polynomial algorithm for the MLSP-PC with general concave costs at all of the stages, and we introduce a novel approach to overcome the limitations of previous approaches. In contrast to traditional approaches to lot-sizing problems, in which the problem is decomposed by time periods and is analyzed unidirectionally in time, we solve the problem by introducing the concept of a basis path, which is characterized by time and stage. Our dynamic programming algorithm proceeds both forward and backward in time along this basis path, enabling us to solve the problem in polynomial time.

In This Issue

In This Issue

Incentive effects of bonus taxes in a principal-agent model

Several countries have implemented bonus taxes for corporate executives in response to the current financial crisis. Using a principal-agent model, this paper investigates the incentive effects of bonus taxes by analyzing the agent's and principal's behavior. Specifically, we show how bonus taxes affect the agent's incentives to exert effort and the principal's decision regarding the composition of the compensation package (fixed salary and bonus rate). We find that, surprisingly, a bonus tax can increase the bonus rate and decrease the fixed salary if the agent is highly risk averse. Additionally, a bonus tax can induce the principal to pay higher bonuses even though the agent's effort unambiguously decreases. Nevertheless, a bonus tax reduces the overall salary of the agent. Further results are derived with respect to the existence and uniqueness of the equilibrium for a general effort cost function.

On the Huffman and Alphabetic Tree Problem with General Cost Functions

We address generalized versions of the Huffman and Alphabetic Tree Problem where the cost caused by each individual leaf i, instead of being linear, depends on its depth in the tree by an arbitrary function. The objective is to minimize either the total cost or the maximum cost among all leaves. We review and extend the known results in this direction and devise a number of new algorithms and hardness proofs.It turns out that the Dynamic Programming approach for the Alphabetic Tree Problem can be extended to arbitrary cost functions, resulting in a time O(n 4) optimal algorithm using space O(n 3). We identify classes of cost functions where the well-known trick to reduce the runtime by a factor of n via a “monotonicity” property can be applied.For the generalized Huffman Tree Problem we show that even the k-ary version can be solved by a generalized version of the Coin Collector Algorithm of Larmore and Hirschberg (in Proc. SODA’90, pp. 310–318, 1990) when the cost functions are nondecreasing and convex. Furthermore, we give an O(n 2logn) algorithm for the worst case minimization variants of both the Huffman and Alphabetic Tree Problem with nondecreasing cost functions.Investigating the limits of computational tractability, we show that the Huffman Tree Problem in its full generality is inapproximable unless P = NP, no matter if the objective function is the sum of leaf costs or their maximum. The alphabetic version becomes NP-hard when the leaf costs are interdependent.

Population Induced Instabilities in Genetic Algorithms for Constrained Optimization

Evolutionary computation techniques, like genetic algorithms, have received a lot of attention as optimization techniques but, although they exhibit a very promising potential in curing the problem, they have not produced a significant breakthrough in the area of systematic treatment of constraints. There are two mainly ways of handling the constraints: the first is to produce an infeasibility measure and add it to the general cost function (the well known penalty methods) and the other is to modify the mutation and crossover operation in a way that they only produce feasible members. Both methods have their drawbacks and are strongly correlated to the problem that they are applied. In this work, we propose a different treatment of the constraints: we induce instabilities in the evolving population, in a way that infeasible solution cannot survive as they are. Preliminary results are presented in a set of well known from the literature constrained optimization problems.

Semantic query optimization in the presence of types

Both semantic and type-based query optimization rely on the idea that queries may exhibit non-trivial rewritings if the state space of the database is restricted. While these two problems have always been studied as separate problems in previous work, in this paper we present a unifying, logic-based query optimization framework that builds upon the classical chase algorithm and brings both problems together. As a major challenge, our novel setting requires chasing conjunctive queries with union and negation in the presence of dependencies containing negation and disjunction. Tackling this problem, we study the applicability of the chase in this setting, develop novel conditions that guarantee its termination, identify fragments for which minimal query computation (w.r.t. a generic cost function) is always possible, and investigate the complexity of related decision problems.

Using Bi-level Multi-Objective Programming in Passenger Structure Optimization for Comprehensive Transportation Channel

The economic structure is the lifeblood of national economic development. Passenger structure within comprehensive transportation channel (CTC) is the key to play a higher efficiency and to operate normally of an integrated transport system. This paper analyzes the ideas of PTS optimization within CTC using bi-level planning strategies. And then a bi-level multi-objective programming model is established in this paper, in which the upper level takes the builders and government’s concern into account, such as system efficiency, transport capacity, capital investment. The lower level is a network equilibrium model based on a generalized cost function, while Channel saturation entropy index is introduced in the response function. A particle swarm optimization algorithm is designed to efficiently solve this NP-hard model. Finally, numerical implementations based on Beijing-Shanghai Channel are carried out to account for the performance of our model and algorithm.

Policy Evaluation of Multimodal Transportation Network The Case of Inter-island Freight Transportation in Indonesia

This paper outlines the development of an analytical model of multimodal, multicommodity freight transportation in Indonesia. The model is used to evaluate strategic planning of inter-island freight transportation. The demand for inter-island freight transportation is estimated using econometric demand models which account for the socioeconomic characteristics of the regions and commodity types. The supply side is concerned with modeling the inter-island transportation network, including links, such as the land access network, and transfer points which are connected by the links, and a generalized cost function. System optimization is obtained by identifying the combination of links and transfers that minimize the total generalized transport cost. The model is applied to the evaluation of the impacts of several policy scenarios which contribute to the improvement of the inter-island freight transportation network. The model has shown its capability of estimating system costs of transportation network that can be utilized to assess the policy implications.

SGM to solve NMF – Application to Hyperspectral Data

This article deals with the problem of minimization of a general cost function under non-negativity and flux conservation con- straints. The proposed algorithm is founded on the Split Gradient Method (SGM) adapted here to solve the Non Negative Matrix Factorization (NMF). We show that SGM can be easily regularized, allowing to introduce some physical constraints. Finally, to validate the algorithm, we propose an example of application to hyperspectral data unmixing.

Economic model predictive control of switched nonlinear systems

We focus on the development of a Lyapunov-based economic model predictive control (LEMPC) method for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule. In contrast to steady-state operation of conventional model predictive control (MPC) methods which use a quadratic objective function in their formulations, LEMPC utilizes a general (non-quadratic) cost function which may directly address economic considerations and may lead to time-varying closed-loop operation. Appropriate stabilizability assumptions for the switched nonlinear system are made and suitable constraints are imposed on the proposed LEMPC formulation to guarantee closed-loop stability of the switched nonlinear system and ensure satisfaction of the prescribed switching schedule policy while dictating time-varying operation that optimizes the economic cost function. The proposed control method is demonstrated through a chemical process example described by a switched nonlinear system.

A New Performance Metric for Construction of Robust and Efficient Wireless Backbone Network

With the popularity of wireless devices and the increasing demand of network applications, it is emergent to develop more effective communications paradigm to enable new and powerful pervasive applications, and to allow services to be accessed anywhere, at anytime. However, it is extremely challenging to construct efficient and reliable networks to connect wireless devices due to the increasing communications need and the dynamic nature of wireless communications. In order to improve transmission throughput, many efforts have been made in recent years to reduce traffic and hence transmission collisions by constructing backbone networks with the minimum size. However, many other important issues need to be considered. Instead of simply minimizing the number of backbone nodes or supporting some isolated network features, in this work, we exploit the use of algebraic connectivity to control backbone network topology design for concurrent improvement of backbone network robustness, capacity, stability and routing efficiency. In order to capture other network features, we provide a general cost function and introduce a new metric, connectivity efficiency, to trade off algebraic connectivity and cost for backbone construction. We formally prove the problem of formulating a backbone network with the maximum connectivity efficiency that is NP-hard, and design both centralized and distributed algorithms to build more robust and efficient backbone infrastructure to better support the application needs. We have made extensive simulations to evaluate the performance of our work. Compared to literature studies on constructing wireless backbone networks, the incorporation of algebraic connectivity into the network performance metric could achieve much higher throughput and delivery ratio, and much lower end-to-end delay and routing distances under all test scenarios. We hope our work could stimulate more future research in designing more reliable and efficient networks. Our performance studies demonstrate that, compared to peer work, the incorporation of algebraic connectivity into network performance metric could achieve much higher throughput and delivery ratio, and much lower end-to-end delay and routing distances under all test scenarios. We hope our work could stimulate more future research in designing more reliable and efficient networks.

Development of a transfer‐cost‐based logit assignment model for the Beijing rail transit network using automated fare collection data

SUMMARYLiterature review indicates that little is known about traveler behavior, such as transfer and route choices, in large transit systems because of the number of alternative routes involved and lack of empirical data. Even though many transit route assignment models have been developed and ample automated fare collection data have been collected, nearly no study has quantified how accurate resulting flow assignments are, especially for transfer flows. However, as a multi‐stakeholder system, it is essential to estimate passenger flows over the Beijing rail transit network for revenue sharing and daily management/operation purpose. In this paper, major factors (including total travel time and transfer cost) that influence passenger flow pattern in the Beijing rail transit network are considered in a logit‐based network flow assignment model. Specifically, a full transfer cost function, including transfer walking time, vehicle waiting time, and a penalty to additional transfers, is proposed to better simulate passengers' transfer behaviors. A generalized cost function for urban rail transit network is presented, and the corresponding route choice behavior of travelers is analyzed. An improved logit‐based model is then presented for solving this network flow assignment problem. The depth‐first method is used to search for “effective paths” among all O–D pairs. The average errors of estimated transfer flows from the proposed assignment model, which is proven to be more realistic in searching a set of effective paths, are below 20%. The results indicate that the models being developed in this study are capable of reasonably reproducing passengers' transfer and route choices and thus helpful for understanding the transfer behaviors of passengers of large rail transit networks. Copyright © 2012 John Wiley & Sons, Ltd.