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Project scheduling problem (PSP) is to determine the resource allocation schedule for the trade-off between the project cost and the completion time. In this paper, PSP in the environment with uncertainty and randomness simultaneously is considered. In detail, the concepts of uncertain variable and uncertain random variable are introduced. Based on some concepts and theorems of chance theory, an uncertain random project scheduling model is built. For some special case, the proposed uncertain random programming model is transformed to a crisp mathematical programming model. Besides, uncertain random simulation techniques and genetic algorithm are integrated into a hybrid intelligent algorithm for searching the quasi-optimal schedule. [ABSTRACT FROM AUTHOR]

Recently, Gregori et al. have discussed ( Fuzzy Sets Syst 2011;161:2193-2205) the so-called strong fuzzy metrics when looking for a class of completable fuzzy metric spaces in the sense of George and Veeramani and state the question of finding a nonstrong fuzzy metric space for a continuous t-norm different from the minimum. Later on, Gutiérrez García and Romaguera solved this question ( Fuzzy Sets Syst 2011;162:91-93) by means of two examples for the product and the Lukasiewicz t-norm, respectively. In this direction, they posed to find further examples of nonstrong fuzzy metrics for continuous t-norms that are greater than the product but different from minimum. In this paper, we found an example of this kind. On the other hand, Tirado established ( Fixed Point Theory 2012;13:273-283) a fixed-point theorem in fuzzy metric spaces, which was successfully used to prove the existence and uniqueness of solution for the recurrence equation associated with the probabilistic divide and conquer algorithms. Here, we generalize this result by using a class of continuous t-norms known as ω-Yager t-norms. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a new data mining method that integrates adaptive B-spline regression and traffic flow theory to develop multi-regime traffic stream models (TSMs). Parameter estimation is implemented adaptively and optimally through a constrained bi-level programming method. The slave programming determines positions of knots and coefficients of the B-spline by minimizing the error of B-spline regression. The master programming model determines the number of knots through a regularized function, which balances model accuracy and model complexity. This bi-level programming method produces the best fitting to speed-density observations under specific order of splines and possesses great flexibility to accommodate the exhibited nonlinearity in speed-density relationships. Jam density can be estimated naturally using spline TSM, which is sometimes hardly obtainable in many other TSM. Derivative continuity up to one order lower than the highest spline degree can be preserved, a desirable property in some application. A five-regime B-spline model is found to exist for generalized speed-density relationships to accommodate five traffic operating conditions: free flow, transition, synchronized flow, stop and go traffic, and jam condition. A typical two-regime B-spline form is also explicitly given, depending only on free-flow speed, optimal speed, optimal density, and jam density. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper designs emission charging schemes to ensure traffic emissions not exceeding the emission budgets in emission regulation areas. In a network where all links are tollable, we prove that, under mild conditions, there exists a non-negative link-based toll scheme that achieves the transportation conformity requirement while minimizing total emissions. We further consider only tolling in the emission regulation areas and formulate a model to determine optimal area-based emission charges to ensure the conformity. The model is formulated as a mathematical program with complementarity constraints. A solution framework is developed to solve the model, leveraging on a derivative-free pattern search algorithm and integrating MOVES to estimate vehicular emissions more accurately. The proposed models are demonstrated on two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Modern heuristic optimization algorithms have gained considerable attention in different research fields due to their conceptual simplicity and their ability to deal with different complex optimization problems. Motivated by promising results from the application of these emerging tools on other power system optimization problems, this paper presents a comparative study on the capabilities of three heuristic optimization algorithms for solving the problem of optimal dynamic centralized transmission expansion planning (CTEP). Among the studied algorithms are: Evolutionary particle swarm optimization, differential evolution, and a newly developed tool named mean-variance mapping optimization. Considering a predefined indicative generation expansion plan, which is usually contemplated in regulations for the power system planning in most Latin American countries, modified versions of the well-known Garver's system and the IEEE-118 bus multi-area system are used to evaluate the performance of each algorithm for solving the dynamic CTEP with a medium-term planning horizon of 10 years. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY There has been a growing interest in utilizing forest biomass for energy generation in district heating systems to reduce dependence on fossil fuels. However, variability in forest biomass availability and quality over time and its complex and costly supply chain have made investments in forest biomass energy generation projects less attractive. In this paper, a linear programming model is developed to minimize the delivery cost of forest biomass to the gate of heating plants and determine the optimal monthly flow of biomass to the plants. The model has a 1-year planning horizon with monthly time steps. It determines (1) the amount of woodchips that should be transported to the plants from supply sources directly and through the terminal storages, (2) the amount of biomass that should be stored at supply sources and at terminal storages, and (3) the amount of biomass that should be chipped at supply sources and at terminal storages. The model was applied to a potential district heating system in Williams Lake, BC, Canada. The results of the optimization model indicated that it would not be economical to carry out the chipping process at the terminal storage. Biomass should be chipped at supply sources, and woodchips should be sent to the terminal storage and/or directly to the plant. Of the total optimum annual flow of woodchips to the plant, 90% is transported directly, while 10% is transported to the plant via the terminal storage. It would cost $43.38 Odt−1 to deliver forest biomass to the plant. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Multi-objective evolutionary algorithm (MOEA) based on Pareto optimality has emerged as an important approach for optimal reactive power dispatch (ORPD) problem. However, because of the deficiency of adopting evolution operators with single search characteristics, existing MOEA for multi-objective ORPD (MORPD) often fails to maintain universal and robust performance in different phases of optimization process. On the basis of running multiple algorithms simultaneously and adaptive selection strategy, this paper proposes a new optimal method for MORPD. Firstly, an algorithm candidate pool containing four different algorithms is constructed through the analysis of characteristics of state-of-the-art MOEA while considering the rules of consistency and complementarity. Then, during the optimizing search, the quantity of offspring individuals generated by each candidate algorithm at different stages of optimization process is determined adaptively by learning from its previous experience in generating promising solutions. The proposed method is tested on the IEEE 30-bus system; its computing performance is compared with existing popular MOEAs from the point of view of Pareto fronts, outer solutions and C measure. Experimental results show that the new method can obtain better performance of convergence during the entire optimization process. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam. [ABSTRACT FROM AUTHOR]

This paper presents a combination of variable neighbourhood search and mathematical programming to minimize the sum of earliness and tardiness penalty costs of all operations for just-in-time job-shop scheduling problem (JITJSSP). Unlike classical E/T scheduling problem with each job having its earliness or tardiness penalty cost, each operation in this paper has its earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. Our hybrid algorithm combines (i) a variable neighbourhood search procedure to explore the huge feasible solution spaces efficiently by alternating the swap and insertion neighbourhood structures and (ii) amathematical programming model to optimize the completion times of the operations for a given solution in each iteration procedure. Additionally, a threshold accepting mechanism is proposed to diversify the local search of variable neighbourhood search. Computational results on the 72 benchmark instances show that our algorithm can obtain the best known solution for 40 problems, and the best known solutions for 33 problems are updated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some strong convergence theorems for a common fixed point of two total quasi-ϕ- asymptotically nonexpansive mappings in Banach space by means of the hybrid method in mathematical programming. The results presented in this paper extend and improve on the corresponding ones announced by Martinez-Yanes and Xu (2006), Plubtieng and Ungchittrakool (2007), Qin et al. (2009), and many others. [ABSTRACT FROM AUTHOR]

The mathematical model for airline network seat inventory control problem is usually investigated to maximize the total revenue under some constraints such as capacities and demands. This paper presents a chance-constrained programming model based on the uncertainty theory for network revenue management, in which the fares and the demands are both uncertain variables rather than random variables. The uncertain programming model can be transformed into a deterministic form by taking expected value on objective function and confidence level on the constraint functions. Based on the strategy of nested booking limits, a solution method of booking control is developed to solve the problem. Finally, this paper gives a numerical example to show that the method is practical and efficient. [ABSTRACT FROM AUTHOR]

It is one of the important issues in the field of today's sewage treatment of researching the MBR membrane flux prediction for membrane fouling. Firstly this paper used the principal component analysis method to achieve dimensionality and correlation of input variables and obtained the three major factors affecting membrane fouling most obvious:MLSS, total resistance, and operating pressure. Then it used the BP neural network to establish the system model of the MBR intelligent simulation, the relationship between three parameters, and membrane flux characterization of the degree of membrane fouling, because the BP neural network has slow training speed, is sensitive to the initial weights and the threshold, is easy to fall into local minimum points, and so on. So this paper used genetic algorithm to optimize the initial weights and the threshold of BP neural network and established the membrane fouling prediction model based on GA-BP network. As this research had shown, under the same conditions, the BP network model optimized by GA of MBR membrane fouling is better than that not optimized for prediction effect of membrane flux. It demonstrates that the GA-BP network model of MBR membrane fouling is more suitable for simulation of MBR membrane fouling process, comparing with the BP network. [ABSTRACT FROM AUTHOR]

Stability of switching systems with an infinite number of subsystems is important in some structure of systems, like fuzzy systems, neural networks, and so forth. Because of the relationship between stability of a set of matrices and switching systems, this paper first studies the stability of a set of matrices, then and the results are applied for stability of switching systems. Some new conditions for globally uniformly asymptotically stability (GUAS) of discrete-time switched linear systems with an infinite number of subsystems are proposed. The paper considers some examples and simulation results. [ABSTRACT FROM AUTHOR]

A web service is a programmatically available application logic exposed over the internet and it has attracted much attention in recent years with the rapid development of e-commerce. Very few web services exist in the field of mathematics. The aim of this paper is to seamlessly provide user-centric mathematical web services to the service requester. In particular, this paper focuses on mathematical web services for prepositional logic and set theory which comes under discrete mathematics. A sophisticated user interface with virtual keyboard is created for accessingweb services. Experimental results show that the web services and the created user interface are efficient and practical. [ABSTRACT FROM AUTHOR]

Recently, machine-to-machine (M2M) communication has been studied in the single cell system. However, in the multicell system multiple M2M type devices at the edge of a cell may suffer from the strong interference that consists of the intercell interference from other cells and the intracell interference from other M2M devices in the local cell. In this paper, we study the relay beamforming strategy to guarantee the quality of service (QoS) requirements of the multiple destination devices in multicell systems. We minimize the transmit power of the base stations (BSs) and relays to save the power of M2M devices, while guaranteeing the receive signal-to-interference-and-noise ratio (SINR) of the destination devices. The main contribution of this paper is that we propose an iterative algorithm to jointly optimize the BS and relay beamforming weights with minimizing the BS and relay power under the receive SINR constraints in the perfect channel state information (CSI). Using the semidefinite relaxation (SDR) technology, the optimization problems for the BS and relay beamforming weights can be effectively solved. In addition, we also discuss the issue of imperfect CSI in practice. Simulation results validate our theoretical analysis and demonstrate that our proposed iterative scheme can achieve near-optimal performance within a few iterations. [ABSTRACT FROM AUTHOR]

Current researches on temporal networks mainly tend to detect community structure. A number of community detection algorithms can obtain community structure on each time slice or each period of time but rarely present the evolution of community structure. Some papers discussed the process of community structure evolution but lacked quantifying the evolution. In this paper, we put forward the concept of Community Vitality (CV), which shows a community's life intensity on a time slice. In the process of computing CV, the "dead communities" can also be distinguished. Moreover, CV cannot only be used to quantify the life intensity of a community but also be used to describe the process of community evolution over time. More specifically, the change of community's structure will be found if CVs for different time slices of a community were compared, while the community with big value of CV can be selected if CVs for different communities were compared. Furthermore, community vitality change rate (CVCR) is proposed for revealing communities' structure change. The results of our experiments show that community vitality is a novel and effective way to understand or model the community evolution. [ABSTRACT FROM AUTHOR]

This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper. [ABSTRACT FROM AUTHOR]

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approachMurata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches. [ABSTRACT FROM AUTHOR]

This paper considers a multiuser transmit beamforming problem under uncertain channel state information (CSI) subject to SINR constraints in a downlink multiuser MISO system. A robust transmit beamforming formulation is proposed. This robust formulation is to minimize the transmission power subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the receivers. The challenging problem is that the worst-case SINR constraints correspond to an infinite number of nonconvex quadratic constraints. In this paper, a natural semidifinite programming (SDP) relaxation problem is proposed to solve the robust beamforming problem. The main contribution of this paper is to establish the tightness of the SDP relaxation problem under proper assumption, which means that the SDP relaxation problem definitely yields rank-one solutions under the assumption. Then the SDP relaxation problem provides globally optimum solutions of the primal robust transmit beamforming problem under proper assumption and norm-constrained CSI errors. Simulation results show the correctness of the proposed theoretical results and also provide a counterexample whose solutions are not rank one. The existence of counterexample shows that the guess that the solutions of the SDP relaxation problem must be rank one is wrong, except that some assumptions (such as the one proposed in this paper) hold. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a stochastic multiobjective model for generation maintenance scheduling (GMS) problem and a solution method to solve it. The proposed model properly considers both competing objectives and uncertainty sources of GMS problem. Three competing objective functions including total cost, risk measure, and total emission are simultaneously minimized in the proposed model. Moreover, forced outages of generating units throughout the GMS horizon are characterized by externally generated scenarios. Stochastic programming as an efficient approach to model uncertainty sources has been used in the proposed stochastic multiobjective GMS. Augmented normalized normal constraint (A‐NNC) method is developed as an efficient multiobjective mathematical programming approach to obtain Pareto optimal solutions for the proposed model. Further, a stochastic decision maker based on out‐of‐sample analysis is suggested to find the most preferred solution for GMS problem. The IEEE 118‐bus test system is used to investigate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry. [ABSTRACT FROM AUTHOR]

We obtain in this paper the solutions of the following recursive sequences xn+1 = xnxn-3/xn-2(±1 ± xnxn-3), n = 0, 1, . . ., where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative behavior of the solutions such as the boundedness, the global stability, and the periodicity character of the solutions in each case have been studied. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the obtained results. [ABSTRACT FROM AUTHOR]

Tracking the actions of vehicles at crossroads and planning safe trajectories will be an effective method to reduce the rate of traffic accident at intersections. It is to resolve the problem of the abrupt change because of the existence of drivers' voluntary choices. In this paper, we make approach of an improved IMM tracking method based on trajectory generation, abstracted by trajectory generation algorithm, to improve this situation. Because of the similarity between human-driving trajectory and programming trajectory which is generated by trajectory-generated algorithm, the improved IMM method performs well in tracking moving vehicles with some sudden changes of its movement. A set of data is collected for experiments when an object vehicle takes a sudden left turn in intersection scenario. To compare the experiment results between IMM method with trajectory generation model and the one without, tracking error of the former decreases by 75% in particular scenario. [ABSTRACT FROM AUTHOR]

This paper is concerned with a pair of second-order mixed symmetric dual programs involving nondifferentiable functions. Weak, strong, and converse duality theorems are proved for afore-mentioned pair using the notion of second-order F-convexity/pseudoconvexity assumptions. [ABSTRACT FROM AUTHOR]

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems. [ABSTRACT FROM AUTHOR]

This paper proposed a panel data clustering model based on D-vine and C-vine and supported a semiparametric estimation for parameters. These models include a two-step inference function for margins, two-step semiparameter estimation, and stepwise semiparametric estimation. In similarity measurement, similarity coefficients are constructed by a multivariate Hierarchical Nested Archimedean Copula (HNAC) model and compound PCC models, which are HNAC and D-vine compound model and HNAC and C-vine compound model. Estimation solutions and models evaluation are given for these models. In the case study, the clustering results of HNAC and D-vine compound model and HNAC and C-vine compound model are given, and the effect of different copula families on clustering results is also discussed. The result shows the models are effective and useful. [ABSTRACT FROM AUTHOR]

Regarding the problem of the existing intuitionistic fuzzy entropy formulas in ordering the partial entropy, the constraint condition that is consistent with the intuitionistic facts is proposed in this paper, the axiomatic definition of entropy which fully reflects the intuition and fuzziness of intuitionistic fuzzy sets is given, and the improved intuitionistic fuzzy entropy formula is constructed according to the entropy axiomatic definition and its properties are studied. Finally, we compare the improved formula with the existing intuitionistic fuzzy entropy formulas, and the result turns out that the improved formula can solve the problem in the entropy ordering theoretically and practically. [ABSTRACT FROM AUTHOR]

This paper investigates the resource allocation problem for a multicarrier underlay cognitive radio system, under the assumption that only statistical Channel State Information (CSI) about the primary channels is available at the secondary user. More specifically, we maximize the system utility under primary and secondary user outage constraints and the total power constraint. The secondary user transmission is also constrained by the interference threshold imposed by the primary user. Moreover, the secondary receiver adapts its decoding strategy, which is either treating interference as noise or using successive interference cancellation or superposition coding. This leads to a nonconvex optimization problem, with either perfect or statistical CSI. Consequently, we propose a sequential-based algorithm to efficiently obtain a solution to the problem. The simulation results show that the sequential algorithm is convergent and that our global proposed scheme achieves larger secondary and sum rates than other algorithms where the decoding strategy is not adapted. [ABSTRACT FROM AUTHOR]

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for the expected cost-to-go functions modeling used in the stochastic dynamic programming (SDP) algorithm. The SDP technique is applied to the longterm operation planning of electrical power systems. Using state space discretization, the Convex Hull algorithm is used for constructing a series of hyperplanes that composes a convex set. These planes represent a piecewise linear approximation for the expected cost-to-go functions. The mean operational costs for using the proposed methodology were compared with those from the deterministic dual dynamic problem in a case study, considering a single inflow scenario. This sensitivity analysis shows the convergence of both methods and is used to determine the minimum discretization level. Additionally, the applicability of the proposed methodology for two hydroplants in a cascade is demonstrated. With proper adaptations, this work can be extended to a complete hydrothermal system. [ABSTRACT FROM AUTHOR]

The present paper deals with the properties of geodesic η-preinvex functions and their relationships with η-invex functions and strictly geodesic η-preinvex functions. The geodesic η-pre-pseudo-invex and geodesic η-pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed. [ABSTRACT FROM AUTHOR]

Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variancecovariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decisionmakers to choose the most appropriate model for their decision-making situation. [ABSTRACT FROM AUTHOR]

A fleet sizing problem (FSP) in a road freight transportation company with heterogeneous fleet and its own technical back-up facilities is considered in the paper. The mathematical model of the decision problem is formulated in terms of multiple objective mathematical programming based on queuing theory. Technical and economical criteria as well as interests of different stakeholders are taken into account in the problem formulation. The solution procedure is composed of two steps. In the first one a sample of Pareto-optimal solutions is generated by an original program called MEGROS. In the second step this set is reviewed and evaluated, according to the Decision Maker's (DM's) model of preferences. The evaluation of solutions is carried out with an application of an interactive multiple criteria analysis method, called Light Beam Search (LBS). Finally, the DM selects the most desirable, compromise solution. [ABSTRACT FROM AUTHOR]

The goals of this paper are to present a two-stage programming model for the capacity expansion problem under uncertainty of demand and explore the impact of this uncertainty on cost. The model is a mixed integer nonlinear programming (MINLP) model with the consideration of uncertainty used to maximize the expected present value of utility profits over the planning horizon, under the constraints of rate of return and reserve margin regulation. The results reveal that the uncertainty harms the profit seriously. In this paper both microeconomics and mathematical programming are used to analyse the problem. We try to observe the economic behaviour of the utility with uncertainty involved. We also investigate the influence on the cost of uncertainty of each economic parameter. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The irregular strip packing problem (ISPP) is a class of cutting and packing problem (C&P) in which a set of items with arbitrary formats must be placed in a container with a variable length. The aim of this work is to minimize the area needed to accommodate the given demand. ISPP is present in various types of industries from manufacturers to exporters (e.g., shipbuilding, clothes, and glass). In this paper, we propose a parallel Biased Random-Key Genetic Algorithm (µ-BRKGA) with multiple populations for the ISPP by applying a collision-free region (CFR) concept as the positioning method, in order to obtain an efficient and fast layout solution. The layout problem for the proposed algorithm is represented by the placement order into the container and the corresponding orientation. In order to evaluate the proposed (µ-BRKGA) algorithm, computational tests using benchmark problems were applied, analyzed, and compared with different approaches. [ABSTRACT FROM AUTHOR]

In this study, a new nonlinear mathematical programming model of mixed integer was presented to formulate the problem of designing a sustainable closed loop supply chain, in which the three aspects of sustainability, i.e., social effect such as job creation, customer satisfaction, and distributors, environmental effects such as reducing air pollution, and economic effects such as reducing supply chain costs, increasing supply chain reliability, quality of returned products by customers, and product routing were considered. In order to solve the proposed model, a new hybrid metaheuristic algorithm based on the distinctive features of gray wolf algorithm and genetic algorithm was proposed in addition to MOPSO and NSGA-II algorithms. After tuning their parameters by the Taguchi method, their performance in problems with different dimensions was tested and evaluated by MID, DM, and SM criteria. The results of statistical analysis of indices indicated that no significant difference between the performance of the three algorithms at 5% error level. In general, GW-NS, NSGA-II and MOPSO algorithms had better performance in terms of MID index, respectively. In addition, GW-NS, NSGA-II, and MOPSO algorithms performed better in terms of DM index. NSGA-II, MOPSO, and GW-NS algorithms performed better in terms of SM index, respectively. In addition, the variability of DM index in all three algorithms was almost the same, but in MID index, GW-NS algorithm, and in SM index, MOPSO algorithm had the highest change and less sustainability. [ABSTRACT FROM AUTHOR]

According to the case-based reasoning method and prospect theory, this paper mainly focuses on finding a way to obtain decision-makers’ preferences and the criterion weights for stochastic multicriteria decision-making problems and classify alternatives. Firstly, we construct a new score function for an intuitionistic fuzzy number (IFN) considering the decision-making environment. Then, we aggregate the decision-making information in different natural states according to the prospect theory and test decision-making matrices. A mathematical programming model based on a case-based reasoning method is presented to obtain the criterion weights. Moreover, in the original decision-making problem, we integrate all the intuitionistic fuzzy decision-making matrices into an expectation matrix using the expected utility theory and classify or rank the alternatives by the case-based reasoning method. Finally, two illustrative examples are provided to illustrate the implementation process and applicability of the developed method. [ABSTRACT FROM AUTHOR]

Network DEA models assess production systems that contain a set of network-structured subsystems. Each subsystem has input and output measures from and to the external network and has intermediate measures that link to other subsystems. Most published studies demonstrate how to employ DEA models to establish network DEA models. Neither static nor dynamic network DEA models adjust the links. This paper applies the virtual gap measurement (VGM) model to construct a mixed integer program to solve dynamic network DEA problems. The mixed integer program sets the total numbers of “as-input” and “as-output” equal to the total number of links in the objective function. To obtain the best-practice efficiency, each DMU determines a set of weights for inputs, outputs, and links. The links are played either “as-input” or “as-output.” Input and as-input measures reduce slack, whereas output and as-output measures increase slacks to attain their target on the production frontier. [ABSTRACT FROM AUTHOR]

This paper is focused on the topology design of compliant mechanisms undergoing large displacement (over 20% of the structural dimension). Based on the artificial spring model and the geometrically nonlinear finite element analysis, the optimization problem is formulated so as to maximize the output displacement under a given material volume constraint. A modified additive hyperelasticity technique is proposed to circumvent numerical instabilities that occurred in the low-density or intermediate-density elements during the optimization process. Compared to the previous method, the modified technique is very effective and can provide more accurate response analysis for the large-displacement compliant mechanism. The whole optimization process is carried out by the gradient-based mathematical programming method. Numerical examples of a force-inverting mechanism and a microgripping mechanism are presented. The obtained optimal solutions verify the applicability of the proposed numerical techniques and show the necessity of considering large displacement in the design problem. [ABSTRACT FROM AUTHOR]

With the rapid urbanization in developing countries, urban agglomeration area (UAA) forms. Also, transportation demand in UAA grows rapidly and presents hierarchical feature. Therefore, it is imperative to develop models for transit hubs to guide the development of UAA and better meet the time-varying and hierarchical transportation demand. In this paper, the multiperiod hierarchical location problem of transit hub in urban agglomeration area (THUAA) is studied. A hierarchical service network of THUAA with a multiflow, nested, and noncoherent structure is described. Then a multiperiod hierarchical mathematical programming model is proposed, aiming at minimizing the total demand weighted travel time. Moreover, an improved adaptive clonal selection algorithm is presented to solve the model. Both the model and algorithm are verified by the application to a real-life problem of Beijing-Tianjin-Hebei Region in China. The results of different scenarios in the case show that urban population migration has a great impact on the THUAA location scheme. Sustained and appropriate urban population migration helps to reduce travel time for urban residents. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid method for modeling and solving supply chain optimization problems with soft, hard, and logical constraints. Ability to implement soft and logical constraints is a very important functionality for supply chain optimization models. Such constraints are particularly useful for modeling problems resulting from commercial agreements, contracts, competition, technology, safety, and environmental conditions. Two programming and solving environments, mathematical programming (MP) and constraint logic programming (CLP), were combined in the hybrid method. This integration, hybridization, and the adequate multidimensional transformation of the problem (as a presolving method) helped to substantially reduce the search space of combinatorial models for supply chain optimization problems. The operation research MP and declarative CLP, where constraints are modeled in different ways and different solving procedures are implemented, were linked together to use the strengths of both. This approach is particularly important for the decision and combinatorial optimization models with the objective function and constraints, there are many decision variables, and these are summed (common in manufacturing, supply chain management, project management, and logistic problems). The ECLiPSe system with Eplex library was proposed to implement a hybrid method. Additionally, the proposed hybrid transformed model is compared with the MILP-Mixed Integer Linear Programming model on the same data instances. For illustrative models, its use allowed finding optimal solutions eight to one hundred times faster and reducing the size of the combinatorial problem to a significant extent. [ABSTRACT FROM AUTHOR]

In order to classify a finite group using its elements orders, the order classes are defined. This partition determines the number of elements for each order. The aim of this paper is to find the order classes of 2-generator p-groups of class 2. The results obtained here are supported by Groups, Algorithm and Programming (GAP). [ABSTRACT FROM AUTHOR]

Fusing classifiers’ decisions can improve the performance of a pattern recognition system. Many applications areas have adopted the methods of multiple classifier fusion to increase the classification accuracy in the recognition process. From fully considering the classifier performance differences and the training sample information, a multiple classifier fusion algorithm using weighted decision templates is proposed in this paper. The algorithm uses a statistical vector to measure the classifier’s performance and makes a weighed transform on each classifier according to the reliability of its output. To make a decision, the information in the training samples around an input sample is used by the k-nearest-neighbor rule if the algorithm evaluates the sample as being highly likely to be misclassified. An experimental comparison was performed on 15 data sets from the KDD’99, UCI, and ELENA databases. The experimental results indicate that the algorithm can achieve better classification performance. Next, the algorithm was applied to cataract grading in the cataract ultrasonic phacoemulsification operation. The application result indicates that the proposed algorithm is effective and can meet the practical requirements of the operation. [ABSTRACT FROM AUTHOR]

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm. [ABSTRACT FROM AUTHOR]

With an ever‐increasing number of plug‐in electric vehicles (PEVs), there is a fast‐growing interest in PEVs' charging impact on the stability and the operating cost of power grid as well as the ecological environment. The centralized coordinated charging method is one of the promising solutions to mitigate such undesired impacts as elevating load peaks, increasing energy losses, and decreasing node voltage. However, the computational complexity is a critical issue to obtain the coordinated charging strategies especially for a large number of PEVs. In this context, it is very essential to analyze the computational performance of the centralized coordinated charging methods. In this paper, a paradigm for analyzing the computational performance is provided. Three centralized methods with different standpoint, viz., to minimize carbon emissions, to minimize load variance, and to minimize generation cost, are investigated to conduct a computational performance analysis from the grid operator perspective. First, the optimization theory is employed to transform the three engineering problems into the mathematical programming models. Then, whether the mathematical programming models are convex or nonconvex is analyzed. The results show that the first two mathematical programming models are convex, and the third mathematical programming model is nonconvex. And it demonstrates that the centralized scheduling model that is convex programming has a better computational performance theoretically. At last, simulations are carried out to verify the theoretical computational performance for different types of centralized coordinated charging methods. [ABSTRACT FROM AUTHOR]

Summary: Phasor measurement units (PMUs) can obtain synchronized voltage and current phasors to increase the accuracy of state estimation results. Optimal PMU placement (OPP) reduces the required number of PMUs to make the system fully observable. In this paper, two mathematical programming formulations, which are mixed integer linear programming (MILP) and nonlinear programming (NLP), for power grid observability modeling to solve the OPP problem are presented. Power flow and zero injection measurement modeling along with restricted communication facilities, PMU failure, and limited channel capacity contingencies are investigated. MILP zero injection formulation is improved to overcome the observability redundancy and optimality drawbacks. A new formulation for nonlinear programming‐based PMU placement for zero injection measurement is proposed. MILP and NLP methods are compared to illustrate the advantages and disadvantages of each method. The comparison and proposed formulations are examined on IEEE 14‐, 57‐, 118‐, 300‐bus test systems and a large 2383‐bus Polish system to demonstrate their effectiveness. [ABSTRACT FROM AUTHOR]

One of the main goals of supply chain management is to ensure proper flows of products and information through all nodes to supply them in the right place at the right time. To achieve this objective, it is very important to consider flows of products and finances among supply chain nodes. Traditionally, operational and financial processes have been optimized as separate problems. The developed model addresses the problem of designing a supply chain network and tries to integrate both areas of operations and financial aspects to maximize the value created and measured by the Shareholder Value Analysis (SVA). The results show that with appropriate financial decisions, creating more value for the company and its shareholders is achievable. The developed model with a new financial approach is able to improve the total created shareholder value as much as 0.7% larger than the SVA obtained without financial aspects and 0.93% larger than the value created by the basic model. The main reason for an increase in value creation is due to new operational and financial aspects, which mainly show the possibility of closing facilities and bank debt repayments. To validate and show the applicability of the proposed model, it was solved by GAMS-BARON solver with data provided from the literature. Sensitivity analyses on financial parameters were performed to evaluate the results. [ABSTRACT FROM AUTHOR]

Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP). Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods. [ABSTRACT FROM AUTHOR]

Safety verification determines whether any trajectory starting from admissible initial states would intersect with a set of unsafe states. In this paper, we propose a numerical method for verifying safety of a network of interconnected hybrid dynamical systems with a state constraint based on bilinear sum-of-squares programming. The safety verification is conducted by the construction of a function of states called barrier certificate. We consider a finite number of interconnected hybrid systems satisfying the input-to-state property and the networked interconnections satisfying a dissipativity property. Through constructing a barrier certificate for each subsystem and imposing dissipation-inequality-like constraints on the interconnections, safety verification is formulated as a bilinear sum-of-squares feasibility problem. As a result, safety of the interconnected hybrid systems could be determined by solving an optimization problem, rather than solving differential equations. The proposed method makes it possible to verify the safety of interconnected hybrid systems, which is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

The role of initial credit distribution scheme (ICDS) in managing network mobility has long been overlooked in previous studies of tradable credit scheme (TCS), which may make their results disputable in the reality, as the travelers possessing leftover credits can get some subsidy from the credit market and offset part of travel cost. In this paper, the disequilibrium phenomenon of previous user equilibrium (UE) solution is shown when traveler’s cognitive illusion (CI) is considered. Then, a new UE condition with TCS is defined with the ICDS and CI explicitly considered. To comprehensively reveal the impacts of ICDS on UE solution, four different types of ICDS are introduced and analyzed in a unified variational inequality (VI) modeling framework. The uniqueness of the UE link flow and market equilibrium (ME) credit price is also investigated. Furthermore, the mathematical program with equilibrium constraint (MPEC) for the optimal ICDS design problem is established, with the optimization objective being maximizing network reserve capacity. A modified relaxation algorithm is adopted to solve the MPEC. The numerical example shows that a properly designed ICDS can not only improve the network reserve capacity, but also decrease the travel cost of all the travelers in the network simultaneously. [ABSTRACT FROM AUTHOR]