Search

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0331) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0331). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam's opinion diffusion model. For a given selection of the coefficients in our model, this proposal yields the original Galam's model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow it to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem. Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature. Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations). Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The transition towards climate neutrality will result in an increase in electrical vehicles, as well as other electric loads, leading to higher loads on electrical distribution grids. This paper presents an optimisation algorithm that enables the integration of more loads into distribution grid infrastructure using information from smart meters and/or smart meter gateways. To achieve this, a mathematical programming formulation was developed and implemented. The algorithm determines the optimal charging schedule for all electric vehicles connected to the distribution grid, taking into account various criteria to avoid violating physical grid limitations and ensuring non-discriminatory charging of all electric vehicles on the grid while also optimising grid operation. Additionally, the expandability of the infrastructure and fail-safe operation are considered through the decentralisation of all components. Various scenarios are modelled and evaluated in a simulation environment. The results demonstrate that the developed optimisation algorithm allows for higher transformer loads compared to a P(U) control approach, without causing grid overload as observed in scenarios without optimisation or P(U) control. [ABSTRACT FROM AUTHOR]

In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost. [ABSTRACT FROM AUTHOR]

This paper is devoted to the management of advance admission requests for obstetric care. Pregnant women in China select one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy. Schedulers must make the admission decision instantly based on the availability of the most critical resource, that is, hospital beds for postnatal care. The random delay between admission requests and postnatal care has created a distinct advance admission control problem. To address this issue, we propose a basic model that assumes a unit bed requirement for one day. Each admission generates a unit of revenue and each unit of overcapacity use incurs an overcapacity cost. With the objective of maximizing the expected net revenue, we establish an optimal policy for unlimited requests, that is, an expected arrival time quota (EATQ) policy that accepts a fixed quota of advance admission requests with the same expected date of confinement. We then propose an extended model for general capacity requirements. Using the Poisson approximation, we establish the optimality of the EATQ policy, which is shown to be solvable by a simple linear programming model. We compare the numerical results from the different policies and conduct a sensitivity analysis. The EATQ policy is demonstrated to be the best option in all test instances and notably outperforms the current admission rules used in hospitals, which usually accept admission requests according to some empirical monthly quota of the expected delivery month. The Poisson approximation is shown to be effective for determining the optimal EATQ policy for both stationary and nonstationary arrivals. Summary of Contribution: First, this paper investigates the advance admission control problem for obstetric care. Pregnant women in China choose one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy but the most critical resource is hospitalization beds needed for postnatal care. The random delay between admission request and postnatal care makes the problem unique and challenging to solve. It belongs to the scope of computing and operations research. Second, this paper formulates a dynamic programming model, analyzes the structural properties of the optimal control policy, and finally proposes a mathematical programming model to determine the optimal quota. Numerical experiments show the validity of the proposed approach. It covers the research contents of theories on dynamic stochastic control, mathematic programming model, and experiments. Moreover, this paper is motivated by the practical problem (advance admission control) in obstetric units of Shanghai. Using these optimality properties, solution approaches, and numerical results, this paper provides guidance on how to manage advance obstetric admission requests. [ABSTRACT FROM AUTHOR]

This paper deals with the mixed-model assembly line balancing problem. This type of line is applied to more than one similar model of a product in an intermixed order. Despite their widespread use, these lines have received little attention in the literature. Metaheuristics, heuristics, and mathematical programming techniques are developed to solve these types of assembly line balancing problems. However, linear physical programming method has never been used. In this paper, a linear physical programming model is proposed for balancing a mixed-model assembly line. The performance of the proposed model is applied to a numerical example to analyze the usage of the methodology. Five objectives are considered in the model, and the outperformance of the methodology is demonstrated by comparing it to a different approach. According to the results, it has been seen that the proposed linear physical programming model is practical and useful approach for mixed-model assembly line balancing problems. [ABSTRACT FROM AUTHOR]

A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie on the same hyperplane. The use of the quadratic approximation criterion for such a problem led to the appearance of the total least squares method. In this paper, we use the minimax criterion to estimate the measure of correction of the initial data. It leads to a nonlinear mathematical programming problem. It is shown that this problem can be reduced to solving a finite number of linear programming problems. However, this number depends exponentially on the number of parameters. Some methods for overcoming this complexity of the problem are proposed. [ABSTRACT FROM AUTHOR]

In this paper, an airport ground service task assignment problem is studied. A task represents a service, which must be performed by one or multiple ground crew of a shift with required qualification/proficiency within a prescribed time period. For every assigned task, define "task priority" times "task duration" as the "benefit" generated. The objective is to maximize the summation of "benefit" for all the assigned tasks. The problem is modeled as an integer linear programming problem with mathematical formulation. A branch-and-price algorithm is proposed for solving the problem instances to optimality. To expedite the column generation process, an acceleration strategy is proposed. The computational results show that our proposed branch-and-price algorithm is capable of solving large-sized instances and the acceleration strategy is quite effective in reducing the computational time. Moreover, the impact of changing various characteristics of tasks and shifts on the performance of the algorithm is studied in detail with supporting computational experiments. In particular, the impact of reducing the qualifications is significant with 20.82% improvement in the objective value. [ABSTRACT FROM AUTHOR]

Purpose: In recent years, significant energy consumption and facing global warming have led to concern worldwide. Therefore, governments have turned to deterrent actions such as imposing daily tariffs in different intervals to tackle energy consumption. This article addresses unrelated parallel machine energy-efficient scheduling problems by considering sequence-independent setup times and energy consumption tariffs. The objective function is that jobs should be assigned to machines and processed in different intervals so that the cost of consumed energy becomes as less as possible. It should be noted that the assumed sequence-independent setup times are addressed in two different modes, setup times jointed to processing time and setup times disjointed from processing time. Design/methodology/approach: To optimize the total energy consumption cost in unrelated parallel machine scheduling problems with sequence-independent setup times jointed to processing time and disjointed from processing time, mixed-integer linear programming (MILP) models have been proposed from two different points of view. The first model has been formulated according to the predecessor jobs of a special job, while the second model has been conducted based on the immediate predecessor job. Also, a fix and relax heuristic (FRH) algorithm has been conducted to solve large-scale instances. All mathematical models and the heuristic algorithm have been coded in the Visual C# 2017 environment and implemented using the CPLEX 12.8 Concert Technology on a PC with 32GB RAM and Intel Corei7 4.0 GHz CPU (4 cores). Also, a sizeable number of instances have been solved to evaluate the efficiency of mathematical models and the heuristic algorithm and to ensure their accuracy. Findings: According to numerical analysis, both mathematical models solved the instances of up to 20 jobs and 80 machines optimally for sequence-independent setup-times jointed to processing time, and sequence-independent disjointed from processing time problems. However, generally speaking, the mathematical model based on predecessor jobs was more efficient than another mathematical model, especially in terms of run time. Moreover, the proposed fix and relax-based heuristic algorithm solved instances of up to 20 machines and 190 jobs for the disjointed setup times problem, and up to 20 and 220 instances for the jointed setup times problem. It should be noted that all instances were generated analogously to the literature. Research limitations/implications: A vast number of exogenous factors contributed to the scheduling problems in the real world, which can disturb the scheduling process easily, frequent power outages, machine breakdown, and operator absence. Besides, considering all the real world's possibilities raises extreme complexity in problems. Therefore, similar to other studies, some assumptions were considered as follows: - machines are always available at all times; - idle is allowable for machines; - the energy consumption rate of various machines is different for each job; - each machine's energy consumption rate during processing and setups is different for each job, it is assumed as constant; - preemption is not allowed in the job's processing and setups; - all jobs are available at the beginning of the planning horizon; and - each machine can process or do the setup for only one job at a time. Practical implications Given that unrelated parallel machines are one of the most practical scheduling environments, this article can be effective in production sites and operation lines that contain such a kind of machine. Besides, unrelated parallel machines cover identical and related parallel machines. Consequently, this paper is the building blocks of cost-effective and environmentally friendly scheduling programs. Also, the application of unrelated parallel machines is not merely restricted to production problems. In other words, unrelated parallel machine scheduling problems can be used in other real-world cases, such as airplane scheduling and elevator scheduling. Originality/value - In this paper, unrelated parallel machine energy-efficient scheduling has been addressed considering sequence-independent setup times. Since it was a common belief that sequence-independent setup times could be included in processing times, sequence-independent setup times have been neglected so far. However, in this innovative study for the first time, an unrelated parallel machine energy efficient problem was investigated with sequence-independent setup times. Mathematical programming models and a heuristic algorithm were proposed for such a practical problem. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The paper presents a model for the selection of a route for the transport of dangerous goods using DEA (Data Envelopment Analysis) models and fuzzy logic systems. The presented model is used to define the risk on road sections during the transport of dangerous goods as well as to select the optimal route for the realization of the transport task. Methods: The model consists of two phases. The first phase includes the application of DEA models in which formed input and output models are connected in the output DEA final form which shows routes with a satisfactory level of traffic safety and at the same time eliminates routes with low traffic safety. The second phase involves the application of fuzzy logic systems, and as a way out of the fuzzy system, preference is given to one route. Route evaluation is based on six criteria, namely: route length, number of access points, AADT (annual average daily traffic), the number of traffic accidents with fatalities, the number of traffic accidents with the injured and the number of traffic accidents with material damage. When the values of the input criteria are entered, a calculation and evaluation is performed, and, as an exit from the fuzzy system, preference is given to one of the entered routes (the route with the lowest level of risk). The criteria used were defined on the basis of expert assessments. Results: A user program that represents decision support in traffic service. Conclusion: The user platform was created for the Matlab R2015a software package with the ability to be adapted to specific problems. [ABSTRACT FROM AUTHOR]

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances. [Display omitted] • Considering a multi-skill multi-mode resource-constrained project scheduling problem with preemption. • Presenting a new multi-objective mixed-integer linear programming model for problem with a time lag between activities. • Minimizing three objectives: the total project risk, project makespan, and total project cost simultaneously. • Investigating the real project of building a sports center in a prominent engineering company to validate the model. • Proposing chance-constrained programming with the stochastic parameter and AUGMECON2 method for the first time. [ABSTRACT FROM AUTHOR]

The search of separation hyperplanes is an efficient way to find rules with classification purposes. This paper presents an alternative mathematical programming formulation to existing methods to find a discriminant hyperplane. The hyperplane H is found by minimizing the sum of all the distances to the area assigned to the group each individual belongs to. It results in a convex optimization problem for which we find an equivalent linear programming problem. We demonstrate that H exists when the centroids of the two groups are not equal. The method is effective dealing with low and high dimensional data where reduction of the dimension is proposed to avoid overfitting problems. We show the performance of this approach with different data sets and comparisons with other classifications methods. The method is called LPDA and it is implemented in a R package available in https://github.com/mjnueda/lpda. [ABSTRACT FROM AUTHOR]

This paper studies the energy efficiency optimization problem for coordinated multipoint (CoMP)-enabled and backhaul-constrained ultra-dense small-cell networks (UDNs). Energy efficiency is an eternal topic for future wireless communication networks; however, taking actual bottleneck of the backhaul link and the coordinated network architecture into consideration, it is difficult to find an effective way to improve the energy efficiency of the network. Aiming at this problem, we propose to combine cell association, subchannel allocation, backhaul resource allocation, and sleep/on of the cells together to develop an optimization algorithm for energy efficiency in UDN and then solve the formulated energy efficiency optimization problem by means of improved modified particle swarm optimization (IMPSO) and linear programming in mathematics. Simulation results indicate that nearly 13 % energy cost saving and 21 % energy efficiency improvement can be obtained by combining IMPSO with linear programming, and the backhaul link data rate can be improved by 30 % as the number of small cells increases. From the results, it can be found that by combining IMPSO with linear programming, the proposed algorithm can improve the network energy efficiency effectively at the expense of limited complexity. [ABSTRACT FROM AUTHOR]

The internationalisation of the manufacturing operations process includes decision-making about new facility implementation (NFI) and global supplier network development (GSND), whose first step is to analyse the situation of a company and its environment. The purpose of this paper is to investigate the optimal design of a manufacturing production and distribution network for global small- and medium-sized enterprises (SMEs). This research uses a mixed-integer linear programming (MILP) model to support decision-making in the analysis stage of the internationalisation of manufacturing operations for global SMEs. A realworld case study is presented to illustrate the application of the proposed model. Different scenarios were evaluated not only to identify the strengths and limitations of the mathematical programming model, but to also provide support for the next strategic decisions that the examined company has to make in the near future. [ABSTRACT FROM AUTHOR]

Linear programming problems in fuzzy environment have been investigated by many researchers in the recent years. Some researchers have solved these problems by using primal-dual method with linear and exponential membership functions. These membership functions are particular form of the reference functions. In this paper, we introduce a pair of primal-dual PPs in Atanassov's intuitionistic fuzzy environment (AIFE) in which the membership and non-membership functions are taken in the form of the reference functions and prove duality results in AIFE by using an aspiration level approach with different view points, viz., optimistic, pessimistic and mixed. Since fuzzy and AIF environments cause duality gap, we propose to investigate the impact of membership functions governed by reference functions on duality gap. This is specially meaningful for fuzzy and AIF programming problems, when the primal and dual objective values may not be bounded. Finally, the duality gap obtained by the approach has been compared with the duality gap obtained by existing approaches. [ABSTRACT FROM AUTHOR]

This paper proposes to address the problem of the simultaneous optimization of the liner shipping route and ship schedule designs by incorporating port time windows. A mathematical programming model was developed to minimize the carrier's total operating cost by simultaneously optimizing the port call sequence, ship arrival time per port of call, and sailing speed per shipping leg under port time window constraints. In view of its structure, the nonlinear nonconvex optimization model is further transformed into a mixed-integer linear programming model that can be efficiently solved by extant solvers to provide a global optimal solution. The results of the numerical experiments performed using a real-world case study indicated that the proposed model performs significantly better than the models that handle the design problems separately. The results also showed that different time windows will affect the optimal port call sequence. Moreover, port time windows, bunker price, and port efficiency all affect the total operating cost of the designed shipping route. [ABSTRACT FROM AUTHOR]

Power systems with high penetration of wind resources must cope with significant uncertainties originated from wind power prediction error. This uncertainty might lead to wind power curtailment and load shedding events in the system as a big challenge. Efficient modeling and incorporation of wind power uncertainty in generation and reserve scheduling can prevent these events. This paper presents a new framework for wind power cumulative distribution function (CDF) modeling and its incorporation in a new chance-constrained economic dispatch (CCED) problem. The proposed CDF modeling uses few moments of wind power random samples. To validly capture the actual features of the wind power distribution such as main mass, high skewness, tails, and especially boundaries from the moments, an efficient moment problem is presented and solved using the beta kernel density representation (BKDR) technique. Importantly, a new polynomial cost function for efficient modeling of wind power misestimation costs is proposed for the CCED problem that eliminates the need for an analytical CDF and enables the use of an accurate piecewise linearization technique. Using this technique, the non-linear CCED problem is converted to a mixed-integer linear programming (MILP)-based problem that is convex with respect to the continuous variables of the problem. Therefore, it is solved via off-the-shelf mathematical programming solvers to reach more optimal results. Numerical simulations using the IEEE 118-bus test system show that compared with conventional approaches, the proposed MILP-based model leads to lower power system total cost, and thereby is suggested for practical applications. [ABSTRACT FROM AUTHOR]

An enormous challenge for state estimation (SE) in power distribution networks with high penetration of photovoltaic generators lies in how to deal with measurement uncertainty. Driven by this motivation, an interval arithmetic (IA) based SE is proposed in this paper, which considers interval modeling for measurement uncertainty. The proposed SE is formulated as two interval optimization models based on the unknown-but-bounded theory, and solution bounds of state variables are obtained using a two-stage linear programming approach. In particular, the proposed SE is extended to realistic power distribution networks with mixed microphasor measurement units (μPMU), voltage magnitude, smart meters and feeder terminal units. Case studies and results are illustrated and discussed to demonstrate the performance of the proposed IA-based SE. It could provide the operators intuitive and effective bounds of system states for advanced power industrial applications under consideration of uncertainty. [ABSTRACT FROM AUTHOR]

In China, state-owned monopoly on multiproduct pipeline network leads to low energy efficiency, expensive logistics costs and high greenhouse gas emissions in the downstream oil supply chain. In response to increasing pressures applied by the conflict between supply and demand and the need for emission mitigation, the government has promoted pipeline network reform for years. However, the selection of an appropriate reform scheme is controversial, and no researcher has conducted quantitative analysis on this issue. This paper quantifies the impacts of pipeline network reform on the downstream oil supply chain of China so as to provide policy implications. An integrated evaluation framework is established by coupling a mathematical programming technique with the energy-economy-environment (3E) assessment method. Five future scenarios are designed including the baseline (BAU) and four types of reform policies: third-party access (TPA), pipeline network integration (PNI), business cooperation (BC) and third-party access combined with business cooperation (TPA-BC). The results indicate that (i) all reform schemes have significant benefits for aspects of 3E; (ii) the scenarios can be ranked by 3E performance as follows: TPA-BC > BC > PNI > TPA > BAU; and (iii) only when the pipeline networks need to reserve a high capacity margin can the advantages of PNI compared to TPA be revealed; otherwise, the gap between them is small. [ABSTRACT FROM AUTHOR]

In his CAV 2004 paper, Tiwari has proved that, for a class of linear programs over the reals, termination is decidable. And Tiwari has shown that the termination of a linear program P 1 whose assignment matrix A ˜ is not in the Jordan canonical form is equivalent to that of a linear program J 1 , whose assignment matrix A is in the Jordan Canonical Form. In most cases, the method of Tiwari provides only a so-called N -nonterminating point. In this paper, we propose two new methods to decide whether Program P 1 terminates or not over the reals. Our methods are based on the construction of a subset of the set NT of non-terminating points of Program J 1 . Any point in such a subset is a witness to non-termination of Program J 1 . Furthermore, it is shown that Program J 1 is non-terminating if and only if such a subset is nonempty. In terms of the property, the first method is given to check whether Program J 1 terminates or not. Different from the existing methods, the point obtained by our first method is a non-terminating point, rather than a N -nonterminating point. More importantly, such a subset is also proven to be A B ˆ -invariant for some positive integer B ˆ . This enables us to check directly the termination of Program J 1 by verifying the satisfiability of finitely many quantified formulas over the reals. This suggests our second method for checking the termination of Program J 1 . [ABSTRACT FROM AUTHOR]

A Multi-Level Programming Problem (MLPP) is a hierarchical optimization problem where the constraint region of the first level is implicitly determined by the other optimization problems. In this paper, an integer multi-level programming problem is considered. At each level, there are multiple objective functions which are linear fractional and the feasible region is assumed to be a convex polyhedron. Here, the variables are bounded. An algorithm is developed for ranking and scanning the set of feasible solutions. These ranked solutions are used to find the efficient solution of Multi- Level Linear Fractional Programming Problem (MLLFPP). An example is illustrated and solved using LINGO 17. [ABSTRACT FROM AUTHOR]

• We analyze time-of-use rates with respect to model predictive controls. • We show that thermal storage potential can vary greatly for differing climates. • We build a model predictive control framework for indoor temperature setpoints. • We analyze of the impacts of different variable electric rates. • The framework is capable of reducing cooling electricity costs by 30%. Heating, ventilation and air conditioning for residential and commercial buildings requires a substantial share of electric energy, and ultimately drives summer peak demand in the United States. Variable electric rates are becoming more common in the residential market, as utilities try to encourage users to shift their energy demand. Model predictive controls, one method of reducing energy usage, employ an optimization model to minimize peak demand, energy usage, or electricity costs. This paper details the development of a co-simulation framework to rapidly model and simulate building energy use and optimize cooling setpoint controls. The framework integrates commercially available software to: (i) simulate all energy interactions between the building, internal gains, outdoor environment, and heating and cooling systems via a building energy simulation program (EnergyPlus), (ii) algebraically formulate an optimization problem (with AMPL) using a black-box, reduced-order model for rapid calculations, (iii) employ Simulink as the environment that links calls to EnergyPlus and AMPL, and (iv) solve the optimization model (with CPLEX) to minimize electricity costs and user discomfort. Variable electric time-of-use rates are analyzed in the context of total cooling electricity costs, thermal comfort of users, and peak demand shedding. The framework uses a model predictive control formulation capable of reducing cooling electricity costs by up to 30%; however, cost savings and peak demand shedding are highly dependent on the time-of-use electricity rate schedule. [ABSTRACT FROM AUTHOR]

In this paper, we introduce total dual integrality of the linear complementarity problem (LCP) by analogy with the linear programming problem. The main idea of defining the notion is to propose the LCP with orientation, a variant of the LCP whose feasible complementary cones are specified by an additional input vector. Then we naturally define the dual problem of the LCP with orientation and total dual integrality of the LCP. We show that if the LCP is totally dual integral, then all basic solutions are integral. If the input matrix is sufficient or rank-symmetric, and the LCP is totally dual integral, then our result implies that the LCP always has an integral solution whenever it has a solution. We also introduce a class of matrices such that any LCP instance having the matrix as a coefficient matrix is totally dual integral. We investigate relationships between matrix classes in the LCP literature such as principally unimodular matrices. Principally unimodular matrices are known that all basic solutions to the LCP are integral for any integral input vector. In addition, we show that it is coNP-hard to decide whether a given LCP instance is totally dual integral. [ABSTRACT FROM AUTHOR]

Two-stage stochastic optimization, in which a long-term master problem is coupled with a family of short-term subproblems, plays a critical role in various application areas. However, most existing algorithms for two-stage stochastic optimization only work for special cases, and/or are based on the batch method, which requires huge memory and computational complexity. To the best of our knowledge, there still lack efficient and general two-stage online stochastic optimization algorithms. This paper proposes a two-stage online successive convex approximation (TOSCA) algorithm for general two-stage nonconvex stochastic optimization problems. At each iteration, the TOSCA algorithm first solves one short-term subproblem associated with the current realization of the system state. Then, it constructs a convex surrogate function for the objective of the long-term master problem. Finally, the long-term variables are updated by solving a convex approximation problem obtained by replacing the objective function in the long-term master problem with the convex surrogate function. We establish the almost sure convergence of the TOSCA algorithm and customize the algorithmic framework to solve three important application problems. Simulations show that the TOSCA algorithm can achieve superior performance over existing solutions. [ABSTRACT FROM AUTHOR]

Highlights • A new rigorous bilevel decomposition strategy for MILPs with strong linking constraints. • An extended cross decomposition method based on the bilevel decomposition strategy. • Application of the extended cross decomposition method to stochastic programming with CVaR constraints. • Case studies with a variety of scenario instances showing significant computational advantages of the proposed methods. Abstract Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming. [ABSTRACT FROM AUTHOR]

This paper presents a mixed-integer linear mathematical programming model for the integrated planning problem of the part quality inspection and preventive maintenance activities in serial multi-stage manufacturing system. The model concurrently determines the right time and place for performing the above-mentioned activities while the production stages are linearly deteriorating. These two decisions are made while the model is to minimize the total cost including the production, maintenance, inspection, scrap, replacement, and the penalty of shipped defective items to customer(s). A numerical example and a real case study are investigated to validate and verify the proposed model. The results show that the determination of inspection locations along a manufacturing line in different periods of time regarding the impact of preventive maintenance activities on defective production probability results in a more efficient manufacturing system. [ABSTRACT FROM AUTHOR]

This paper presents a nonintrusive load monitoring (NILM) algorithm based on mixed-integer linear programming. The formulation deals with the problem of multiple switching that arises when disaggregating individual appliance’s consumptions from a compound power measurement. Mixed-integer linear constraints are used to efficiently represent the load signatures of each appliance. Also, a window-based strategy is used to enhance the computational performance of the proposed NILM algorithm. The disaggregation can be made using only active power measurements at a low sampling rate, which is available in most energy meters. Moreover, if available, other signatures can be added to the model to improve its accuracy, such as reactive power signatures or harmonics. The performance of the algorithm is evaluated using three test cases from the almanac of minutely power dataset. The proposed method is also compared with a disaggregation method called aided linear integer programming. Results demonstrate the ability of the proposed method to accurately identify and allocate individual energy signatures in a computationally efficient manner, which makes it suitable for inexpensive home energy management. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the index tracking strategy using mathematical programming. First, we use a non-linear programming formulation for the index tracking problem, considering a limited number of assets. Since the problem is difficult to be solved in reasonable time by commercial mathematical packages, we apply a hybrid solution approach, combining mathematical programming and genetic algorithm. We show the efficiency of the proposed approach comparing the results with optimal solutions, with previous developed methods, and from real-world market indexes. The computational experiments focus on Ibovespa (the most important Brazilian market index), but we also present results for consolidated markets such as S&P 100 (USA), FTSE 100 (UK) and DAX (Germany). The proposed framework shows its ability to obtain very good results (gaps from the optimal solution smaller than 5 % in 8 min of CPU time) even for a highly volatile index from a developing country. [ABSTRACT FROM AUTHOR]

The problem ( LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for ( LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems. [ABSTRACT FROM AUTHOR]

The school bus routing problem (SBRP) is crucial because of its impact on economic and social objectives. A single bus is assigned to each route, picking up students and arriving at the school within a specified time window. SBRP aims to find the fewest buses needed to cover all of the routes while minimizing the total travel distance and meeting required constraints. We propose a mathematical formulation responding to the overbooking policies applied in a real-world school district. According to our empirical studies, the probability of a student riding a bus varies from 22% to 77%, opening the opportunity to overbook the buses to improve utilization of their capacity. However, SBRP with overbooking has not attracted much attention in previous studies. In this work, overbooking is modeled via chance constrained programming. Additionally, to account for the uncertainty of the total travel time of the buses, a constraint limiting the probability of being late to school is also proposed in this paper. As a result of the NP-hard nature of the problem, a cascade simplification algorithm is proposed to partition the multiple stage SBRP problems into multiple multi-depot and one-school subproblems that are solved sequentially, where the results for one are data inputs for the next. Furthermore, we develop column-generation-based algorithms to solve the scheduling problem, and different instances of the problem are examined. Our computational experiments on a real-world school district demonstrate desirable cost savings in terms of the total number of buses used. [ABSTRACT FROM AUTHOR]

The planning of outbound baggage handling at international airports is challenging. Outgoing flights have to be assigned and scheduled to handling facilities at which the outgoing baggage is loaded into containers. To avoid disruptions of the system the objective is to minimize workload peaks over the entire system. The resource demand of the jobs that have to be scheduled depends on the arrival process of the baggage. In this paper we present a time-indexed mathematical programming formulation for planning the outbound baggage. We propose an innovative decomposition procedure in combination with a column generation scheme to solve practical problem instances. The decomposition significantly reduces the symmetry effect in the time-indexed formulation and also speeds up the computational time of the corresponding Dantzig-Wolfe formulation. To further improve our column generation algorithm we propose state-of-the-art acceleration techniques for the primal problem and the pricing problem. Computational results based on real data from a major European airport show that the proposed procedure reduces the maximal workloads by more than 60% compared to the current assignment procedure used. The online appendix is available at . [ABSTRACT FROM AUTHOR]

Linear matching (LM) is a simple and effective method for solving image matching problems. In many cases, image matching problems are nonlinear due to involvement of the geometric transformations; therefore, an essential step for utilizing linear models for image matching is to linearize the geometric transformation matrices that introduce nonlinear terms into image matching problems. Existing LM methods usually use low-order transformations to artificially initialize a linear model. In this paper, we propose a residual-consensus driven LM algorithm that generalizes existing LM methods by allowing higher order transformations to automatically initialize a linear model. Based on the observation that transformation models generated from inlier subsets exhibit correlated behaviors (termed residual consensus hereafter), we develop a residual-consensus robust estimation algorithm to project the nontrivial linear transformation problem into a much smaller subspace, and thus enable efficient optimizations through linear programming. The experimental results on synthetic and real databases demonstrate the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

Manufacturing process optimization is an ever-actual goal. Within this goal, machining parameters optimization is a very important task. Machining parameters strongly influence the manufacturing costs, process productivity and piece quality. Literature presents a series of optimization methods. The results supplied by these methods are comparable and it is difficult to establish which method is the best. For machining parameters optimization, this paper proposes a novel, simple and efficient method, without additional costs related to new software packages. This approach is based on linear mathematical programming. The optimization mathematical models are, however, nonlinear. Therefore, mathematical model linearization is required. The major and difficult problem is the linearization of the objective function. This represents the key element of the proposed optimization method. In this respect, the paper proposes an original mathematical procedure for calculating the part of the objective function that refers to the analytical integration of the tool life into the model. This calculus procedure was transposed into an original software tool. For demonstrating the validity of the method, a comparison is presented among the results obtained by certain optimization techniques. It results that the proposed method is simple and as good as those presented by the literature. [ABSTRACT FROM AUTHOR]

In the planning phase of district energy systems, optimization models based on mathematical programming are a widely used approach. Most optimization models determine the optimal energy system design based on a single representative year. However, this approach is unable to consider changing economic and technological boundary conditions over the system's lifetime. As a result, these one-period models fall short for districts with 5th generation district heating and cooling (5GDHC) networks, which are typically developed over long time periods and are built in multiple construction phases. In this paper, we present two multi-period optimization approaches for designing 5GDHC districts: The first approach is a forward-looking model which determines the optimal investment pathway by using a perfect foresight of future parameter developments. In the second approach, a one-period model is solved repeatedly for every investment period without knowledge of future parameter developments. Both approaches are compared to a one-period model for a real-world 5GDHC district in Germany. In comparison with a one-period design approach, the forward-looking method leads to total cost savings of up to 17 % and the sequential method of up to 11 %. By using a forward-looking model, gas-fired technologies are sized smaller while the capacity of electricity-driven technologies in the energy hub as well as photovoltaic modules and thermal energy storages in buildings increases compared to a one-period model. The case study shows that a multi-period modeling approach is an important addition to design optimization models for 5GDHC networks and can have a significant impact on the optimal design. [ABSTRACT FROM AUTHOR]

This paper addresses the development of an innovative home energy management system (HEMS). The presented HEMS relies on a mixed-integer linear programming (MILP)-based model predictive control. The system takes advantage of the powerful formulation capabilities of a MILP-based mathematical programming problem with the capabilities of model predictive control to optimize, at each sample instant the HEMS operation using a receding-horizon formulation. The system is designed for a residence located in Algarve, Portugal. The results of the presented system are compared with the real experimental results obtained by a commercial PV-battery management system. Additionally, an analysis of the system's performance is conducted, in terms of operation planning for 2021 market prices compared to 2022 prices, where there was a significant rise of buying price due to the energy world context. In all simulations performed, it is verified that the MILP-based model predictive control presents better results, with statistical relevance. [ABSTRACT FROM AUTHOR]

• We present soft linking of energy system capacity expansion models. • Zero emission neighbourhoods make European decarbonization more cost-efficient. • Neighbourhood energy systems replace investments in nuclear, wind, and fossil gas. • Politically decreasing EU ETS emission caps earlier could avoid CO 2 price spikes. Climate policy is transforming the energy system and the building sector. Since these sectors overlap, we need to understand how the short-term operational link between them impact their long-term development subject to overlapping climate policies. This paper investigates how the integrated development of the European heat and electricity system is influenced by net-zero emission neighbourhoods that compensate own carbon emissions with local renewable energy. The study is made in the context of EUs emission trading system. In our approach, we soft-link two mathematical programming models to couple energy transition policies at the European level with the neighbourhood scale. Results suggest that zero emission neighbourhoods make European decarbonisation more cost-efficient. When low carbon energy technologies in neighbourhoods become competitive, investments in large-scale technologies are reduced on the European level, including nuclear and fossil gas power and heating. Thus, early policy support to neighbourhood technologies could prevent stranded assets later in the transition. Further, results imply that more stringent emission caps earlier could help avoiding CO 2 allowance price spikes later. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of price multiplicity in network-constrained pool-based electricity markets under marginal pricing. This problem consists in the existence of multiple vectors of locational marginal prices for the same optimal market-clearing dispatch solution. As a consequence, delicate conflicts of interest may arise among market participants. Price multiplicity may take place even in auction designs based on convex formulations for the market-clearing procedure. An effective duality-based solution approach is proposed in this paper to handle the issue of price multiplicity. Once the optimal market-clearing dispatch is known, we propose the subsequent solution of a simple pricing problem in order to determine the vector of locational marginal prices. Unlike previously reported methodologies, the proposed approach presents two salient features: 1) it is based on sound mathematical programming, and 2) it is computationally inexpensive since it relies on the solution of a linear program. Numerical results are provided to illustrate the performance of the proposed tool. [ABSTRACT FROM PUBLISHER]

The paper lists the problems hindering the use in business practices of the results of solving direct and inverse problems in linear programming. It is shown that overcoming these obstacles lies in the way of using of developed by the author and described in this paper method of structural optimization and algorithms for its implementation. Here are some examples of solutions by the method of structural optimization of production planning problems. [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]

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate \mathcal O(1/\lambda T) , but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain \mathcal O(\sqrt\log (1/\delta)/T) with $\delta$ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately \mathcal {O}(\log (\log (T)/\delta)/\lambda T) . [ABSTRACT FROM AUTHOR]

This paper proposes a reliable facility location design model under imperfect information with site-dependent disruptions; i.e., each facility is subject to a unique disruption probability that varies across the space. In the imperfect information contexts, customers adopt a realistic “trial-and-error” strategy to visit facilities; i.e., they visit a number of pre-assigned facilities sequentially until they arrive at the first operational facility or give up looking for the service. This proposed model aims to balance initial facility investment and expected long-term operational cost by finding the optimal facility locations. A nonlinear integer programming model is proposed to describe this problem. We apply a linearization technique to reduce the difficulty of solving the proposed model. A number of problem instances are studied to illustrate the performance of the proposed model. The results indicate that our proposed model can reveal a number of interesting insights into the facility location design with site-dependent disruptions, including the benefit of backup facilities and system robustness against variation of the loss-of-service penalty. [ABSTRACT FROM AUTHOR]

The refined oil transportation problem investigated in this paper lies on the intersection of the scheduling and routing of tramp shipping and the petroleum supply chain, with unprecedented large-scale and complex rules. Two mixed-integer linear programming formulations are developed for the assignment between tasks, vessels, and timing issues. The first model uses a time-slot concept under a continuous-time representation, where the constraints that deal with vessel assignment, capacity, timing, demand, and slack stock control are considered. The second model uses a discrete-time representation with time assignment, portal counting, and strict stock control constraints. By virtue of the data collected from an oil company, this modeling approach is validated and used to generate feasible scheduling solutions with lower costs than are currently achieved in the real situation. Finally, the impact of the model parameters is analyzed under different optimization scenarios. [ABSTRACT FROM AUTHOR]

In this paper, a load balancing mechanism based on cell breathing was proposed for the hybrid EPON-WiMAX network. The hybrid EPON-WiMAX network integrates the emerging Ethernet Passive Optical Network (EPON) and Worldwide Interoperability for Microwave Access (WiMAX) technologies to support high bandwidth, broadband access, mobility, and Quality of Service (QoS) guarantee. Load balancing is required due to uneven distribution of traffic among different WiMAX base stations (BS) as well as mobility of WiMAX Subscriber Station (SS). Cell breathing is a well-known load balancing technique adopted in wireless networks. By changing the transmission powers of the base stations, the cell breathing technique is able to adjust the traffic, both uplink and downlink, load of base stations. In the integrated EPON-WiMAX network, transmission powers of WiMAX base stations can be optimally allocated at the EPON optical networking unit (ONU). In this paper, we formulate the cell breathing-based load balancing problem into a linear programming problem. Our goal is to find the best power adjustment that maximizes system throughput. To alleviate the time complexity of solving the linear programming problem, we propose a Heaviest Load First Algorithm (HLFA) to obtain the near optimal solution. The solution obtained by the HLFA algorithm will not waste any transmission power to make the entire system energy-efficiency. We demonstrate the performance of HLFA via extensive simulations. The simulation results show that the HLFA can provide the best solution to achieve load balancing and enhance the system throughput as compared to existing solutions. Furthermore, HLFA maintains good performance even when the system has multiple overloaded ONU-BSs. [ABSTRACT FROM AUTHOR]

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. [ABSTRACT FROM AUTHOR]

In this paper, we study fuzzy multi-attribute group decision-making (FMAGDM) problems with multidimensional preference information in the form of pairwise alternatives and incomplete weight information. We develop a new group decision-making (GDM) method considering regret aversion of the decision-makers (DMs). Firstly, we define a fuzzy regret/rejoice function and a computational formula for the perceived utility of alternative decisions. We propose a perceived utility value-based group consistency index (which reflects the total consistency) and a group inconsistency index (which represents the total inconsistency) for pairwise rankings of alternatives based on regret theory and an a priori multidimensional preference order given by the DMs. Then, under the circumstances of an unknown fuzzy ideal solution, we set up a mathematical programming model to determine the optimal attribute weights and a defuzzified fuzzy ideal solution with the idea of the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). We compute the DMs’ optimal comprehensive perceived utility values and obtain the ranking order of alternatives. Finally, we illustrate the application of the developed procedures with an air-fighter selection problem. The rationality and validity of the proposed method is demonstrated by comparing with two other GDM methods, including the fuzzy LINMAP (FLINMAP) method and the prospect theory-based GDM method. [ABSTRACT FROM AUTHOR]

In wireless sensor networks (WSNs), the data observed by different nodes must be relayed safely to the base station over intermediate nodes. In the network environment, some sensor nodes can act suspiciously when they enter someone else's control or due to other equipment failure. Data packets that are sent through suspicious nodes may be randomly dropped or may be not delivered as desired. In this paper, we investigate the impact of disabling suspicious nodes communications on network lifetime through a linear programming framework. We build a mathematical programming framework and perform comprehensive numerical analysis. Our results show that the decrease in WSN lifetime is less than 8.0% if the number of suspicious nodes is not higher than 10%. [ABSTRACT FROM AUTHOR]