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In recent years, there has been an increasing need to understand the complex interdependencies between critical infrastructure systems, for example, electric power, natural gas, and potable water. Whereas open-source and commercial tools for the independent simulation of these systems are well established, frameworks for cosimulation with other systems are nascent and tools for co-optimization are scarce—the major challenge being the hidden combinatorics that arise when connecting multiple-infrastructure system models. Building toward a comprehensive solution for modeling interdependent infrastructure systems, this work presents InfrastructureModels, an extensible, open-source mathematical programming framework for co-optimizing multiple interdependent infrastructures. This work provides new insights into methods and programming abstractions that make state-of-the-art independent infrastructure models composable with minimal additional effort. To that end, this paper presents the design of the InfrastructureModels framework, documents key components of the software's implementation, and demonstrates its effectiveness with three case studies on canonical co-optimization tasks arising in interdependent infrastructure systems. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work was funded by Los Alamos National Laboratory's Directed Research and Development project "The Optimization of Machine Learning: Imposing Requirements on Artificial Intelligence" and the U.S. Department of Energy's Office of Electricity Advanced Grid Modeling projects "Joint Power System and Natural Gas Pipeline Optimal Expansion Planning" and "Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability." This work was carried out under the U.S. DOE contract no. [DE-AC52-06NA25396]. 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.2022.0118) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0118). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel data-driven optimization approach for trajectory-based air traffic flow management (ATFM). A key aspect of the proposed approach is the inclusion of airspace users' trajectory preferences, which are computed from traffic data by combining clustering and classification techniques. Machine learning is also used to extract consistent trajectory options, whereas optimization is applied to resolve demand-capacity imbalances by means of a mathematical programming model that judiciously assigns a feasible four-dimensional trajectory and a possible ground delay to each flight. The methodology has been tested on instances extracted from the Eurocontrol data repository. With more than 32,000 flights considered, we solve the largest instances of the ATFM problem available in the literature in short computational times that are reasonable from the practical point of view. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefits. Indeed, computing efficient solutions to the problem facilitates a consensus between the network manager and airspace users. In view of the level of accuracy of the solutions and the excellent computational performance, we are optimistic that the proposed approach can make a significant contribution to the development of the next generation of air traffic flow management tools. [ABSTRACT FROM AUTHOR]

The issue of transportation is a particular type of mathematical programming that facilitates searching for and determining an optimal distribution network, considering the set of suppliers and recipients. This paper uses a numerical example to present a solution to a transport problem utilizing classical computation methods, i.e., the northwest corner, the least cost in a matrix, and the VAM approximation method. The objective of the paper was to develop tools in the form of algorithms that would then be implemented in three various computing environments (R, GNU Octave, and Matlab) that allow us to optimize transport costs within an assumed supply network. The model involved determining decision variables and indicating limiting conditions. Furthermore, the authors interpreted and visualized the obtained results. The implementation of the proposed solution enables users to determine an optimal transport plan for individually defined criteria. [ABSTRACT FROM AUTHOR]

This study investigates a flow shop scheduling problem with queue time limits and skipping jobs, which are common scheduling requirements for semiconductor and printed circuit board manufacturing systems. These manufacturing systems involve the most complex processes, which are strictly controlled and constrained to manufacture high-quality products and satisfy dynamic customer orders. Further, queue times between consecutive stages are limited. Given that the queue times are limited, jobs must begin the next step within the maximum queue time after the jobs in the previous step are completed. In the considered flow shop, several jobs can skip the first step, referred to as skipping jobs. Skipping jobs exist because of multiple types of products processed in the same flow shop. For the considered flow shop, this paper proposes a mathematical programming formulation and a genetic algorithm to minimize the makespan. The GA demonstrated its strengths through comprehensive computational experiments, demonstrating its effectiveness and efficiency. As the problem size increased, the GA's performance improved noticeably, while maintaining acceptable computation times for real-world fab facilities. We also validated its performance in various scenarios involving queue time limits and skipping jobs, to further emphasize its capabilities. [ABSTRACT FROM AUTHOR]

Demand for electricity is constantly increasing, and production is facing new constraints due to the current world situation. An alternative to standard energy production methodologies is based on the use of renewable sources; however, these methodologies do not produce energy consistently due to weather factors. This results in a significant commitment of the user who must appropriately distribute loads in the most productive time slots. In this paper, a comparison is made between two methods of predicting solar energy production, one statistical and the other meteorological. For this work, a system capable of presenting the scheduling of household appliances is tested. The system is able to predict the energy consumption of the users and the energy production of the solar system. The system is tested using data from three different users, and the mean percentage of consumption reduction is about 77.73%. This is achieved through optimized programming of appliance use that also considers user comfort. [ABSTRACT FROM AUTHOR]

The quality and experience of healthcare systems affect the economy and prosperity of cities all over the world. Governments of several countries are struggling to improve the efficiency of their healthcare systems and decrease healthcare spending costs. In this paper, we discuss one of the most critical and busy processes among healthcare topics: ambulatory care center (ACC) appointment scheduling systems. We investigate the appointment-scheduling issue using a robust optimization framework to minimize operational costs while ensuring the improvement of healthcare service quality. Our findings and insights provide healthcare practitioners with tools to improve operational efficiency and service quality. [ABSTRACT FROM AUTHOR]

In the context of project management, the attention given to project portfolio management has increased in recent years. The use of mathematical programming for portfolio management is also on the rise, because it integrates the project interactions with the multiple objectives of portfolio management into a single model. Among the possible objectives, recent studies have paid special attention to the emerging objective of future preparedness, which has not yet been incorporated into the existing mathematical models. This paper presents a mixed-integer nonlinear optimization model for portfolio selection that considers four main performance measures for project management, namely, value maximization, strategic alignment, balance, and future preparedness. Given the importance of the last measure, the purpose of this paper is to provide a more complete model that provides the marginal contribution and the best combination of projects according to the needs of the company. The model is tested using real data from two companies, one in Brazil and one in Canada, and the results obtained are coherent with their respective practices. [ABSTRACT FROM AUTHOR]

Optimization is an important and decisive task in science. Many optimization problems in science are naturally too complicated and difficult to be modeled and solved by the conventional optimization methods such as mathematical programming problem solvers. Meta-heuristic algorithms that are inspired by nature have started a new era in computing theory to solve the optimization problems. The paper seeks to find an optimization algorithm that learns the expected quality of different places gradually and adapts its exploration-exploitation dilemma to the location of an individual. Using birds' classical conditioning learning behavior, in this paper, a new particle swarm optimization algorithm has been introduced where particles can learn to perform a natural conditioning behavior towards an unconditioned stimulus. Particles are divided into multiple categories in the problem space and if any of them finds the diversity of its category to be low, it will try to go towards its best personal experience. But if the diversity among the particles of its category is high, it will try to be inclined to the global optimum of its category. We have also used the idea of birds' sensitivity to the space in which they fly and we have tried to move the particles more quickly in improper spaces so that they would depart these spaces as fast as possible. On the contrary, we reduced the particles' speed in valuable spaces in order to let them explore those places more. In the initial population, the algorithm has used the instinctive behavior of birds to provide a population based on the particles' merits. The proposed method has been implemented in MATLAB and the results have been divided into several subpopulations or parts. The proposed method has been compared to the state-of-the-art methods. It has been shown that the proposed method is a consistent algorithm for solving the static optimization problems. [ABSTRACT FROM AUTHOR]

Purpose: Today, the digital gaming industry has a significant impact on the economic, cultural, and social spheres around the world. The advent of real and virtual reality games, particularly in medical science, has taken this industry out of the realm of mere entertainment and has become one of the applied industries. This study aims to optimize the combination of indigenous digital game development strategies, using a goal mathematical programming model. Compared to other common methods, the proposed approach can be a good alternative to studying and using mathematical planning in strategic management, when strategies are evaluated and selected. Design/methodology/approach: The research method of this study is typically mixed qualitative and quantitative for which, the main data were collected using library studies and theoretical framework review, in-depth and structured interviews with 12 experts and specialists in the digital games industry. A filled questionnaire was collected after coding variables. Thematic analysis (reasoning and rational analysis) was used to extract and classify the components. Also, an integration of House of Quality (HOQ), Analytical Hierarchy Process (AHP), and Simple Additive Weighting (SAW) techniques were used to determine the variables and parameters required in the mathematical model of the research. Finally, a goal programming model was used to determine the optimal combination of the strategies. Findings: A portfolio of optimal strategies was proposed that were effective in removing barriers and challenges in the game industry, which facilitated the achievement of game development goals with desirable capabilities in implementation. The mentioned strategies were capabilities empowerment and development of game-making experts, targeting and enriching the content of homemade games, financing and facilitating investment, and increasing the level of competitiveness of game-making groups. Research limitations/implications: The limited number of expert group members and the researcher's low access to them, in addition to creating problems related to the distribution and collection of questionnaires, review and increase the computational accuracy of validity and reliability, and also calculating the compatibility rate in the pairwise comparison questionnaires were the challenges and limitations of this study. Practical implications: The digital games industry has a great potential for growth and development, and its favorable economic, cultural and social effects are undeniable. Some of the practical findings of this study are the creation of an elite network and a strong relationship between gaming enthusiasts and the university, empowerment of game developers' knowledge and game studios in the gaming ecosystem, and monitoring and support of governmental and non-governmental policy-making institutions. Originality/value: In this paper, a new approach was proposed for evaluating and optimizing strategies for developing indigenous digital games to overcome their challenges and meet the relevant objectives in compliance with their feasibility (ease) of implementation. Also, the use of mathematical modeling in evaluating and selecting optimal strategies in this industry distinguishes this study from the literature. [ABSTRACT FROM AUTHOR]

Purpose: This research develops a model to improve the quality and freshness of sold vegetables through a funding program between farmers and retailers. Through this program, retailers who are interested in the distribution of first quality vegetables provide funds to farmers to increase their production this type of vegetables through the acquisition of new machinery, technology, or training. Design/methodology/approach: The problem is solved through a multi-objective mathematical programming model that simultaneously optimizes the supply chain profits, the waste of vegetables, the economic unfairness among farmers, the unfairness in the distribution of funds, and the freshness of sold vegetables. The ε-constraint method is used to obtain several non-dominated solutions to the problem after linearizing the non-lineal equations related to the unfairness objectives. Findings: Results show that it is possible to improve the indicators related to the vegetable waste, the economic unfairness, the unfairness in the distribution of funds and the freshness of vegetables while maintaining similar to optimal profits for the supply chain. Interesting trade-offs between the five objectives are identified, which can be used by supply chain members to select the most appropriate solution to be implemented in the real supply chain. Originality/value: This research models aspects relevant to the agri-food sector that have not been previously modelled for the problem under study. The main novelties of this paper are the consideration of the limited shelf life of the vegetables as well as the requirement of ensuring a minimum freshness at the moment of their sale, the price dependence on the quality and freshness of vegetables, the optimization of vegetable waste and the freshness of vegetables sold, as well as the joint optimization of the five previously defined objectives. [ABSTRACT FROM AUTHOR]

Energy-aware scheduling in a manufacturing environment with real-time energy pricing is a challenging problem. The purpose of this paper is to study a nonpreemptive scheduling problem on a single-machine to minimize the total tardiness and total energy cost under time-of-use electricity tariffs, which is a mixed-integer multi-objective mathematical programming model. To achieve these objectives, we develop several new holistic genetic algorithms. The proposed model is solved via several methods including weighted sum method and multiobjective genetic algorithms based on dominance rank (GA-1), weighted sum aggregation (GA-2), dominance ranking procedure and crowding distance comparison (GA-3), and heuristic approach (GA-H). This paper illustrates that operations management, which is typically observed as a significant technique that allows manufacturing to operate in challenging data enabled environment in an industrial internet of things ecosystem, can also carefully optimize a production process to improve energy cost in order to manage environmental challenges. Thus, the findings provide information on when to start each job. We provide detailed experimental results evaluating the performance of the proposed algorithms. In a case study, we illustrate how the results of the multiobjective model could be utilized in decision making using the technique for order preference by similarity to ideal solution method. [ABSTRACT FROM AUTHOR]

The prominence of managing municipal solid waste (MSW) in an efficient and effective manner is increasing from day to day. In this paper, the solid waste management (SWM) system of İstanbul is analyzed by applying the techniques from mathematical programming methodology. In this manner, the solutions of the two optimization problems which aim to minimize the total cost and the environmental effects of SWM, respectively, are presented in this study. Additionally, a sensitivity analysis is performed and a multi-objective problem that combines two problems is presented. In this regard, the application of five MSW management technologies which are currently in use in İstanbul on six waste components is analyzed; and the optimal solution regarding the best mixture of these technologies is developed on a given waste composition. Besides, this optimal solution is compared with the current practice in İstanbul; and recommendations are presented about possible future investments for the policymakers. The results of the study emphasize the importance of material recovery and incineration facilities to improve profitability and to minimize environmental side effects. In particular, material recovery facility (MRF) should be expanded to be able to treat all of metal, paper and plastic from a cost management perspective. Incineration (INC) facility should also be expanded in order to treat plastics or organic waste from a Greenhouse Gas (GHG) minimization perspective. In addition to this, landfill appears to be the most prominent treatment technique according to the current problem parameters. However, regarding the waste composition, the amount of organic waste must be decreased by more than 37% for other waste streams to be treated in different facilities other than landfill. Anaerobic digestion and composting facilities need to be more cost-effective for becoming economically feasible. The methodology represented in this study can be extended and generalized to other cities around the world once the correct problem parameters are specified. Image 105510 • Applying multi-objective optimization to solid waste management problem. • Importance of material recovery and incineration to improve profitability. • Landfill appears to be the most prominent treatment technique. • Must decrease the operating costs of composting and anaerobic digestion processes. • Applicable method to other cities after specifying the correct problem parameters. [ABSTRACT FROM AUTHOR]

The value and overall efficacy of a satellite mission are directly affected by its task scheduling strategy and the associated amount of work performed in orbit. Despite subject to many constraints, task scheduling is ultimately restricted by the amount of power available at any given moment. In this paper, we propose a mathematical integer programming (IP) formulation designed to maximize the number of tasks to be executed by a satellite, constrained to the amount of power available at any moment along the course of an orbit. The optimization model is formulated to contemplate task priority, minimum and maximum number of task activation, minimum and maximum execution time, minimum and maximum period of a given task and execution window. The variant power input vector was calculated based on the solar cells efficiency, and also on an analytical model used to estimate the irradiance field according to parameters of orbit and attitude. To demonstrate the applicability of our methodology, we conduct several experiments considering three satellite sizes with different orbits and task parameters. The results show that the proposed offline scheduling algorithm generates an optimal energy effective scheduling plan, allowing the best possible use of available energy resources while ensuring the quality of service (QoS). • We present an optimal task scheduling strategy for small satellites. • Test results under representative scenarios for different task parameters are presented. • The proposed offline scheduling algorithm generates an optimal energy effective scheduling plan. [ABSTRACT FROM AUTHOR]

Using convenient stratification criteria such as geographical regions or other natural conditions like age, gender, etc., is not beneficial in order to maximize the precision of the estimates of variables of interest. Thus, one has to look for an efficient stratification design to divide the whole population into homogeneous strata that achieves higher precision in the estimation. In this paper, a procedure for determining Optimum Stratum Boundaries (OSB) and Optimum Sample Sizes (OSS) for each stratum of a variable of interest in health surveys is developed. The determination of OSB and OSS based on the study variable is not feasible in practice since the study variable is not available prior to the survey. Since many variables in health surveys are generally skewed, the proposed technique considers the readily-available auxiliary variables to determine the OSB and OSS. This stratification problem is formulated into a Mathematical Programming Problem (MPP) that seeks minimization of the variance of the estimated population parameter under Neyman allocation. It is then solved for the OSB by using a dynamic programming (DP) technique. A numerical example with a real data set of a population, aiming to estimate the Haemoglobin content in women in a national Iron Deficiency Anaemia survey, is presented to illustrate the procedure developed in this paper. Upon comparisons with other methods available in literature, results reveal that the proposed approach yields a substantial gain in efficiency over the other methods. A simulation study also reveals similar results. [ABSTRACT FROM AUTHOR]

Caching at mobile devices and leveraging device-to-device (D2D) communication are two promising approaches to support massive content delivery over wireless networks. The analysis of cache-enabled wireless networks is usually carried out by assuming that devices are uniformly distributed, however, in social networks, mobile devices are intrinsically grouped into disjoint clusters. In this regards, this paper proposes a spatiotemporal mathematical model that tracks the service requests arrivals and account for the clustered devices geometry. Two kinds of devices are assumed, particularly, content clients and content providers. Content providers are assumed to have a surplus memory which is exploited to proactively cache contents from a known library, following a random probabilistic caching scheme. Content clients can retrieve a requested content from the nearest content provider in their proximity (cluster), or, as a last resort, the base station (BS). The developed spatiotemporal model is leveraged to formulate a joint optimization problem of the content caching and spectrum partitioning in order to minimize the average service delay. Due to the high complexity of the optimization problem, the caching and spectrum partitioning problems are decoupled and solved iteratively using the block coordinate descent (BCD) optimization technique. To this end, an optimal and suboptimal solutions are obtained for the bandwidth partitioning and probabilistic caching subproblems, respectively. Numerical results highlight the superiority of the proposed scheme over conventional caching schemes under equal and optimized bandwidth allocations. Particularly, it is shown that the average service delay is reduced by nearly 100% and 350%, compared to the Zipf and uniform caching schemes under equal bandwidth allocations, respectively. [ABSTRACT FROM AUTHOR]

Federated learning is a communication-efficient training process that alternate between local training at the edge devices and averaging of the updated local model at the center server. Nevertheless, it is impractical to achieve perfect acquisition of the local models in wireless communication due to the noise, which also brings serious effect on federated learning. To tackle this challenge in this paper, we propose a robust design for federated learning to decline the effect of noise. Considering the noise in two aforementioned steps, we first formulate the training problem as a parallel optimization for each node under the expectation-based model and worst-case model. Due to the non-convexity of the problem, regularizer approximation method is proposed to make it tractable. Regarding the worst-case model, we utilize the sampling-based successive convex approximation algorithm to develop a feasible training scheme to tackle the unavailable maxima or minima noise condition and the non-convex issue of the objective function. Furthermore, the convergence rates of both new designs are analyzed from a theoretical point of view. Finally, the improvement of prediction accuracy and the reduction of loss function value are demonstrated via simulation for the proposed designs. [ABSTRACT FROM AUTHOR]

Initial thickness imperfections of thin membranes due to manufacturing are inevitable and commonly observed. This paper presents an experimental and numerical investigation on how thickness imperfections affect the wrinkling of stretched membrane structures. With the measured data from a limited number of samples, we model the uncertain deviation of membrane thickness from that of a perfect geometry as a non-probabilistic bounded field with spatial dependency. After representing the bounded field as a linear function of a reduced set of uncertain coefficients by using a series expansion, the effect of thickness imperfections on the membrane wrinkling is investigated. To this end, the upper and lower bounds of out-of-plane displacements for membranes with initial imperfections are evaluated by a mathematical programming. The proposed wrinkling evaluation problem is then solved efficiently by using the Kriging-based optimization algorithm, with validation done by Monte Carlo simulation. The results show that initial thickness imperfections play a critical role in the wrinkling behavior of membranes. [ABSTRACT FROM AUTHOR]

An optimal planning model of the sectional switch and tie line for the distribution network is proposed considering the tradeoff between the system reliability and economy. First, the fault incidence matrices are established for the distribution network, and the explicit analytical expression of the system reliability index is realized by the algebraic operation of the fault incidence matrices and fault parameter vectors. Then, the 0–1 integer quadratically constrained optimization model is established for the sectional switch configuration considering the capacity constraint of the tie line. Finally, the sectional switches and tie lines are optimized jointly to ensure the economic investment and maximize the system reliability. The distribution network in Taiwan Power Company is used to verify the applicability of the proposed optimization method. Compared with the intelligent optimization algorithm, the mathematical programming method in this paper can always find the global optimal switch configuration quickly. In addition, the influence of the tie line capacity constraints on the sectional switch configuration is also considered, which can provide practical reference for the power network planners in the optimization design of the distribution network. [ABSTRACT FROM AUTHOR]

In recent years, the size (weight and volume) of cruise ships are experiencing spectacular increase, coherently with the increase in energy consumption and carbon emissions. However, the regulations about pollutant emissions imposed by the International Maritime Organization are becoming more and more strict. In order to face up to this issue, the energy system of cruise ships is constantly being modified. In this paper, the structure of the cruise ship's energy system with multiple facilities such as an internal combustion engine, gas turbine, dual fuel engine, PV panels, and the wind turbine is pre-established. Then, a multi-objective mathematical programming model is formulated to determine the selection and capacity of facilities with minimal total annual cost and size, while the emissions, energy balance and technical constraints are taken into account. By adopting the augmented ε-constraint method, the design and operation strategies could be obtained. As an illustrated example, the model is applied to a real cruise ship, and the Pareto frontier could provide ship designers with well-balanced solutions based on economic and size priorities, and with the increase in the proportion of size objective, the total annual cost increases and size decreases gradually. Compared with the reference energy system, the optimal energy system could reduce the total annual cost by 12.6% if only the economic objective is considered and reduce the size by 21.1% if only the size objective is considered. In multi-objective condition, the CO, NOx, and SOx emissions could be reduced by 29.1%–61.3%, 42.8%–61.3%, and 42.8%–61.3% per year, respectively. Moreover, a sensitivity analysis is conducted, and the result shows that the size and consumption cost of Marine Gas Oil (MGO) and Liquefied Natural Gas (LNG) are more sensitive to the change of the proportion of size objective compared to Heavy fuel oil (HFO) and Marine diesel oil (MDO). • A multi-objective model for the design optimization of cruise ship energy system is developed. • An augmented ε-constraint method is introduced to solve the optimization problem. • The proposed model could obtain the optimal strategies of the cruise ship energy system with minimal total annual cost and size. • The effectiveness of the proposed methodology is verified through a real cruise ship. [ABSTRACT FROM AUTHOR]

Recently, the concept of network virtualization and network slicing attracted significant attention from both industry and academia as a key component of the evolving 5G architecture to allow the efficient entrance of vertical industries and tackle increased aggregate traffic by flexible network re-configurability. However, the potential price to be paid for facilitating network slicing in a multi-tenant virtual network is the underutilization of the scarce wireless network resources due to the different tenant requirements and the inherent dynamics of the traffic. A potential way to avoid such sacrifice of radio resources is to allow efficient inter-tenant resource sharing. To this end, this paper proposes a novel optimization framework for flexible inter-tenant resource sharing embedded with transmission power control to aggressively improve network capacity, the utilization of wireless access resources, user data rate as well as energy efficiency. More specifically, we define two novel resource sharing mechanisms called tight coupling and loose coupling, respectively, via mixed integer linear programming formulations. Furthermore, two resource and power joint allocation algorithms are designed to solve the optimization problem in polynomial time. Based on 3GPP network parameterization, a rigorous analysis via a wide set of numerical investigations reveal that significant gains in network throughput, individual user rate, and energy efficiency can be achieved compared with current baseline network slicing methods and constant power resource sharing algorithms. [ABSTRACT FROM AUTHOR]

A professional service firm often faces challenges in matching its available workforce with the demands for service delivery. In this paper, we coin the labor strategy optimization (LSO) problem to prescribe an optimal staffing plan for meeting the target revenues of a professional service firm. It simultaneously optimizes the capacity, capability, location, and flexibility of a firm's workforce at the strategic level. Our modeling framework captures the richness and complexity of a general service transformation process. Mathematical programming based models are developed for both the deterministic and stochastic versions of the problem. A prototype of the LSO technology was implemented at the former HP Consulting & Integration organization. Through a comprehensive computational study, managerial insights are drawn and discussed about the optimal labor strategy under various supply-side risks and uncertainties. The optimal labor strategy provides a cost effective and reliable basis for more detailed workforce optimization concerning scheduling and assignment decisions. Our study also offers a data-driven approach to take advantage of large amount of disparate data, from different organizations and geographical locations of a firm, for improving the workforce planning decisions. [ABSTRACT FROM AUTHOR]

Graph cuts are widely used in computer vision. To speed up the optimization process and improve the scalability for large graphs, Strandmark and Kahl introduced a splitting method to split a graph into multiple subgraphs for parallel computation in both shared and distributed memory models. However, this parallel algorithm (the parallel BK-algorithm) does not have a polynomial bound on the number of iterations and is found to be non-convergent in some cases due to the possible multiple optimal solutions of its sub-problems. To remedy this non-convergence problem, in this paper, we first introduce a merging method capable of merging any number of those adjacent sub-graphs that can hardly reach agreement on their overlapping regions in the parallel BK-algorithm. Based on the pseudo-boolean representations of graph cuts, our merging method is shown to be effectively reused all the computed flows in these sub-graphs. Through both splitting and merging, we further propose a dynamic parallel and distributed graph cuts algorithm with guaranteed convergence to the globally optimal solutions within a predefined number of iterations. In essence, this paper provides a general framework to allow more sophisticated splitting and merging strategies to be employed to further boost performance. Our dynamic parallel algorithm is validated with extensive experimental results. [ABSTRACT FROM PUBLISHER]

To satisfy the rapidly growing demands of wireless communications, new structures have been proposed for the fifth-generation (5G) mobile communication networks, such as cloud radio access networks (C-RANs), which have advantages including high energy efficiency, large network capacity, and high flexibility. This paper concentrates on the problem of remote radio head (RRH) activation, user association, and power allocation in C-RANs. To tackle the problem with $l_{0}$ norm, we transform it into a mixed-integer nonlinear programming (MINLP) problem. Instead of solving it by centralized solvers, we propose a novel algorithm based on Benders decomposition, which can obtain the optimal solution of the MINLP problem. To solve the primal problem in Benders decomposition efficiently, we adopt the alternating direction method of multipliers (ADMM) to achieve a parallel implementation. To further reduce the complexity of solving the MINLP problem, a distributed two-stage iterative algorithm combining the ADMM and the max-sum algorithm is also proposed. The simulation results demonstrate that the first proposed algorithm can obtain the optimal solution, and the second proposed algorithm outperforms conventional algorithms significantly. [ABSTRACT FROM AUTHOR]

In grey-level image restoration, a prior knowledge of degraded areas allows, thanks to the selective filtering, to achieve a good protection of the image features. In this paper, we propose a quadratic programming-based technique that deals with the issue of details preservation during the restoration process. Based on the classical model of image restoration, we build a modified model by introducing a set of binary variables that indicate the pixel categories. We combine each pixel with the median of its neighbours in a decision rule so that one of them generates the optimal solution. The obtained model is a nonlinear mixed-integer problem where resolution by exact methods is not feasible. In this regard, we use both of the continuous Hopfield neural network and the genetic algorithm to solve the suggested model. Performance of our method is demonstrated numerically and visually by several computational tests. [ABSTRACT FROM AUTHOR]

The paper presents an optimization model and its implementation using a hybrid approach for the Capacitated Vehicle Routing Problem with Pick-up and Alternative Delivery (CVRPPAD). The development of the CVRPPAD was motivated by postal items distribution issues. The model proposed combines various features of Vehicle Routing Problem variants. The novelty of this model lies in the introduction of alternativeness of item delivery points, differentiation of delivery point types in terms of their capacity (parcel lockers) and possibility of collecting the items during the execution of delivery routes. The model also takes into account a possibility of introducing time windows related to delivery time. The proposed data structure in the form of sets of facts facilitates the implementation of the model in all environments, Constraint Logic Programming (CLP), Mathematical Programming (MP), metaheuristics, databases, etc. The model is implemented in the MP, hybrid CLP/MP, and hybrid CLP/heuristic environments. The hybrid CLP/MP approach is the authors' original solution, which has already been used to solve Supply Chain Management problems, scheduling problems, routing problems etc. For large size problems, considering their combinatorial character, the proposed CLP/MP approach is ineffective. Its effectiveness will improve when MP is replaced by a heuristic. All implementations were performed on the same data instances (facts), which made it possible to compare them according to the solution search time, number of decision variables and number of constraints. The directions into which the model can be further developed were also presented. [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]

Accidents, bad weathers, traffic congestions, etc. led to the uncertainties of travel times in real-life road networks, which greatly affected the quality of individual’s life and the reliability of transportation system. This paper addressed the school bus routing problem in such a stochastic and time-dependent road environment. Firstly, the problem was set based on a single-school configuration, and the students were picked up at their homes, which was in line with the current situation of school bus systems in China. Thus, it could be regarded as an independent problem of school bus route generation in random dynamic networks, which could be solved as a variant of extended Vehicle Routing Problem. However, due to the fluctuation and uncertainty of link travel times, the arrival time at each stop including the destination was varying. Therefore, the selection of optimal path connecting the current service node with the next one was treated as a sub-problem in this study, where the reliability of travel times in the stochastic and time-varying network was highly concerned by such time-rigid commuters. To this end, a Robust Optimal Schedule Times model with a hard time windows constraint was built to generate a most cost-reliable route for school buses. By the use of Robust Optimization method, it was intended to minimize the worst-case total cost which combined the cost of earlier schedule delays with the disutility of travel times. It was also proved that the proposed model could be converted into solving a conventional problem in deterministic dynamic networks for a reduction of computation complexity, which provided the potential of applying to the practical problems. Finally, the validity of the proposed model and its performance evaluation was analyzed through a small-scale computational instance, where all the link travel times in the simulated network were attributed to both time-varying and stochastic. Then, a mathematical programming solver was used to find the exact optimal solution. The results indicated that the model was valid, and the necessity of considering the stochastic and time-dependent nature of transportation networks was also confirmed in the case study. [ABSTRACT FROM AUTHOR]

As there are various risks of failure in its execution, a composite web service (CWS) requires a transactional mechanism to guarantee its reliable execution. Though the existing service selection methods have considered that its transactional properties may affect its quality of service (QoS) such as its execution time, some of these methods can just give the locally optimal transactional CWS while others can give globally optimal CWS only under a given fixed transactional workflow. This paper addresses the issue of selecting and composing web services via a genetic algorithm (GA) and gives a transaction and QoS-aware selection approach. First, it introduces transactional properties of a single web service and CWS and the transactional rules used to compose them. Next, it conducts the performance analysis of basic workflow patterns such as sequential, parallel, selectable, and loop patterns and develops an algorithm to compute the execution time of a complex CWS. Then, it presents a GA-based approach, which takes into account the execution time, price, transactional property, stability, and penalty-factor, to achieve globally optimal service selection. Finally, this paper reports experimental results that compare the proposed approach with the exhaustive search algorithm, transactional-QoS-driven selection algorithm, and transactional service selection algorithm. The experimental results show that the proposed algorithm is efficient and effective and can give a globally optimal transactional CWS. [ABSTRACT FROM PUBLISHER]

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution. [ABSTRACT FROM AUTHOR]

This paper develops an equilibrium-based model for ex ante analysis of capacity withholding under financial virtual divestiture in a day-ahead market, including one dominant producer and a number of small producers considered as a price-taking competitive fringe. We model the offering problem of the dominant producer as a bilevel optimization problem. In the upper-level problem, the dominant producer derives optimal strategy of physical capacity withholding restricted by operational limits of its own generating units and conditions stated in the financial virtual divestiture. In the lower-level problem, market operator clears the day-ahead market on an hourly basis. We recast the bilevel optimization problem as a mathematical programming with equilibrium constraints problem and convert it to a mixed integer linear programming problem. We show how the application of the financial virtual divestiture may mitigate market power in the day-ahead market, through a case study. The numerical results demonstrate that the dominant producer can exploit technological diversification of its own generating units to exercise market power, even in the presence of this market power mitigation policy. [ABSTRACT FROM PUBLISHER]

An effective means for analyzing the impact of novel operating schemes on power systems is time-domain simulation, for example, for investigating optimization-based curtailment of renewables to alleviate voltage violations. Traditionally, interior-point methods are used for solving the non-convex AC optimal power flow (OPF) problems arising in this type of simulation. This paper presents an alternative algorithm that better suits the simulation framework, because it can more effectively be warm started, has linear computational and memory complexity in the problem size per iteration and globally converges to Karush–Kuhn–Tucker (KKT) points with a linear rate if they exist. The algorithm exploits a difference-of-convex-functions reformulation of the OPF problem, which can be performed effectively. Numerical results are presented comparing the method to state-of-the-art OPF solver implementations in MATPOWER, leading to significant speedups compared to the latter for smaller systems and comparable performance for larger cases. [ABSTRACT FROM PUBLISHER]

This paper studies the joint transceiver design and power splitting (JTDPS) for a downlink multiuser multiple-input multiple-output (MU-MIMO) simultaneous wireless information and power transfer (SWIPT) system. Aiming to minimize the transmit power by jointly optimizing the transmitter at a base station, the power splitting (PS) factors, and information decoding receivers at mobile stations (MSs) subject to both the predefined mean-square error (MSE) and the given energy harvesting (EH) constraints. The formulated problem is a nonconvex JTDPS optimization problem, which cannot be solved directly. To solve it, an iterative optimization framework composed of joint transmitter and PS factor optimization (JTxPS) subproblem and a receiver side minimum mean-square error (MMSE) minimization subproblem is proposed. By iteratively solve the two subproblems, the original optimization problem is solved. The sufficient and necessary conditions for the feasibility of the formulated JTDPS and the JTxPS problems are analyzed. Theoretical analysis shows that the JTxPS subproblem is also nonconvex and can be solved by using convex semidefinite programming (SDP). Considering the high computational complexity of the SDP-based scheme, a low-complexity suboptimal scheme based on the traditional MMSE transceiver design is also proposed. Simulations are done to validate the theoretical analysis, and results show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

Large construction and infrastructure projects are a billion-dollar business, but few studies have addressed the integrated operations in this unique domain of the construction supply chain (CSC). The comparison between the CSC and a conventional supply chain enables us to examine its framework and establish a quantitative optimization model for the CSC. To introduce the integrated operations concept into the CSC, many uncertainties need to be first dealt with, for which a multiobjective uncertain optimization model is developed. As the optimization of the owner and fabricator's costs and the service level are the main objectives, a hybrid genetic algorithm with fuzzy-random method is developed to solve the optimization model. An integrated multiobjective purchasing and production planning model is then constructed and applied to a hydropower construction project in Southwest China. The results illustrate that efficient integrated operations are critical for the CSC performance. The optimization results also indicate that considering of uncertain rush orders and delay times can be vital for optimum CSC performance. With this proposed method, construction managers can quickly respond to changing uncertain demand. This paper has highlighted that project managers need to collaborate with other stakeholders to ensure optimal CSC performance. [ABSTRACT FROM AUTHOR]

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]

Abstract: In this paper, we present several hysteretic models formulated using an energy approach. In each case, the behavior of the model is completely described by specifying two scalar-valued functions—a stored energy function and a dissipation potential. Consequently, different types of mathematical programs arise in incremental non-linear analyses involving these models. It is relatively well-known how classical plasticity models can be described using an energy approach, and lead to mathematical programming problems. However, in this paper, we demonstrate that plasticity models with non-associated flow rules, softening plasticity or strength degradation models, and damage or stiffness degradation models can be represented in this framework as well. The energy approach serves to unify formulation and implementation of a broad class of hysteretic models. In addition, it helps motivate regularization strategies needed in optimization and inverse problems. The types of models considered in this paper are ones commonly applied in earthquake engineering. MATLAB implementations are included as online supplemental data with this paper to illustrate the conceptual simplicity of implementing models formulated using this approach. [Copyright &y& Elsevier]

This paper proposes a new control chart, denoted by $$ {\overset{-}{X}}^{att} $$ , for evaluating the stability of a process mean. This chart is based on attribute inspection rather than physical measurements (taken with an instrument such as a caliper or precise balance) of the quality characteristics of interest of the sampled items. Based on a go-no-go gauge device (which generates five categorizations), the average of a quality characteristic of interest is controlled. In equally spaced times, samples of n items are collected, and the averages are estimated by means of $$ {\overset{-}{X}}^{att} $$ based solely on the obtained categorization to decide whether the process is in control. Once the distribution of $$ {\overset{-}{X}}^{att} $$ is calculated, the decision problem is defined in terms of a mathematical programming formulation to find the dimensions to be used in the go-no-go gauge and to find the control limits that minimize the average run length (ARL) for the out-of-control situation and that are constrained to a prefixed ARL for the under-control situation. As shown by extensive computational experiments, the newly introduced $$ {\overset{-}{X}}^{att} $$ control chart outperforms the conventional $$ \overset{-}{X} $$ control chart for small shifts in the means and is still competitive otherwise. Because the new $$ {\overset{-}{X}}^{att} $$ control chart uses attributes, it can be considered a viable alternative to the conventional $$ \overset{-}{X} $$ control chart. [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 reports on early work and concept development for Optimal Mine Site Energy Supply, where the specific energy supply requirements and constraints for mineral production operations are considered against methodologies that have been applied for other sectors and in other energy policy regimes. The primary motivation for this research is to help ensure that Canadian mineral producers will achieve reduced production costs through improvements in the efficiency with which they consume energy resources. Heat has not yet been considered for the mining sector in an integrated manner, which makes polygeneration of great interest. The methodology that optimizes configuration of polygeneration systems for mine sites has not been reported before. The variety of mining circumstances, temporal variations in energy prices, institutional inertia, and conservatism in design for mines are some of the reasons for this. This paper reviews some aspects of precedent energy management practice in mineral operations, which highlights energy challenges characteristic of the sector and sets out the initial formulation of optimal mine site energy supply. The review indicates the additional benefits of energy supply systems for mine sites that concurrently meet all utilities. [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 the multiattribute decision-making (MADM) problem with intuitionistic fuzzy values that represent information regarding alternatives on the attributes. Assuming that the weight information of the attributes is not known completely, we use an approach that utilizes the relative comparisons based on the advantage and disadvantage scores of the alternatives obtained on each attribute. The relative comparison of the intuitionistic fuzzy values in this research use all the three parameters, namely membership degree (“the more the better”), nonmembership degree (“the less the better”), and hesitancy degree (“the less the better”), thereby leading to the tradeoff values of all the three parameters. The score functions (advantage and disadvantage scores) used for this purpose are based on the positive contributions of these parameters, wherever applicable. Furthermore, these scores are used to obtain the strength and weakness scores leading to the satisfaction degrees of the alternatives. The optimal weights of the attributes are determined using a multiobjective optimization model that simultaneously maximizes the satisfaction degree of each alternative. The optimal solution is used for ranking and selecting the best alternative on the basis of the overall attribute values. To validate the proposed methodology, we present a numerical illustration of a real-world case. The methodology is further extended to treat MADM problem with interval-valued intuitionistic fuzzy information. Finally, a thorough comparison is done to demonstrate the advantages of the solution methodology over the existing methods used for the intuitionistic fuzzy MADM problems. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents new definitions for process intensification identifying two main categories called unit intensification and plant intensification. This paper also proposes general mathematical programming formulations for the different categories of intensification through a disjunctive formulation to consider the use of existing units or to include additional units. The ideas of process integration (energy, mass and property integration) are very useful for process intensification helping in maximizing throughput for a given process, minimizing process inventory for a given throughput or in minimizing utilities and feedstock for a given throughput (this means that process intensification is broader than process integration). This paper identifies that process intensification is a wider approach than single unit intensification as it was considered by most of the previous works. A case study is presented to show the applicability of the proposed models and definitions. [Copyright &y& Elsevier]

In the present paper, the ultimate load of the reinforced concrete slabs [16] is determined using the finite element method and mathematical programming. The acting efforts and displacements in the slab are obtained by a perfect elasto-plastic analysis developed by finite element method. In the perfect elasto-plastic analysis the Newton-Raphson method [20] is used to solve the equilibrium equations at the global level of the structure. The relations of the plasticity theory [18] are resolved at local level. The return mapping problem in the perfect elasto-plastic analysis is formulated as a problem of mathematical programming [12]. The Feasible Arch Interior Points Algorithm proposed by Herskovits [8] is used as a return mapping algorithm in the perfect elasto-plastic analysis. The proposed algorithm uses Newton's method for solving nonlinear equations obtained from the Karush-Kuhn-Tucker conditions [11] of the mathematical programming problem. At the end of this paper, it is analyzed six reinforced concrete slabs and the results are compared with available ones in literature. [ABSTRACT FROM AUTHOR]

We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its value, and determines whether to purchase the item or to permanently dismiss the item. The customer's objective is to maximize the value of the purchased item. In this paper, we consider the problem from the perspective of the seller, who wishes to maximize profit associated with the sold item. Hence, the seller seeks an optimal sequence of items to sell, given that the customer acts according to some near-optimal decision-making rules. Our paper takes the perspective that the customer may not act optimally due to imperfect decision-making strategies and/or to the seller's uncertainty in the items' values to the customer. We consider max-min and max-expectation objectives when customer behavior is not completely predictable, and discuss the problem tractability in these cases. [ABSTRACT FROM AUTHOR]

Time–cost trade-off analysis is addressed as an important aspect of any construction project planning and control. Nonexistence of a unique solution makes the time–cost trade-off problems very difficult to tackle. As a combinatorial optimization problem one may apply heuristics or mathematical programming techniques to solve time–cost trade-off problems. In this paper, a new multicolony ant algorithm is developed and used to solve the time–cost multiobjective optimization problem. Pareto archiving together with innovative solution exchange strategy are introduced which are highly efficient in developing the Pareto front and set of nondominated solutions in a time–cost optimization problem. An 18-activity time–cost problem is used to evaluate the performance of the proposed algorithm. Results show that the proposed algorithm outperforms the well-known weighted method to develop the nondominated solutions in a combinatorial optimization problem. The paper is more relevant to researchers who are interested in developing new quantitative methods and/or algorithms for managing construction projects. [ABSTRACT FROM AUTHOR]

Abstract: Multipurpose batch processes entail various operational policies that have been widely investigated in published literature. In this paper, no-intermediate-storage (NIS), zero-wait (ZW) and common-intermediate-storage (CIS) operational policies are of particular interest. In all these policies, no dedicated storage facility is available between two consecutive units. Unlike the other operational policies, these particular policies bear some subtle practical infeasibility that has gone unnoticed in literature. In essence, this infeasibility has been reported as optimal, thus assumed to be feasible, by various authors using mathematical programming techniques. It pertains to a unit transferring product to one or more units whilst simultaneously receiving feed from another, which is practically infeasible and as such need not be considered as a possible solution. This feature is particularly conspicuous in batch processes with complex recipes wherein production paths can be in opposite directions. This paper presents the unique feature of the S-graph framework to isolate cross-transfer during optimization, whereas the available mathematical programming methods inherently fail neither to detect nor to eliminate this infeasibility. A few examples taken from published literature are presented for demonstration purposes. [Copyright &y& Elsevier]

This paper makes a contribution to the branch and cut approach to the capacitated vehicle-routing problem (CVRP). In the CVRP, the demands of a set of customers have to be met at minimum total travel cost using vehicles of identical capacity based at a single depot. The potential of maximally violated mod-p cutting-planes (Caprara et al. 2000) for the CVRP is investigated via a computational study. The foundation of the assessment is formed by classes of problem-specific constraints taken from the literature. In several separation algorithms for the CVRP, it is advantageous to shrink inclusionwise maximal minimum-weight cuts in support graphs as preprocessing. It is mentioned how a partition of the set of customers into such mincuts can be computed in a fast and elegant way using the mincut algorithm of Hao and Orlin (1994). Interestingly, maximally violated mod-p cuts, which are general-purpose cuts of Chvátal-Gomory type, stand comparison with problem-specific cuts for the CVRP and they are clearly useful on top of such cuts. The first-time proven optimal solution of the CVRP instance B-n68-k9 is reported. The computation used a branching strategy with far lookahead and relied on maximally violated mod-p cuts. This paper on maximally violated cuts belongs to a set of papers originating from Applegate et al. (1995) where a separation of maximally violated combs for the traveling-salesman problem (TSP) is suggested. [ABSTRACT FROM AUTHOR]

Because of the strong competition in the equipment market, the aim of the manufacturers is to reduce the product price as much as possible, fulfill the high-quality standards, and improve the reliability and efficiency of the transformers. The capitalization of the costs enables to handle the different economic and technological parameters together in the same cost function. Large power autotransformers are usually designed for specific economic and technical conditions specified by the customer. At the tender design stage, the most economical solution has to be found in a limited time, and a great number of feasible transformer designs have to be compared to find the optimal solution. Nowadays, the solution of this design process is mainly based on the experience of the transformer designer, but mathematical programming models can facilitate the process. It is well known that the design of shell-type power transformers can be optimized by geometric programming. The constructed models of geometric programming can be solved accurately with the interior-point-method-based solvers. According to the results, this kind of modeling is not applicable for the core-form transformers. However, with branch-and-bound search, the geometric programming method can also be used for these cases. This paper introduces a new algorithm, which can also handle the autotransformer designs with different positions of the regulating winding by applying a more general metaheuristic routine to perform the calculation of the short-circuit impedance. [ABSTRACT FROM AUTHOR]