Application of critical shear crack theory on punching of flat slabs

This article deals with the punching capacity of a flat slab fragment supported by an internal atypically elongated column. Based on the results of this analysis and the application of Critical Shear Crack Theory, the reliability of two design models was determined. The CSCT model is a mechanical model where the shear force transferred by concrete in shear crack can be determined by accounting for the roughness and opening of a critical shear crack. The crack width is proportional to the slab rotation, which was obtained from a nonlinear program Atena and from experimental test and shear capacity was obtained by integrating the shear strength along the control perimeter. The aim of this analysis was to compare the application of CSCT in non-linear analysis and experimental test to point out the significant difference between obtained results, which shows the importance of experimental tests realization. Non-linear analyses provided unsafe results. Contrary the currently used EC2 model provided safe results when reduction of the control perimeter was applied. The best results were obtained in a combination of the CSCT model with measured rotations of the slab specimen.

Microgrid Protection through Adaptive Overcurrent Relay Coordination

The inclusion of distributed energy resources (DER) in Microgrids (MGs) comes at the expense of increased changes in current direction and magnitude. In the autonomous mode of MG operation, the penetration of synchronous distributed generators (DGs) induces lower short circuit current than when the MG operates in the grid-connected mode. Such behavior impacts the overcurrent relays and makes the protection coordination difficult. This paper introduces a novel adaptive protection system that includes two phases to handle the influence of fault current variations and enable the MG to sustain its operation. The first phase optimizes the power flow by minimizing the generators’ active power loss while considering tolerable disturbances. For intolerable cases, the second phase opts to contain the effect of disturbance within a specific area, whose boundary is determined through correlation between primary/backup relay pairs. A directional overcurrent relay (DOCR) coordination optimization is formulated as a nonlinear program for minimizing the operating time of the relays within the contained area. Validation is carried out through the simulation of the IEEE 9, IEEE 14, and IEEE 15 bus systems as an autonomous MG. The simulation results demonstrate the effectiveness of our proposed protection system and its superiority to a competing approach in the literature.

Integration of Mixed-Integer Nonlinear Program and Project Management Tool to Support Sustainable Cost-Optimal Construction Scheduling

This paper presents the integration of mixed-integer nonlinear program (MINLP) and project management tool (PMT) to support sustainable cost-optimal construction scheduling. An integrated structure of a high-level system for exact optimization and PMT was created. To ensure data compatibility between the optimization system and PMT and to automate the process of obtaining a cost-optimal schedule, a data transformation tool (DTT) was developed within a spreadsheet application. The suggested system can determine: (i) an optimal project schedule with associated network diagram and Gantt chart in continuous or discrete time units; (ii) optimal critical and non-critical activities, including their early start, late start, early finish, late finish along with total and free slack times; and (iii) minimum total project cost along with the allocation of direct and indirect costs. The system provides functionalities such as: (i) MINLP can be updated, and schedules can be re-optimized; (ii) the optimal schedule can be saved as a baseline to track changes; (iii) different optimization algorithms can be engaged whereby switching between them does not require model changes; (iv) PMT can be used to track task completion in the optimized schedule; (v) calendar settings can be changed; and (vi) visual reports can be generated to support efficient project management. Results of cost-optimal project scheduling are given in a conventional PMT environment, which raises the possibility that the proposed system will be more widely used in practice. Integration of MINLP and PMT allows each software to be used for what it was initially designed. Their combination leads to additional information and features of optimized construction schedules that would be significantly more difficult to achieve if used separately. Application examples are given in the paper to show the advantages of the proposed approach.

Visual analytics for nonlinear programming in robot motion planning

Nonlinear programming is a complex methodology where a problem is mathematically expressed in terms of optimality while imposing constraints on feasibility. Such problems are formulated by humans and solved by optimization algorithms. We support domain experts in their challenging tasks of understanding and troubleshooting optimization runs of intricate and high-dimensional nonlinear programs through a visual analytics system. The system was designed for our collaborators’ robot motion planning problems, but is domain agnostic in most parts of the visualizations. It allows for an exploration of the iterative solving process of a nonlinear program through several linked views of the computational process. We give insights into this design study, demonstrate our system for selected real-world cases, and discuss the extension of visualization and visual analytics methods for nonlinear programming. Graphic abstract

Transit Planning Optimization Under Ride-Hailing Competition and Traffic Congestion

With the soaring popularity of ride-hailing, the interdependence between transit ridership, ride-hailing ridership, and urban congestion motivates the following question: can public transit and ride-hailing coexist and thrive in a way that enhances the urban transportation ecosystem as a whole? To answer this question, we develop a mathematical and computational framework that optimizes transit schedules while explicitly accounting for their impacts on road congestion and passengers’ mode choice between transit and ride-hailing. The problem is formulated as a mixed integer nonlinear program and solved using a bilevel decomposition algorithm. Based on computational case study experiments in New York City, our optimized transit schedules consistently lead to 0.4%–3% system-wide cost reduction. This amounts to rush-hour savings of millions of dollars per day while simultaneously reducing the costs to passengers and transportation service providers. These benefits are driven by a better alignment of available transportation options with passengers’ preferences—by redistributing public transit resources to where they provide the strongest societal benefits. These results are robust to underlying assumptions about passenger demand, transit level of service, the dynamics of ride-hailing operations, and transit fare structures. Ultimately, by explicitly accounting for ride-hailing competition, passenger preferences, and traffic congestion, transit agencies can develop schedules that lower costs for passengers, operators, and the system as a whole: a rare win–win–win outcome.

Distribution planning problem of a supply chain of perishable products under disruptions and demand stochasticity

PurposeThe emergence of risk in today's business environment is affecting every managerial decision, majorly due to globalization, disruptions, poor infrastructure, forecasting errors and different uncertainties. The impact of such disruptive events is significantly high for perishable items due to their susceptibility toward economic loss. This paper aims to design and address an operational planning problem of a perishable food supply chain (SC).Design/methodology/approachThe proposed model considers the simultaneous effect of disruption, random demand and deterioration of food items on business objectives under constrained conditions. The study describes this situation using a mixed-integer nonlinear program with a piecewise approximation algorithm. The proposed algorithm is easy to implement and competitive to handle stationary as well as nonstationary random variables in place of scenario techniques. The mathematical model includes a real-life case study from a kiwi fruit distribution industry.FindingsThe study quantifies the performance of SC in terms of SC cost and fill rate. Additionally, it investigates the effects of disruption due to suppliers, transport losses, product perishability and demand stochasticity. The model incorporates an incentive-based strategy to provide cost-cutting in the existing business plan considering the effect of deterioration. The study performs sensitivity analysis to show various “what-if” situations and derives implications for managerial insights.Originality/valueThe study contributes to the scant literature of quantitative modeling of food SC. The research work is original as it integrates a stochastic (uncertain) nature of SC simultaneously coupled with the effect of disruption, transport losses and product perishability. It incorporates proactive planning strategies to minimize the disruption impact and the concept of incremental quantity discounts on lot sizes at a destination node.

On refinement strategies for solving $${\textsc {MINLP}\mathrm{s}}$$ by piecewise linear relaxations: a generalized red refinement

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program ($${\textsc {MINLP}}$$ MINLP ) context. We show that the red refinement meets sufficient convergence conditions for a known $${\textsc {MINLP}}$$ MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure results in piecewise linear relaxations that can be modeled by the well-known incremental method established by Markowitz and Manne (Econometrica 25(1):84–110, 1957). Finally, numerical results from the field of alternating current optimal power flow demonstrate the applicability of the red refinement in such $${\textsc {MIP}}$$ MIP -based $${\textsc {MINLP}}$$ MINLP solution frameworks.

Single and Multiobjective optimal control of epidemic models involving vaccination and treatment

Introduction: A rigorous multiobjective optimal control strategy (that does not require the use of weighting functions) of the epidemic models that consider vaccination and treatment strategies is presented. Modifications of the standard susceptible-infectious-removed, susceptible-exposed-infectious-removed, and the modified susceptible-infectious-removed models are dynamically optimized to minimize the number of infected individuals while, controlling the rate at which the individuals are vaccinated and treated. Method:The optimization program, Pyomo , where the differential equations are automatically converted to a Nonlinear Program using the orthogonal collocation method is used for performing the dynamic optimization calculations. The Lagrange-Radau quadrature with three collocation points and 10 finite elements are chosen. The resulting nonlinear optimization problem was solved using the solver BARON 19.3, accessed through the Pyomo-GAMS27.2 interface. Results: The computational results how that the multiobjective optimal control profiles generated by this strategy are very similar to those produced when weighting functions are used. Conclusion: The main conclusion of this work is to demonstrate that one can perform a rigorous dynamic optimization of epidemic models without the use of weighting functions that have the potential to produce some uncertainty and doubt in the results, in addition to dealing with unnecessary additional variables.

Choosing the number of time intervals for solving a model predictive control problem of nonlinear systems

Model predictive control (MPC) is a control strategy that can handle state and control multi-variables at same time. To use the MPC using direct methods for solving the a dynamic optimization problem, one needs, for example, to transform the optimization problem into a nonlinear programming (NLP) problem by dividing the prediction horizon into equal time intervals. In this work, we suggest a tool and procedures for helping to choose a ‘compromise’ number of time intervals with a needed accuracy, objective cost, number of turned NLP iterations and computational time. On the other hand, we offer a simplified nonlinear program to ensure the convergence of a class of finite optimal control problem by modifying the state box constraints. In particular, a special type of box constraints were used to the constrained optimal control problem to enforce the state trajectories to reach the desired stationary point. These box constraints are characterized by some parameters that are easily optimized by our proposed nonlinear program. Our proposed tools are tested using two case studies; nonlinear continuous stirred tank reactor (CSTR) and nonlinear batch reactor.