This paper studies linear programming (LP) relaxations for solving polynomial programming problems. A polynomial programming problem can be equivalently formulated as a quadratically constrained quadratic program (QCQP) by introducing new variables that represent nonlinear monomials and substituting them within the original formulation. Whereas Reformulation-Linearization Technique (RLT)-based LP relaxations constructed for the original formulation are tight, the relaxations generated using the equivalent lower degree formulations are smaller and require less computational effort to optimize in comparison to the effort the former requires.
In this study, we analyze the strength and tractability of the standard RLT, the J-set, and recursive McCormick relaxations for polynomial programming problems, and identify the superior relaxation depending on the problem characteristics. Extensive computational results are provided to demonstrate the relative effectiveness of the standard RLT, J-set, and recursive McCormick algorithms using problems from the literature and randomly generated test instances.

Little work has explored moral reasoning in adults with autism spectrum disorder (ASD). The present research used two novel scenario-based tasks to investigate how adults with and without ASD reason about moral rules and apply them in everyday interactions. The Rule Transgressions task examined decision-making in situations where breaking a rule might lead to a personal advantage. People with ASD did not differ from control participants in how frequently they chose to carry out the transgressions or their ratings of acceptability.
However, they gave fewer sophisticated rationales to explain why the transgressions were wrong. The Social Intentionality task examined how participants judged and reacted to intentional and accidental transgressions performed by a story character. Both groups judged and responded more harshly to intentional transgressions than unintentional ones, but participants with ASD gave harsher responses overall. The findings suggest some preservation of the understanding of moral rules in ASD, but difficulties in applying and reasoning about these.

This paper addresses the equilibrium traffic assignment problem involving battery electric vehicles (BEVs) with flow-dependent electricity consumption. Due to the limited driving range and the costly/time-consuming recharging process required by current BEVs, as well as the scarce availability of battery charging/swapping stations, BEV drivers usually experience fear that their batteries may run out of power en route. Therefore, when choosing routes, BEV drivers not only try to minimize their travel costs, but also have to consider the feasibility of their routes. Moreover, considering the potential impact of traffic congestion on the electricity consumption of BEVs, the feasibility of routes may be determined endogenously rather than exogenously.
A set of user equilibrium (UE) conditions from the literature is first presented to describe the route choice behaviors of BEV drivers considering flow-dependent electricity consumption. The UE conditions are then formulated as a nonlinear complementarity model. The model is further formulated as a variational inequality (VI) model and is solved using an iterative solution procedure. Numerical examples are provided to demonstrate the proposed models and solution algorithms. Discussions of how to evaluate and improve the system performance with non-unique link flow distribution are offered. A robust congestion pricing model is formulated to obtain a pricing scheme that minimizes the system travel cost under the worst-case tolled flow distribution. Finally, a further extension of the mathematical formulation for the UE conditions is provided.

Column generation is a linear programming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one; often an optimal dual solution to the linear programming relaxation of the restricted master problem is used.
We consider a zero–one linear programming problem that is approached by column generation and present a generic sufficient optimality condition for the restricted master problem to contain the columns required to find an integer optimal solution to the complete problem. The condition is based on dual information, but not necessarily on an optimal dual solution. It is however most natural to apply the condition in a situation when an optimal or near-optimal dual solution is at hand.
We relate our result to a few special cases from the literature, and make some suggestions regarding possible exploitation of the optimality condition in the construction of column generation methods for integer programs.

Structural and geotechnical engineers regularly use response spectra to assess the response of civil infrastructure to earthquakes; however, the underlying concepts of response spectra are often difficult for civil engineering students to grasp. Hardware specifications for two low cost response spectrum devices (RSDs) facilitate an inductive approach for teaching response spectrum concepts to students. The RSDs, which consist of wooden masses, compression springs, and accelerometers, can be excited manually or on a portable shake table to show the effects of mass and stiffness on the dynamic response of structures subjected to earthquake ground motion. Auxiliary Python scripts record real time accelerometer data, enabling students to compare the observed RSD response to numerical computations.

This paper addresses the parallel flowshop scheduling problem with stochastic processing times, where a product composed of several components has to be finished at a particular moment. These components are processed in independent parallel factories, and each factory can be modeled as a permutation flowshop. The processing time of each operation at each factory is a random variable following a given probability distribution. The aim is to find the robust starting time of the operations at each factory in a way that all the components of the product are completed on a given deadline with a user-defined probability. A simheuristic algorithm is proposed in order to minimize each of the following key performance indicators: (i) the makespan in the deterministic version; and (ii) the expected makespan or a makespan percentile in the stochastic version. A set of computational experiments are carried out to illustrate the performance of the proposed methodology by comparing the outputs under different levels of stochasticity.