The inequity aversion pricing problem aims to maximize revenue while providing prices to people connected in a social network such that connected people receive prices that are not too different. This problem is known...
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The inequity aversion pricing problem aims to maximize revenue while providing prices to people connected in a social network such that connected people receive prices that are not too different. This problem is known to be NP-hard even when the number of prices offered is three. This paper provides an extended graph formulation for the problem whose LP-relaxation is shown to be very strong. We show that the extended graph relaxation is integral on a network without any cycle. We develop extended cycle inequalities and show that the extended cycle inequalities cut off all the fractional extreme points of the extended graph relaxation on a cycle. We generalize cycle inequalities to zero half cuts performing a Chvatal-Gomory procedure on a cycle. Computational experiments show that the extended graph relaxation results in an integer solution for most problem instances with very small gaps (less than 3%) from optimality for the remaining instances. The addition of zero half cuts reduces the integrality gap significantly on the few difficult instances.
Multi-component devices such as flow machines, heat exchangers, and electric motors present parts with different physical properties and operating in different states. Optimisation algorithms may improve the performan...
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Multi-component devices such as flow machines, heat exchangers, and electric motors present parts with different physical properties and operating in different states. Optimisation algorithms may improve the performance of these devices, and the simultaneous optimisation of a set of parts may harness the interaction of these parts to generate improved designs. Particularly, rotating flow devices such as pumps and turbines present rotating and stationary components. If a description of the fluid flow between the rotating and stationary parts is desired, it is necessary to model solid at different velocities. However, the standard topology optimisation formulation for fluid flow problems considers only a single stationary solid or a single rotating solid in a rotating reference frame. Thus, this work proposes a topology optimisation formulation capable of solving fluid flow problems with different solid velocities. The idea is to add mutually exclusive Darcy terms to the linear momentum equation. Each Darcy term models a different rotation and only one term may be active at each element. The method uses two discrete design variable fields. The moving limits of the optimisation algorithm are adjusted to handle the two discrete design variable fields, and extra constraints are added to ensure proper phase transitions. The algorithm is applied to two design problems: a Tesla pump and a labyrinth seal. The governing equations are solved by the Finite Element Method, and the optimisation is solved by an approach based on the Topology Optimisation of Binary Structures (TOBS) algorithm, with each linearized subproblem being solved through integer linear programming with a branch-and-bound algorithm.
In this work, we address the strategic placement and optimal sizing of electric vehicle charging stations for cities as well as highway traffic to minimize overall cost. We formulate the problem as a Mixed integer Lin...
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Vector bin packing is an NP-hard problem in which a set of item vectors must be packed into a minimum number of bins such that, in each bin, the sum of the vectors does not exceed the bin’s vector capacity. Vector bi...
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We study the extremal behaviour of some integer-valued bivariate time series. Assuming that the distributional behaviour of the innovations is the one introduced in Hüsler et al. (Methodol Comput Appl Probab 24:2...
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For integers k≥3, c≥2, and s≥0, let Mk∗(c,s) be the least integer such that any set of at least Mk∗(c,s) points in the plane in general position, colored with c colors, contains a monochromatic k-gon (not necessari...
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K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis [6] faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-va...
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In this paper, we focus on integer sequences corresponding to the number of vertices in k-iterated line digraphs. We begin by introducing the core concepts related to digraphs. Then, we describe a method, proposed by ...
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An FPGA routing architecture consists of wire segments of different lengths. FPGA routers attempt to use longer wires for distant connections and shorter ones for closer connections. Due to the overhead associated wit...
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Recently, character information has been successfully introduced into the encoder-decoder event detection model to relieve the trigger-word mismatch problem, thus achieving impressive results in the languages without ...
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Recently, character information has been successfully introduced into the encoder-decoder event detection model to relieve the trigger-word mismatch problem, thus achieving impressive results in the languages without natural delimiters (i.e., Chinese). However, it is introduced into the encoder or the decoder separately, which makes the advantage of character information not be captured and represented adequately for event detection. In this article, we proposed a novel method to model character information in both the encoding and decoding stages to advance the neural event detection model. In particular, the proposed method can encode both words and characters and predict their event types jointly and further leverage interactions between word and its characters to optimize the inference. Experimental results show that the proposed model outperforms previous event detection methods on the ACE2005 Chinese benchmark. We release our code at Github.(1)
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