Roger Z. Ríos-Mercado

Kidney-paired donation programs assist patients in need of a kidney to swap their incompatible donor with another incompatible patient–donor pair for a suitable kidney in return. The kidney exchange problem (KEP) is a mathematical optimization problem that consists of finding the maximum set of matches in a directed graph representing the pool of incompatible pairs. Depending on the specific framework, these matches can come in the form of (bounded) directed cycles or directed paths. This gives rise to a family of KEP models that have been studied over the past few years. Several of these models require an exponential number of constraints to eliminate cycles and chains that exceed a given length. In this paper, we present enhancements to a subset of existing models that exploit the connectivity properties of the underlying graphs, thereby rendering more compact and tractable models in both cycle-only and cycle-and-chain versions. In addition, an efficient algorithm is developed for detecting violated constraints and solving the problem. To assess the value of our enhanced models and algorithm, an extensive computational study was carried out comparing with existing formulations. The results demonstrated the effectiveness of the proposed approach. For example, among the main findings for edge-based cycle-only models, the proposed (*PRE(i)) model uses a new set of constraints and a small subset of the full set of length-k paths that are included in the edge formulation. The proposed model was observed to achieve a more than 98% reduction in the number of such paths among all tested instances. With respect to cycle-and-chain formulations, the proposed (*ReSPLIT) model outperformed Anderson’s arc-based (AA) formulation and the path constrained-TSP formulation on all instances that we tested. In particular, when tested on a difficult sets of instances from the literature, the proposed (*ReSPLIT) model provided the best results compared to the AA and PC-based models.

The electricity markets continuous and secure operation depends on accurately predicting real-time demand. This study presents an innovative Analogue Moving Average (AnMA) method that uses classical statistical techniques like correlation, regression, and moving averages to improve the accuracy of load demand forecasting. AnMA is designed to correct for biases and unforeseen changes in load demand and offers several desirable attributes, such as high accuracy, speed, robustness, low maintenance, repeatability, and a low computational cost. The study evaluates the performance of AnMA against Naive, exponential smoothing, and Autoregressive Moving Average (ARMA) benchmarks for forecasting horizons ranging from five minutes to two hours multi-step ahead, using data from the preceding four months. The results show that AnMA is competitive with the benchmarks in terms of accuracy while offering dramatically lower computational costs, making it an efficient and highly attractive method.

The uniform capacitated vertex k -center problem is an ???????? -hard combinatorial optimization problem that models real situations where k centers can only attend a maximum number of customers, and the travel time or distance from the customers to their assigned center has to be minimized. This article introduces a polynomial-time constructive heuristic algorithm that exploits the relationship between this problem and the minimum capacitated dominating set problem. The proposed heuristic is based on the one-hop farthest-first heuristic that has proven effective for the uncapacitated version of the problem. We carried out different empirical evaluations of the proposed heuristic, including an analysis of the effect of a parallel implementation of the algorithm, which significantly improved the running time for relatively large instances.