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The partial Latin square extension problem is to fill as many as possible empty cells of a partially filled Latin square. This problem is a useful model for a wide range of applications in diverse domains. This paper presents the first massively parallel evolutionary algorithm algorithm for this computationally challenging problem based on a transformation of the problem to partial graph coloring. The algorithm features the following original elements. Based on a very large population (with more than $10^4$ individuals) and modern graphical processing units, the algorithm performs many local searches in parallel to ensure an intensive exploitation of the search space. The algorithm employs a dedicated crossover with a specific parent matching strategy to create a large number of diversified and information-preserving offspring at each generation. Extensive experiments on 1800 benchmark instances show a high competitiveness of the algorithm compared to the current best performing methods. Competitive results are also reported on the related Latin square completion problem. Analyses are performed to shed lights on the roles of the main algorithmic components. The code of the algorithm will be made publicly available.

The disjunctively constrained knapsack problem consists in packing a subset of pairwisely compatible items in a capacity-constrained knapsack such that the total profit of the selected items is maximized while satisfying the knapsack capacity. DCKP has numerous applications and is however computationally challenging (NP-hard). In this work, we present a threshold search based memetic algorithm for solving the DCKP that combines the memetic framework with threshold search to find high quality solutions. Extensive computational assessments on two sets of 6340 benchmark instances in the literature demonstrate that the proposed algorithm is highly competitive compared to the state-of-the-art methods. In particular, we report 24 and 354 improved best-known results (new lower bounds) for Set I (100 instances) and for Set II (6240 instances), respectively. We analyze the key algorithmic components and shed lights on their roles for the performance of the algorithm. The code of our algorithm will be made publicly available.

Knapsack problems are classic models that can formulate a wide range of applications. In this work, we deal with the Budgeted Maximum Coverage Problem (BMCP), which is a generalized 0-1 knapsack problem. Given a set of items with nonnegative weights and a set of elements with nonnegative profits, where each item is composed of a subset of elements, BMCP aims to pack a subset of items in a capacity-constrained knapsack such that the total weight of the selected items does not exceed the knapsack capacity, and the total profit of the associated elements is maximized. Note that each element is counted once even if it is covered multiple times. BMCP is closely related to the Set-Union Knapsack Problem (SUKP) that is well studied in recent years. As the counterpart problem of SUKP, however, BMCP was introduced early in 1999 but since then it has been rarely studied, especially there is no practical algorithm proposed. By combining the reinforcement learning technique to the local search procedure, we propose a probability learning based tabu search (PLTS) algorithm for addressing this NP-hard problem. The proposed algorithm iterates through two distinct phases, namely a tabu search phase and a probability learning based perturbation phase. As there is no benchmark instances proposed in the literature, we generate 30 benchmark instances with varied properties. Experimental results demonstrate that our PLTS algorithm significantly outperforms the general CPLEX solver for solving the challenging BMCP in terms of the solution quality.

The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by converting it to the well-studied TSP. For this purpose, we first investigate a technique to convert a CTSP instance to a TSP and then apply powerful TSP solvers (including exact and heuristic solvers) to solve the resulting TSP instance. We want to answer the following questions: How do state-of-the-art TSP solvers perform on clustered instances converted from the CTSP? Do state-of-the-art TSP solvers compete well with the best performing methods specifically designed for the CTSP? For this purpose, we present intensive computational experiments on various benchmark instances to draw conclusions., Comment: 26 pages, 6 figures

Site-testing is crucial for achieving the goal of scientific research and analysis of meteorological and optical observing conditions is one of the basic tasks of it. As one of three potential sites to host 12-meter Large Optical/infrared Telescope (LOT), Muztagh-ata site which is located on the Pamirs Plateau in west China's Xinjiang began its site-testing task in the spring of 2017. In this paper, we firstly start with an introduction to the site and then present a statistical analysis of the ground-level meteorological properties such as air temperature, barometric pressure, relative humidity, wind speed and direction, recorded by automatic weather station with standard meteorological sensors for two-year long. We also show the monitoring results of sky brightness during this period., Comment: 16 pages, 19 figures

In this article, we present a detailed analysis of the statistical properties of seeing for the Muztagh-ata site which is the candidate site for hosting future Chinese Large Optical/infrared Telescope (LOT) project. The measurement was obtained with Differential Image Motion Monitor (DIMM) from April 2017 to November 2018 at different heights during different periods. The median seeing at 11 meters and 6 meters are very close but different significantly from that on the ground. We mainly analyzed the seeing at 11 meters monthly and hourly, having found that the best season for observing was from late autumn to early winter and seeing tended to improve during the night only in autumn. The analysis of the dependence on temperature inversion, wind speed, direction also was made and the best meteorological conditions for seeing is given., Comment: 13 pages, 16 figures

The Large Optical/infrared Telescope (LOT) is a ground-based 12m diameter optical/infrared telescope which is proposed to be built in the western part of China in the next decade. Based on satellite remote sensing data, along with geographical, logistical and political considerations, three candidate sites were chosen for ground-based astronomical performance monitoring. These sites include: Ali in Tibet, Daocheng in Sichuan, and Muztagh Ata in Xinjiang. Up until now, all three sites have continuously collected data for two years. In this paper, we will introduce this site testing campaign, and present its monitoring results obtained during the period between March 2017 and March 2019.

Population-based memetic algorithms have been successfully applied to solve many difficult combinatorial problems. Often, a population of fixed size was used in such algorithms to record some best solutions sampled during the search. However, given the particular features of the problem instance under consideration, a population of variable size would be more suitable to ensure the best search performance possible. In this work, we propose variable population memetic search (VPMS), where a strategic population sizing mechanism is used to dynamically adjust the population size during the memetic search process. Our VPMS approach starts its search from a small population of only two solutions to focus on exploitation, and then adapts the population size according to the search status to continuously influence the balancing between exploitation and exploration. We illustrate an application of the VPMS approach to solve the challenging critical node problem (CNP). We show that the VPMS algorithm integrating a variable population, an effective local optimization procedure (called diversified late acceptance search) and a backbone-based crossover operator performs very well compared to state-of-the-art CNP algorithms. The algorithm is able to discover new upper bounds for 13 instances out of the 42 popular benchmark instances, while matching 23 previous best-known upper bounds.

Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications and, however, are computationally difficult. In this work, a general population-based weight learning framework for solving graph coloring problems is presented. Unlike existing methods for graph coloring that are specific to the considered problem, the presented work targets a generic objective by introducing a unified method that can be applied to different graph coloring problems. This work distinguishes itself by its solving approach that formulates the search of a solution as a continuous weight tensor optimization problem and takes advantage of a gradient descent method computed in parallel on graphics processing units. The proposed approach is also characterized by its general global loss function that can easily be adapted to different graph coloring problems. The usefulness of the proposed approach is demonstrated by applying it to solve two typical graph coloring problems and performing large computational studies on popular benchmarks. Improved best-known results (new upper bounds) are reported for several large graphs.

The Set-union Knapsack Problem (SUKP) is a generalization of the popular 0-1 knapsack problem. Given a set of weighted elements and a set of items with profits where each item is composed of a subset of elements, the SUKP involves packing a subset of items in a capacity-constrained knapsack such that the total profit of the selected items is maximized while their weights do not exceed the knapsack capacity. In this work, we present an effective iterated two-phase local search algorithm for this NP-hard combinatorial optimization problem. The proposed algorithm iterates through two search phases: a local optima exploration phase that alternates between a variable neighborhood descent search and a tabu search to explore local optimal solutions, and a local optima escaping phase to drive the search to unexplored regions. We show the competitiveness of the algorithm compared to the state-of-the-art methods in the literature. Specifically, the algorithm discovers 18 improved best results (new lower bounds) for the 30 benchmark instances and matches the best-known results for the 12 remaining instances. We also report the first computational results with the general CPLEX solver, including 6 proven optimal solutions. Finally, we investigate the effectiveness of the key ingredients of the algorithm on its performance.