We study the problem of selecting a set of shelter locations in preparation for natural disasters. Shelters provide victims of a disaster both a safe place to stay and relief necessities such as food, water and medical support. Individuals from the affected population living in a set of population points go to, or are transported to the assigned open shelters. We aim to take both efficiency and inequity into account, thus we minimize a linear combination of: (i) the mean distance between opened shelter locations and the locations of the individuals assigned to them; and (ii) Gini's Mean Absolute Difference of these distances. We develop a stochastic programming model with a set of scenarios that consider uncertain demand and disruptions in the transportation network. A chance constraint is defined on the total cost of opening the shelters and their capacity expansion. In this stochastic context, a weighted mean of the so-called ex ante and ex post versions of the inequity-averse objective function under uncertainty is optimized. Since the model can be solved to optimality only for small instances, we develop a tailored Genetic Algorithm (GA) that utilizes a mixed-integer programming subproblem to solve this problem heuristically for larger instances. We compare the performance of the mathematical program and the GA via benchmark instances where the model can be solved to optimality or near optimality. It turns out that the GA yields small optimality gaps in much shorter time for these instances. We run the GA also on Istanbul data to drive insights to guide decision-makers for preparation.

The Natural Language for Optimization (NL4Opt) Competition was created to investigate methods of extracting the meaning and formulation of an optimization problem based on its text description. Specifically, the goal of the competition is to increase the accessibility and usability of optimization solvers by allowing non-experts to interface with them using natural language. We separate this challenging goal into two sub-tasks:(1) recognize and label the semantic entities that correspond to the components of the optimization problem; (2) generate a meaning representation (i.e. a logical form) of the problem from its detected problem entities. The first task aims to reduce ambiguity by detecting and tagging the entities of the optimization problems. The second task creates an intermediate representation of the linear programming (LP) problem that is converted into a format that can be used by commercial solvers. In this report, we present the LP word problem dataset and shared tasks for the NeurIPS 2022 competition. Furthermore, we investigate and compare the performance of the ChatGPT large language model against the winning solutions. Through this competition, we hope to bring interest towards the development of novel machine learning applications and datasets for optimization modeling.

Community detection is a fundamental problem in computational sciences with extensive applications in various fields. The most commonly used methods are the algorithms designed to maximize modularity over different partitions of the network nodes. Using 80 real and random networks from a wide range of contexts, we investigate the extent to which current heuristic modularity maximization algorithms succeed in returning maximum-modularity (optimal) partitions. We evaluate (1) the ratio of the algorithms’ output modularity to the maximum modularity for each input graph, and (2) the maximum similarity between their output partition and any optimal partition of that graph. We compare eight existing heuristic algorithms against an exact integer programming method that globally maximizes modularity. The average modularity-based heuristic algorithm returns optimal partitions for only 19.4% of the 80 graphs considered. Additionally, results on adjusted mutual information reveal substantial dissimilarity between the sub-optimal partitions and any optimal partition of the networks in our experiments. More importantly, our results show that near-optimal partitions are often disproportionately dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of commonly used modularity-based heuristics for discovering communities: they rarely produce an optimal partition or a partition resembling an optimal partition. If modularity is to be used for detecting communities, exact or approximate optimization algorithms are recommendable for a more methodologically sound usage of modularity within its applicability limits.

Community detection is a classic problem in network science with extensive applications in various fields. The most commonly used methods are the algorithms designed to maximize modularity over different partitions of the network nodes into communities. Using 80 real and random networks from a wide range of contexts, we investigate the extent to which current heuristic modularity maximization algorithms succeed in returning modularity-maximum (optimal) partitions. We evaluate (1) the ratio of their output modularity to the maximum modularity for each input graph and (2) the maximum similarity between their output partition and any optimal partition of that graph. Our computational experiments involve eight existing heuristic algorithms which we compare against an exact integer programming method that globally maximizes modularity. The average modularity-based heuristic algorithm returns optimal partitions for only 16.9% of the 80 graphs considered. Results on adjusted mutual information show considerable dissimilarity between the sub-optimal partitions and any optimal partitions of the graphs in our experiments. More importantly, our results show that near-optimal partitions tend to be disproportionally dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of commonly used modularity-based algorithms for discovering communities: they rarely return an optimal partition or a partition resembling an optimal partition. Given this finding, developing an exact or approximate algorithm for modularity maximization is recommendable for a more methodologically sound usage of modularity in community detection.

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