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Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to find a subset which is robust against (i.e., is good over) a number of possible objective functions due to uncertainty, resulting in the problem of robust subset selection. This paper considers robust subset selection with monotone objective functions, relaxing the submodular property required by previous studies. We first show that the greedy algorithm can obtain an approximation ratio with respect to the correlation and submodularity ratios of the objective functions; and then propose EPORSS, an evolutionary Pareto optimization algorithm that can utilize more time to find better subsets. We prove that EPORSS can also be theoretically grounded, achieving a similar approximation guarantee to the greedy algorithm. In addition, we derive the lower bound of the correlation ratio for the application of robust influence maximization, and further conduct experiments to validate the performance of the greedy algorithm and EPORSS.

The problem of selecting a sequence of items that maximizes a given submodular function appears in many real-world applications. Existing study on the problem only considers uniform costs over items, but non-uniform costs on items are more general. Taking this cue, we study the problem of budgeted sequence submodular maximization (BSSM), which introduces non-uniform costs of items into the sequence selection. This problem can be found in a number of applications such as movie recommendation, course sequence design and so on. Non-uniform costs on items significantly increase the solution complexity and we prove that BSSM is NP-hard. To solve the problem, we first propose a greedy algorithm GBM with an error bound. We also design an anytime algorithm POBM based on Pareto optimization to improve the quality of solutions. Moreover, we prove that POBM can obtain approximate solutions in expected polynomial running time, and converges faster than a state-of-the-art algorithm POSEQSEL for sequence submodular maximization with cardinality constraints. We further introduce optimizations to speed up POBM. Experimental results on both synthetic and real-world datasets demonstrate the performance of our new algorithms.

Previous work introduced the concept of progress states. After expanding a progress state, a greedy best-first search (GBFS) will only expand states with lower heuristic values. Current methods can identify progress states only for a single task and only after a solution for the task has been found. We introduce a novel approach that learns a description logic formula characterizing all progress states in a classical planning domain. Using the learned formulas in a GBFS to break ties in favor of progress states often significantly reduces the search effort.

We revisit Depth-First Proof-Number Search (DFPN), a well-known algorithm for solving two-player games. First, we consider the completeness property of the algorithm and its variants, i.e., whether they always find a winning strategy when there exists one. While it is known that the standard version is not complete, we show that the combination with the simple Threshold Controlling Algorithm is complete, solving an open problem from the area. Second, we modify DFPN to compute a diverse set of solutions rather than just a single one. Finally, we apply this new variant in Chemistry to the synthesis planning of new target molecules (Retrosynthesis). In this domain a diverse set of many solutions is desirable. We apply additional modifications from the literature to the algorithm and show that it outperforms Monte-Carlo Tree-Search, another well-known algorithm for the same problem, according to a natural diversity measure.

Local search is a popular technique to solve combinatorial optimization problems efficiently. To escape local minima one generally uses metaheuristics or try to design large neighborhoods around the current best solution. A somewhat more black box approach consists in using an optimization solver to explore a large neighborhood. This is the large-neighborhood search (LNS) idea that we reuse in this work. We introduce a generic neighborhood exploration algorithm based on restricted decision diagrams (DD) constructed from the current best solution. We experiment DD-LNS on two sequencing problems: the traveling salesman problem with time windows (TSPTW) and a production planning problem (DLSP). Despite its simplicity, DD-LNS is competitive with the state-of-the-art MIP approach on DLSP. It is able to improve the best known solutions of some standard instances for TSPTW and even to prove the optimality of quite a few other instances.

Iterative Budgeted Exponential Search (IBEX) is a general search algorithm that can limit the number of re-expansions performed in common problems like iterative-deepening tree search and search with inconsistent heuristics. IBEX has been adapted into a specific tree algorithm, Budgeted Tree Search (BTS), which behaves like IDA* when the problem instance is well-behaved but keeps the worst-case guarantees when problems are not well-behaved. The analogous algorithms on graphs, Budgeted Graph Search (BGS), do not have these same properties. This paper reformulates BGS into Efficient Budgeted Graph Search (BGSe), showing how to implement the algorithm so that it behaves identically to A* when problems are well-behaved, and retains the best-case performance otherwise. Experimental results validate the performance of BGSe on a range of theoretical and practical problem instances.

We define a new setting related to the evaluation of AND-OR directed acyclic graphs with partially ordered values. Such graphs arise naturally when solving games with incomplete information (e.g. most card games such as Bridge) or games with multiple criteria. In particular, this setting generalises standard AND-OR graph evaluation and computation of optimal strategies in games with complete information. Under this setting, we propose a new algorithm which uses both alpha-beta pruning and cached values. In this paper, we present our algorithm, prove its correctness, and give experimental results on a card game with incomplete information.

We present an efficient Neural Neighborhood Search (N2S) approach for pickup and delivery problems (PDPs). In specific, we design a powerful Synthesis Attention that allows the vanilla self-attention to synthesize various types of features regarding a route solution. We also exploit two customized decoders that automatically learn to perform removal and reinsertion of a pickup-delivery node pair to tackle the precedence constraint. Additionally, a diversity enhancement scheme is leveraged to further ameliorate the performance. Our N2S is generic, and extensive experiments on two canonical PDP variants show that it can produce state-of-the-art results among existing neural methods. Moreover, it even outstrips the well-known LKH3 solver on the more constrained PDP variant. Our implementation for N2S is available online.

In Real-Time Heuristic Search (RTHS) we are given a search graph G, a heuristic, and the objective is to find a path from a given start node to a given goal node in G. As such, one does not impose any trajectory constraints on the path, besides reaching the goal. In this paper we consider a version of RTHS in which temporally extended goals can be defined on the form of the path. Such goals are specified in Linear Temporal Logic over Finite Traces (LTLf), an expressive language that has been considered in many other frameworks, such as Automated Planning, Synthesis, and Reinforcement Learning, but has not yet been studied in the context of RTHS. We propose a general automata-theoretic approach for RTHS, whereby LTLf goals are supported as the result of searching over the cross product of the search graph and the automaton for the LTLf goal; specifically, we describe LTL-LRTA*, a version of LSS-LRTA*. Second, we propose an approach to produce heuristics for LTLf goals, based on existing goal-dependent heuristics. Finally, we propose a greedy strategy for RTHS with LTLf goals, which focuses search to make progress over the structure of the automaton; this yields LTL-LRTA*+A. In our experimental evaluation over standard benchmarks we show LTL-LRTA*+A may outperform LTL-LRTA* substantially for a variety of LTLf goals.

In this paper, we propose a new hyper-heuristic approach that uses reinforcement learning to automatically learn the selection of low-level heuristics across a wide range of problem domains. We provide a detailed analysis and evaluation of the algorithm components, including different ways to represent the hyper-heuristic state space and reset strategies to avoid unpromising areas of the solution space. Our methods have been evaluated using HyFlex, a well-known benchmarking framework for cross-domain hyper-heuristics, and compared with state-of-the-art approaches. The experimental evaluation shows that our reinforcement-learning based approach produces results that are competitive with the state-of-the-art, including the top participants of the Cross Domain Hyper-heuristic Search Competition 2011.

Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to achieve high quality results. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for chance constrained optimization. We study the scenario of stochastic components that are independent and Normally distributed. Considering the simple single-objective (1+1)~EA, we show that imposing an additional uniform constraint already leads to local optima for very restricted scenarios and an exponential optimization time. We therefore introduce a multi-objective formulation of the problem which trades off the expected cost and its variance. We show that multi-objective evolutionary algorithms are highly effective when using this formulation and obtain a set of solutions that contains an optimal solution for any possible confidence level imposed on the constraint. Furthermore, we prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem. Experimental investigations on instances of the NP-hard stochastic minimum weight dominating set problem confirm the benefit of the multi-objective approach in practice.

In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition matroid constraint to (1) propose algorithms with theoretical bound and efficient query complexity; and (2) provide better analysis on theoretical performance guarantee of some existing techniques. We further investigate those algorithms' performance in two applications: Boosting Influence Spread and Video Summarization. Experiments show our algorithms return comparative results to the state-of-the-art algorithms while taking much fewer queries.

Neural network pruning is a popular model compression method which can significantly reduce the computing cost with negligible loss of accuracy. Recently, filters are often pruned directly by designing proper criteria or using auxiliary modules to measure their importance, which, however, requires expertise and trial-and-error. Due to the advantage of automation, pruning by evolutionary algorithms (EAs) has attracted much attention, but the performance is limited for deep neural networks as the search space can be quite large. In this paper, we propose a new filter pruning algorithm CCEP by cooperative coevolution, which prunes the filters in each layer by EAs separately. That is, CCEP reduces the pruning space by a divide-and-conquer strategy. The experiments show that CCEP can achieve a competitive performance with the state-of-the-art pruning methods, e.g., prune ResNet56 for 63.42% FLOPs on CIFAR10 with -0.24% accuracy drop, and ResNet50 for 44.56% FLOPs on ImageNet with 0.07% accuracy drop.

The diversified top-k weight clique (DTKWC) search problem is an important generalization of the diversified top-k clique (DTKC) search problem with extensive applications, which extends the DTKC search problem by taking into account the weight of vertices. In this paper, we formulate DTKWC search problem using mixed integer linear program constraints and propose an efficient hybrid evolutionary algorithm (HEA-D) that combines a clique-based crossover operator and an effective simulated annealing-based local optimization procedure to find high-quality local optima. The experimental results show that HEA-D performs much better than the existing methods on two representative real-world benchmarks.

The p-next center problem (pNCP) is an extension of the classical p-center problem. It consists of locating p centers from a set of candidate centers and allocating both a reference and a backup center to each client, to minimize the maximum cost, which is the length of the path from a client to its reference center and then to its backup center. Among them, the reference center is the closest center to a client and serves it under normal circumstances, while the backup center is the closest center to the reference center and serves the client when the reference center is out of service. In this paper, we propose a weighting-based tabu search algorithm called WTS for solving pNCP. WTS optimizes the pNCP by solving its decision subproblems with given assignment costs with an efficient swap-based neighborhood structure and a hierarchical penalty strategy for neighborhood evaluation. Extensive experimental studies on 413 benchmark instances demonstrate that WTS outperforms the state-of-the-art methods in the literature. Specifically, WTS improves 12 previous best known results and matches the optimal results for all remaining 401 ones in a much shorter time than other algorithms. More importantly, WTS reaches the lower bounds for 10 instances for the first time.