Predicting native conformations of a protein sequence is known as de novo structure prediction and is a central challenge in computational biology. Most computational protocols employ Monte Carlo sampling. Evolutionary search algorithms have also been proposed to enhance sampling of near-native conformations. These approaches bias stochastic search by an energy function, even though current energy functions are known to be inaccurate and drive sampling to non-native energy minima. This paper proposes a multiobjective approach which employs Pareto dominance, rather than total energy, to evaluate a conformation. This multiobjective approach accounts for the fact that terms in an energy function are conflicting optimization criteria. Our analysis is conducted on a diverse set of 20 proteins. Results show that employing Pareto dominance, rather than total energy, to guide stochastic search is more effective at sampling conformations which are both lower in energy and near the protein native structure.

In this short position paper, we consider MaxWalkSAT, a local search algorithm for MAP inference in probabilistic graphical models, and lift it to the first-order level, yielding a powerful algorithm for MAP inference in Markov logic networks (MLNs). Lifted MaxWalkSAT is based on the observation that if the MLN is monadic, namely if each predicate is unary then MaxWalkSAT is completely liftable in the sense that no grounding is required at inference time. We propose to utilize this observation in a straight-forward manner: convert the MLN to an equivalent monadic MLN by grounding a subset of its logical variables and then apply lifted MaxWalkSAT on it. It turns out however that the problem of finding the smallest subset of logical variables which when grounded will yield a monadic MLN is NP-hard in general and therefore we propose an approximation algorithm for solving it.

We propose a new perspective on the automated design of combinatorial search algorithms through an approach that operates at a much higher semantic level than previous algorithm configurators do. Instead of blindly tuning numerical or categorical parameters based on black-box optimization or resorting to a handful of predefined strategies, we propose to automatically search over compositions of search strategies using a light-weight language, while exploiting the semantic knowledge of the modeling language itself to guide the configuration process. Although somewhat reminiscent of the old AI vision that machines will be able to program themselves to solve novel tasks, we believe that the idea restricted to this simple but powerful search language has a chance of success in practice.

CSP solvers usually search a partial assignment search tree.We present a new formalization for CSP solvers, which spansa conceptually different search tree, where each node representssubsets of the original domains for the variables. We experimentwith a simple backtracking algorithm for this searchtree and show that it outperforms a simple backtracking algorithmon the traditional search tree in many cases.

One typically proves infeasibility in satisfiability/constraint satisfaction (or optimality in integer programming) by constructing a tree certificate. However, deciding how to branch in the search tree is hard, and impacts search time drastically. We explore the power of a simple paradigm, that of throwing random darts into the assignment space and then using information gathered by that dart to guide what to do next. This method seems to work well when the number of short certificates of infeasibility is moderate, suggesting that the overhead of throwing darts is more than paid for by the information gained by these darts.

Strong Nash equilibrium (SNE) is an appealing solution concept when rational agents can form coalitions. A strategy profile is an SNE if no coalition of agents can benefit by deviating. We present the first general-purpose algorithms for SNE finding in games with more than two agents. An SNE must simultaneously be a Nash equilibrium (NE) and the optimal solution of multiple non-convex optimization problems. This makes even the derivation of necessary and sufficient mathematical equilibrium constraints difficult. We show that forcing an SNE to be resilient only to pure-strategy deviations by coalitions, unlike for NEs, is only a necessary condition here. Second, we show that the application of Karush-Kuhn-Tucker conditions leads to another set of necessary conditions that are not sufficient. Third, we show that forcing the Pareto efficiency of an SNE for each coalition with respect to coalition correlated strategies is sufficient but not necessary. We then develop a tree search algorithm for SNE finding. At each node, it calls an oracle to suggest a candidate SNE and then verifies the candidate. We show that our new necessary conditions can be leveraged to make the oracle more powerful. Experiments validate the overall approach and show that the new conditions significantly reduce search tree size compared to using NE conditions alone.

Structured prediction is the problem of learning a function from structured inputs to structured outputs with prototypical examples being part-of-speech tagging and image labeling. Inspired by the recent successes of search-based structured prediction, we introduce a new framework for structured prediction called {\em HC-Search}. Given a structured input, the framework uses a search procedure guided by a learned heuristic H to uncover high quality candidate outputs and then uses a separate learned cost function C to select a final prediction among those outputs. We can decompose the regret of the overall approach into the loss due to H not leading to high quality outputs, and the loss due to C not selecting the best among the generated outputs. Guided by this decomposition, we minimize the overall regret in a greedy stage-wise manner by first training H to quickly uncover high quality outputs via imitation learning, and then training C to correctly rank the outputs generated via H according to their true losses. Experiments on several benchmark domains show that our approach significantly outperforms the state-of-the-art methods.

Protein structure prediction is an unsolved problem in computational biology. One great difficulty is due to the unknown factors in the actual energy function. Moreover, the energy models available are often not very informative particularly when spatially similar structures are compared during search. We introduce several novel heuristics to augment the energy model and present a new local search algorithm that exploits these heuristics in a mixed fashion. Although the heuristics individually are weaker in performance than the energy function, their combination interestingly produces stronger results. For standard benchmark proteins on the face centered cubic lattice and a realistic 20x20 energy model, we obtain structures with significantly lower energy than those obtained by the state-of-the-art algorithms. We also report results for these proteins using the same energy model on the cubic lattice.

Heuristic search is a fundamental technique for solving problems in artificial intelligence. However, many heuristic search algorithms, such as A* are limited by the amount of main memory available. External memory search overcomes the memory limitation of A* by taking advantage of cheap secondary storage, such as disk. Previous work in this area assumes that edge costs fall within a narrow range of integer values and relies on uniformed search order. The goal of this dissertation research is to develop novel techniques that enable heuristic search algorithms to solve problems with real values using a best-first search order while exploiting external memory and multiple processors. This work will be organized into four components. The first component will discuss external memory search and present a novel technique for incorporating real-valued edge costs. The second component will present a novel algorithm for solving problems with large branching factors with application to the challenging problem of Multiple Sequence Alignment (MSA). The third component will cover bounded suboptimal external search for practical MSA applications. The final component of this research will be the development of a novel distributed search framework; allowing parallel and external memory heuristic search algorithms to run cooperatively on a commodity computing cluster. Together these four components will enable heuristic search to scale to large problems in practical settings while exploiting modern hardware.

Although the heuristic search algorithm A* is well-known to be optimally efficient, this result explicitly assumes forward search. Bidirectional search has long held promise for surpassing A*'s efficiency, and many varieties have been proposed, but it has proven difficult to achieve robust performance across multiple domains in practice. We introduce a simple bidirectional search technique called Incremental KKAdd that judiciously performs backward search to improve the accuracy of the forward heuristic function for any search algorithm. We integrate this technique with A*, assess its theoretical properties, and empirically evaluate its performance across seven benchmark domains. In the best case, it yields a factor of six reduction in node expansions and CPU time compared to A*, and in the worst case, its overhead is provably bounded by a user-supplied parameter, such as 1%. Viewing performance across all domains, it also surpasses previously proposed bidirectional search algorithms. These results indicate that Incremental KKAdd is a robust way to leverage bidirectional search in practice.