Various tasks in decision making and decision support systems require selecting a preferred subset of a given set of items. Here we focus on problems where the individual items are described using a set of characterizing attributes, and a generic preference specification is required, that is, a specification that can work with an arbitrary set of items. For example, preferences over the content of an online newspaper should have this form: At each viewing, the newspaper contains a subset of the set of articles currently available. Our preference specification over this subset should be provided offline, but we should be able to use it to select a subset of any currently available set of articles, e.g., based on their tags. We present a general approach for lifting formalisms for specifying preferences over objects with multiple attributes into ones that specify preferences over subsets of such objects. We also show how we can compute an optimal subset given such a specification in a relatively efficient manner. We provide an empirical evaluation of the approach as well as some worst-case complexity results.

The identification of performance-optimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide methods for optimizing a target algorithm's performance on a given class of problem instances by varying a set of ordinal and/or categorical parameters. We review a family of local-search-based algorithm configuration procedures and present novel techniques for accelerating them by adaptively limiting the time spent for evaluating individual configurations. We describe the results of a comprehensive experimental evaluation of our methods, based on the configuration of prominent complete and incomplete algorithms for SAT. We also present what is, to our knowledge, the first published work on automatically configuring the CPLEX mixed integer programming solver. All the algorithms we considered had default parameter settings that were manually identified with considerable effort. Nevertheless, using our automated algorithm configuration procedures, we achieved substantial and consistent performance improvements.

Soft goals extend the classical model of planning with a simple model of preferences. The best plans are then not the ones with least cost but the ones with maximum utility, where the utility of a plan is the sum of the utilities of the soft goals achieved minus the plan cost. Finding plans with high utility appears to involve two linked problems: choosing a subset of soft goals to achieve and finding a low-cost plan to achieve them. New search algorithms and heuristics have been developed for planning with soft goals, and a new track has been introduced in the International Planning Competition (IPC) to test their performance. In this note, we show however that these extensions are not needed: soft goals do not increase the expressive power of the basic model of planning with action costs, as they can easily be compiled away. We apply this compilation to the problems of the net-benefit track of the most recent IPC, and show that optimal and satisficing cost-based planners do better on the compiled problems than optimal and satisficing net-benefit planners on the original problems with explicit soft goals. Furthermore, we show that penalties, or negative preferences expressing conditions to avoid, can also be compiled away using a similar idea.

The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers that represent clusters of solutions. The SP-y algorithm generalizes SP to work on the maximum satisfiability (Max-SAT) problem, but the cover interpretation of SP does not generalize to SP-y. In this paper, we formulate the relaxed survey propagation (RSP) algorithm, which extends the SP algorithm to apply to the weighted Max-SAT problem. We show that RSP has an interpretation of estimating marginals over covers violating a set of clauses with minimal weight. This naturally generalizes the cover interpretation of SP. Empirically, we show that RSP outperforms SP-y and other state-of-the-art Max-SAT solvers on random Max-SAT instances. RSP also outperforms state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.

Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR Multi-Valued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is search-based, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inference-based and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.

We consider the problem of optimal planning in stochastic domains with resource constraints, where the resources are continuous and the choice of action at each step depends on resource availability. We introduce the HAO* algorithm, a generalization of the AO* algorithm that performs search in a hybrid state space that is modeled using both discrete and continuous state variables, where the continuous variables represent monotonic resources. Like other heuristic search algorithms, HAO* leverages knowledge of the start state and an admissible heuristic to focus computational effort on those parts of the state space that could be reached from the start state by following an optimal policy. We show that this approach is especially effective when resource constraints limit how much of the state space is reachable. Experimental results demonstrate its effectiveness in the domain that motivates our research: automated planning for planetary exploration rovers.

A new search algorithm for solving distributed constraint optimization problems (DisCOPs) is presented. Agents assign variables sequentially and compute bounds on partial assignments asynchronously. The asynchronous bounds computation is based on the propagation of partial assignments. The asynchronous forward-bounding algorithm (AFB) is a distributed optimization search algorithm that keeps one consistent partial assignment at all times. The algorithm is described in detail and its correctness proven. Experimental evaluation shows that AFB outperforms synchronous branch and bound by many orders of magnitude, and produces a phase transition as the tightness of the problem increases. This is an analogous effect to the phase transition that has been observed when local consistency maintenance is applied to MaxCSPs. The AFB algorithm is further enhanced by the addition of a backjumping mechanism, resulting in the AFB-BJ algorithm. Distributed backjumping is based on accumulated information on bounds of all values and on processing concurrently a queue of candidate goals for the next move back. The AFB-BJ algorithm is compared experimentally to other DisCOP algorithms (ADOPT, DPOP, OptAPO) and is shown to be a very efficient algorithm for DisCOPs.

Addressing the issue of SVMs parameters optimization, this study proposes an efficient memetic algorithm based on Particle Swarm Optimization algorithm (PSO) and Pattern Search (PS). In the proposed memetic algorithm, PSO is responsible for exploration of the search space and the detection of the potential regions with optimum solutions, while pattern search (PS) is used to produce an effective exploitation on the potential regions obtained by PSO. Moreover, a novel probabilistic selection strategy is proposed to select the appropriate individuals among the current population to undergo local refinement, keeping a well balance between exploration and exploitation. Experimental results confirm that the local refinement with PS and our proposed selection strategy are effective, and finally demonstrate effectiveness and robustness of the proposed PSO-PS based MA for SVMs parameters optimization.

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems. The FoBa-gdt algorithm, which uses the gradient information for feature selection at each forward iteration, significantly improves the efficiency of FoBa-obj. In this paper, we systematically analyze the theoretical properties of both forward-backward greedy algorithms. Our main contributions are: 1) We derive better theoretical bounds than existing analyses regarding FoBa-obj for general smooth convex functions; 2) We show that FoBa-gdt achieves the same theoretical performance as FoBa-obj under the same condition: restricted strong convexity condition. Our new bounds are consistent with the bounds of a special case (least squares) and fills a previously existing theoretical gap for general convex smooth functions; 3) We show that the restricted strong convexity condition is satisfied if the number of independent samples is more than $\bar{k}\log d$ where $\bar{k}$ is the sparsity number and $d$ is the dimension of the variable; 4) We apply FoBa-gdt (with the conditional random field objective) to the sensor selection problem for human indoor activity recognition and our results show that FoBa-gdt outperforms other methods (including the ones based on forward greedy selection and L1-regularization).

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems.