The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

Logical and probabilistic reasoning are closely related. Many examples in each group have natural analogs in the other. One example is the strong relationship between weighted MAX-SAT and MPE. This paper presents a simple reduction of MPE to weighted MAX-SAT. It also investigates approximating MPE by converting it to a weighted MAX-SAT problem, then using the incomplete methods for solving weighted MAX-SAT to generate a solution. We show that converting MPE problems to MAX-SAT problems and using a method designed for MAX-SAT to solve them often produces solutions that are vastly superior to the previous local search methods designed directly for the MPE problem.

Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, cross-fertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired

MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current state-of-the-art MAX-SAT algorithms on various widely studied classes of unweighted and weighted MAX-SAT instances, particularly for Random-3-SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAX-SAT instances.

Abstract. Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Walksat performance can be greatly enhanced by weighting variables instead of clauses, giving the best known results on some benchmarks. The new algorithm uses an efficient weight smoothing technique with no smoothing phase. 1

Finding most probable explanations (MPEs) in graphical models, such as Bayesian belief networks, is a fundamental problem in reasoning under uncertainty, and much effort has been spent on developing effective algorithms for this N P-hard problem. Stochastic local search (SLS) approaches to MPE solving have previously been explored, but were found to be not competitive with state-of-theart branch & bound methods. In this work, we identify the shortcomings of earlier SLS algorithms for the MPE problem and demonstrate how these can be overcome, leading to an SLS algorithm that substantially improves the state-of-the-art in solving hard networks with many variables, large domain sizes, high degree, and, most importantly, networks with high induced width. 1

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances.

The paper explores the power of two systematic Branch and Bound search algorithms that exploit partition-based heuristics, BBBT (a new algorithm for which the heuristic information is constructed during search and allows dynamic variable/value ordering) and its predecessor BBMB (for which the heuristic information is pre-compiled) and compares them against a number of popular local search algorithms for the MPE problem as well as against the recently popular iterative belief propagation algorithms. We show empirically that the new Branch and Bound algorithm, BBBT demonstrates tremendous pruning of the search space far beyond its predecessor, BBMB which translates to impressive time saving for some classes of problems. Second, when viewed as approximation schemes, BBBT/BBMB together are highly competitive with the best known SLS algorithms and are superior, especially when the domain sizes increase beyond 2. The

Rationality is a fundamental concept in economics. Most researchers will accept that human beings are not fully rational. Herbert Simon suggested that we are “bounded rational”. However, it is very difficult to quantify “bounded rationality”, and therefore it is difficult to pinpoint its impact to all those economic theories that depend on the assumption of full rationality. Ariel Rubinstein proposed to model bounded rationality by explicitly specifying the decision makers ’ decision making procedures. This paper takes a computational point of view to Rubinstein’s approach. From a computational point of view, decision procedures can be encoded in algorithms and heuristics. We argue that, everything else being equal, the effective rationality of an agent is determined by its computational power – we refer to this as the CIDER Theory (short for the title of this paper). This is not an attempt to propose a unifying definition of bounded rationality. It is merely a proposal of a computational point of view of bounded rationality. This way of interpreting bounded rationality enables us to (computationally) reason about economic systems when the full rationality assumption is relaxed.

In this paper we explore the impact of caching on search in the context of the recent framework of AND/OR search in graphical models. Specifically, we extend the depth-first AND/OR Branch-and-Bound tree search algorithm to explore an AND/OR search graph by equipping it with an adaptive caching scheme similar to good and no-good recording. Furthermore, we present best-first search algorithms for traversing the same underlying AND/OR search graph and compare both depth-first and best-first approaches empirically. We focus on two common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in belief networks and solving Weighted CSPs (WCSP). In an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive AND/OR search algorithms on a variety of benchmarks including random and real-world problem instances.