In this paper, genetic algorithms for the unconstrained binary quadratic programming problem (BQP) are presented. It is shown that for small problems a simple genetic algorithm with uniform crossover is sufficient to find optimum or best-known solutions in short time, while for problems with a high number of variables (n 200) it is essential to incorporate local search to arrive at high-quality solutions. A hybrid genetic algorithm incorporating local search is tested on 40 problem instances of sizes containing between n = 200 and n = 2500. The results of the computer experiments show that the approach is comparable to alternative heuristics such as tabu search for small instances and superior to tabu search and simulated annealing for large instances. New best solutions could be found for 14 large problem instances. 1 INTRODUCTION In the unconstrained binary quadratic programming problem (BQP), a symmetric rational n \Theta n matrix Q = (q ij ) is given, and a binary vector of leng...

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This paper presents a memetic algorithm, a highly eective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a tness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes | besides a highly eective randomized k-opt local search | a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally dierent from traditional crossover operators, since new genetic material is included in the ospring which is not contained in one of the parents.

Abstract. Given a set of objects with profits (any, even negative, numbers) assigned not only to separate objects but also to pairs of them, the unconstrained binary quadratic optimization problem consists in finding a subset of objects for which the overall profit is maximized. In this paper, an iterated tabu search algorithm for solving this problem is proposed. Computational results for problem instances of size up to 7000 variables (objects) are reported and comparisons with other up-to-date heuristic methods are provided. Key words: binary quadratic optimization, iterated tabu search, heuristics. 1.

This paper presents a local search algorithm based on variable depth search, called the k-opt local search, for the maximum clique problem. The k-opt local search performs add and drop moves, each of which can be interpreted as 1-opt move, to search a k-opt neighborhood solution at each iteration until no better k-opt neighborhood solution can be found. To evaluate our k-opt local search algorithm, we repeatedly apply the local search for each of DIMACS benchmark graphs and compare with the state-of-the-art metaheuristics such as the genetic local search and the iterated local search reported previously. The computational results show that in spite of the absence of major metaheuristic components, the k-opt local search is capable of finding better (at least the same) solutions on average than those obtained by these metaheuristics for all the graphs.

We introduce a metaheuristic framework for combinatorial optimization. Our framework is similar to others (e.g. [1]) in that it is modular enough that important components can be independently developed. Ours is different in several aspects. It supports several built-in components such as combinatorial representations and search heuristics to facilitate the creation of a new optimizer for a wide range of combinatorial problems. The inclusion of different types of metaheuristics allows us to compose them and create a hybrid search that is on average better than each individual metaheuristic. Additionally, the system guarantees the feasibility of returned solutions for combinatorial problems that permit infeasible solutions. We, further, propose a generic method to optimize bottle-neck problems efficiently under the local-search framework.

Summary. Two key issues in local search algorithms are the definition of a neighborhood and the way to examine it. In this chapter we consider techniques for examining very large neighborhoods, in particular, ways for exactly searching them. We first illustrate such techniques using three paradigmatic examples. In the largest part of the chapter, we focus on the development and experimental study of very largescale neighborhood search algorithms for two coloring problems. The first example concerns the well-known (vertex) graph coloring problem. Despite initial promising results on the use of very large-scale neighborhoods, our final conclusion was negative: the usage of the proposed very large-scale neighborhoods did not help to improve the performance of effective stochastic local search algorithms. The second example, the graph set T-coloring problem, yielded more positive results. In this case, a very large-scale neighborhood that was specially tailored for this problem and that can be efficiently searched, resulted to be an essential component of a new state-of-the-art algorithm for various instance classes. 1

Abstract. Binary Factor Analysis (BFA) is a typical problem of Independent Component Analysis (ICA) where the signal sources are binary. Parameter learning and model selection in BFA are computationally intractable because of the combinatorial complexity. This paper aims at an efficient approach to BFA. For parameter learning, an unconstrained binary quadratic programming (BQP) is reduced to a canonical dual problem with low computational complexity; for model selection, we adopt the Bayesian Ying-Yang (BYY) framework to make model selection automatically during learning. In the experiments, the proposed approach cdual shows superior performance. Another BQP approximation round is also good in model selection and is more efficient. Two other methods, greedy and enum, are more accurate in BQP but fail to compete with cdual and round in BFA. We conclude that a good optimization is essential in a learning process, but the key task of learning is not simply optimization and an over-accurate optimization may not be preferred. 1

Abstract — Unraveling transcriptional regulatory networks is essential for understanding and predicting cellular responses in different developmental and environmental contexts. Information-theoretic methods of network inference have been shown to produce high-quality reconstructions because of their ability to infer both linear and non-linear dependencies between regulators and targets. In this paper, we introduce MRNETB an improved version of the previous information-theoretic algorithm, MRNET, which has competitive performance with state-of-the-art algorithms. MRNET infers a network by using a forward selection strategy to identify a maximally-independent set of neighbors for every variable. However, a known limitation of algorithms based on forward selection is that the quality of the selected subset strongly depends on the first variable selected. In this paper, we present MRNETB, an improved version of MRNET that overcomes this limitation by using a backward selection strategy followed by a sequential replacement. Our new variable selection procedure can be implemented with the same computational cost as the forward selection strategy. MRNETB was benchmarked against MRNET and two other information-theoretic algorithms, CLR and ARACNE. Our benchmark comprised 15 datasets generated from two regulatory network simulators, 10 of which are from the DREAM4 challenge, which was recently used to compare over 30 network inference methods. To assess stability of our results, each method was implemented with two estimators of mutual information. Our results show that MRNETB has significantly better performance than MRNET, irrespective of the mutual information estimation method. MRNETB also performs comparably to CLR and significantly better than ARACNE indicating that our new variable selection strategy can successfully infer high-quality networks.

Memetic algorithms (MAs) have been shown to be very effective in combinatorial optimization. To provide explanations why, the performance of MAs in terms of efficiency and effectiveness is investigated. Focussing on a special...