Franco Mascia

Reactive Search and Intelligent Optimization

Reactive Search integrates sub-symbolic machine learning techniques into search heuristics for solving complex optimization problems. By automatically adjusting the working parameters, a reactive search self-tunes and adapts, effectively learning by doing until a solution is found. Intelligent Optimization, a superset of Reactive Search, concerns online and off-line schemes based on the use of memory, adaptation, incremental development of models, experimental algorithms applied to optimization, intelligent tuning and design of heuristics. Reactive Search and Intelligent Optimization is an excellent introduction to the main principles of reactive search, as well as an attempt to develop some fresh intuition for the approaches. The book looks at different optimization possibilities with an emphasis on opportunities for learning and self-tuning strategies. While focusing more on methods than on problems, problems are introduced wherever they help make the discussion more concrete, or when a specific problem has been widely studied by reactive search and intelligent optimization heuristics. Individual chapters cover reacting on the neighborhood; reacting on the annealing schedule; reactive prohibitions; model-based search; reacting on the objective function; relationships between reactive search and reinforcement learning; and much more. Each chapter is structured to show basic issues and algorithms; the parameters critical for the success of the different methods discussed; and opportunities and schemes for the automated tuning of these parameters. Anyone working in decision making in business, engineering, economics or science will find a wealth of information here.

Cooperating local search for the maximum clique problem

The advent of desktop multi-core computers has dramatically improved the usability of parallel algorithms which, in the past, have required specialised hardware. This paper introduces cooperating local search (CLS), a parallelised hyper-heuristic for the maximum clique problem. CLS utilises cooperating low level heuristics which alternate between sequences of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, where vertices of the current clique are swapped with vertices not in the current clique. These low level heuristics differ primarily in their vertex selection techniques and their approach to dealing with plateaus. To improve the performance of CLS, guidance information is passed between low level heuristics directing them to particular areas of the search domain. In addition, CLS dynamically reconfigures the allocation of low level heuristics to cores, based on information obtained during a trial, to ensure that the mix of low level heuristics is appropriate for the instance being optimised. CLS has no problem instance dependent parameters, improves the state-of-the-art performance for the maximum clique problem over all the BHOSLIB benchmark instances and attains unprecedented consistency over the state-of-the-art on the DIMACS benchmark instances.

Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools

Several grammar-based genetic programming algorithms have been proposed in the literature to automatically generate heuristics for hard optimization problems. These approaches specify the algorithmic building blocks and the way in which they can be combined in a grammar; the best heuristic for the problem being tackled is found by an evolutionary algorithm that searches in the algorithm design space defined by the grammar. In this work, we propose a novel representation of the grammar by a sequence of categorical, integer, and real-valued parameters. We then use a tool for automatic algorithm configuration to search for the best algorithm for the problem at hand. Our experimental evaluation on the one-dimensional bin packing problem and the permutation flowshop problem with weighted tardiness objective shows that the proposed approach produces better algorithms than grammatical evolution, a well-established variant of grammar-based genetic programming. The reasons behind such improvement lie both in the representation proposed and in the method used to search the algorithm design space.

From Grammars to Parameters: Automatic Iterated Greedy Design for the Permutation Flow-Shop Problem with Weighted Tardiness

Recent advances in automatic algorithm configuration have made it possible to configure very flexible algorithmic frameworks in order to fine-tune them for particular problems. This is often done by the use of automatic methods to set the values of algorithm parameters. A rather different approach uses grammatical evolution, where the possible algorithms are implicitly defined by a context-free grammar. Possible algorithms may then be instantiated by repeated applications of the rules in the grammar. Through grammatical evolution, such an approach has shown to be able to generate heuristic algorithms. In this paper we show that the process of instantiating such a grammar can be described in terms of parameters. The number of parameters increases with the maximum number of applications of the grammar rules. Therefore, this approach is only practical if the number of rules and depth of the derivation tree are bounded and relatively small. This is often the case in the heuristic-generating grammars proposed in the literature, and, in such cases, we show that the parametric representation may lead to superior performance with respect to the representation used in grammatical evolution. In particular, we first propose a grammar that generates iterated greedy IG algorithms for the permutation flow-shop problem with weighted tardiness minimization. Next, we show how this grammar can be represented in terms of parameters. Finally, we compare the quality of the IG algorithms generated by an automatic configuration tool using the parametric representation versus using the codon-based representation of grammatical evolution. In our scenario, the parametric approach leads to significantly better IG algorithms.

Automatic Design of Hybrid Stochastic Local Search Algorithms

Many stochastic local search (SLS) methods rely on the manipulation of single solutions at each of the search steps. Examples are iterative improvement, iterated local search, simulated annealing, variable neighborhood search, and iterated greedy. These SLS methods are the basis of many state-of-the-art algorithms for hard combinatorial optimization problems. Often, several of these SLS methods are combined with each other to improve performance. We propose here a practical, unified structure that encompasses several such SLS methods. The proposed structure is unified because it integrates these metaheuristics into a single structure from which we can not only instantiate each of them, but we also can generate complex combinations and variants. Moreover, the structure is practical since we propose a method to instantiate actual algorithms for practical problems in a semi-automatic fashion. The method presented in this work implements a general local search structure as a grammar; an instantiation of such a grammar is a program that can be compiled into executable form. We propose to find the appropriate grammar instantiation for a particular problem by means of automatic configuration. The result is a semi-automatic system that, with little human effort, is able to generate powerful hybrid SLS algorithms.

Reactive and dynamic local search for max-clique: Engineering effective building blocks

This paper presents the results of an ongoing investigation about how different algorithmic building blocks contribute to solving the maximum clique problem. We consider greedy constructions, plateau searches, and more complex schemes based on dynamic penalties and/or prohibitions, in particular the recently proposed technique of dynamic local search and the previously proposed reactive local search (RLS). We design a variation of the original RLS algorithm where the role of long-term memory (LTM) is increased (RLS-LTM). In addition, we consider in detail the effect of the low-level implementation choices on the CPU time per iteration. We present experimental results on randomly generated graphs with different statistical properties, showing the crucial effects of the implementation, the robustness of different techniques, and their empirical scalability.

An algorithm portfolio for the sub-graph isomorphism problem

This work presents an algorithm for the sub-graph isomorphism problem based on a new pruning technique for directed graphs. During the tree search, the method checks if a new association between two vertices is compatible by considering the structure of their local neighborhoods, represented as the number of limited-length paths of different type originating from each vertex. In addition, randomized versions of the algorithms are studied experimentally by deriving their runtime distributions. Finally, algorithm portfolios consisting of multiple instances of the same randomized algorithm are proposed and analyzed. The experimental results on benchmark graphs demonstrate that the new pruning method is competitive w.r.t. recently proposed techniques. Significantly better results are obtained on sparse graphs. Furthermore, even better results are obtained by the portfolios, when both the average and standard deviation of solution times are considered.

Cooperative Strategies and Reactive Search: A Hybrid Model Proposal

Cooperative strategies and reactive search are very promising techniques for solving hard optimization problems, since they reduce human intervention required to set up a method when the resolution of an unknown instance is needed. However, as far as we know, a hybrid between both techniques has not yet been proposed in the literature. In this work, we show how reactive search principles can be incorporated into a simple rule-driven centralised cooperative strategy. The proposed method has been tested on the Uncapacitated Single Allocation p-Hub Median Problem, obtaining promising results.

Tuning Algorithms for Tackling Large Instances: An Experimental Protocol

Tuning stochastic local search algorithms for tackling large instances is difficult due to the large amount of CPU-time that testing algorithm configurations requires on such large instances. We define an experimental protocol that allows tuning an algorithm on small tuning instances and extrapolating from the obtained configurations a parameter setting that is suited for tackling large instances. The key element of our experimental protocol is that both the algorithm parameters that need to be scaled to large instances and the stopping time that is employed for the tuning instances are treated as free parameters. The scaling law of parameter values, and the computation time limits on the small instances are then derived through the minimization of a loss function. As a proof of concept, we tune an iterated local search algorithm and a robust tabu search algorithm for the quadratic assignment problem.

On the sensitivity of reactive tabu search to its meta-parameters

In this paper, we assess the sensitivity of reactive tabu search to its meta-parameters. Based on a thorough experimental analysis of reactive tabu search applications to the quadratic assignment and the maximum clique problem, we show that its performance is relatively insensitive to its meta-parameters. This is particularly evident when compared to the sensitivity of tabu search to its parameters: tabu search is rather penalized if used with sub-optimal parameter settings. Reactive tabu search does not strongly pay its high parameter robustness in terms of performance, although it does not improve the peak performance of tabu search.