Stochastic Local Search : Foundations & Applications (The Morgan Kaufmann Series in Artificial Intelligence)
Holger H. Hoos, Thomas Stutzle
Format: PDF / Kindle (mobi) / ePub
Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems in many areas of computer science and operations research, including propositional satisfiability, constraint satisfaction, routing, and scheduling. SLS algorithms have also become increasingly popular for solving challenging combinatorial problems in many application areas, such as e-commerce and bioinformatics.
Hoos and Stutzle offer the first systematic and unified treatment of SLS algorithms. In this groundbreaking new book, they examine the general concepts and specific instances of SLS algorithms and carefully consider their development, analysis and application. The discussion focuses on the most successful SLS methods and explores their underlying principles, properties, and features. This book gives hands-on experience with some of the most widely used search techniques, and provides readers with the necessary understanding and skills to use this powerful tool.
*Provides the first unified view of the field.
*Offers an extensive review of state-of-the-art stochastic local search algorithms and their applications.
*Presents and applies an advanced empirical methodology for analyzing the behavior of SLS algorithms.
*A companion website offers lecture slides as well as source code and Java applets for exploring and demonstrating SLS algorithms.
‘∨’ (disjunction) are deﬁned by the following truth tables: 1.2 Two Prototypical Combinatorial Problems ∧ ¬ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ∨ ⊥ ⊥ ⊥ 19 Remark: There are many different notations for the truth values ‘ ’ and ‘⊥’, including ‘0’ and ‘1’, ‘−1’ and ‘+1’, ‘T’ and ‘F’, as well as ‘TRUE’ and ‘FALSE’. Likewise, the propositional operators ‘¬’, ‘∧’ and ‘∨’ are often denoted ‘–’, ‘∗’ and ‘+’, or ‘NOT’, ‘AND’ and ’OR’. Because the variable set of a propositional formula is always ﬁnite, the
any-time algorithms. Generally, systematic and local search algorithms are somewhat complementary in their applications. An example for this can be found in Kautz and Selman’s work on solving SAT-encoded planning problems, where a fast local search algorithm is used for ﬁnding solutions whose optimality is proven by means of a systematic search algorithm [Kautz and Selman, 1996]. As we will discuss later in more detail, local search algorithms are often advantageous in certain situations,
solution s i := 1 Repeat: choose a most improving neighbour s of s in Ni If g(s ) < g(s): s := s i := 1 Else: i := i + 1 Until i > imax Note: N1 , . . . , N imax is a set of neighbourhood relations, typically ordered according to increasing size of the respective local neighbourhoods. Variable Depth Search (VDS): determine initial candidate solution s tˆ:= s While s is not locally optimal: ⎢ ⎢ Repeat: ⎢ ⎢ ⎢ select best feasible neighbour t ⎢ ⎢ If g(t) < g(tˆ): tˆ:= t ⎢ ⎢ Until construction of
introduces new local optima; in addition, as we will see in Chapter 6, it can be difﬁcult to amortise the overhead cost introduced by the dynamically changing evaluation function by a reduction in the number of search steps required for ﬁnding (high-quality) solutions. The use of adaptive constructive search methods for obtaining good initial solutions for subsequent perturbative SLS methods raises a very similar issue; here, the added cost of the construction method needs to be amortised. Beyond
they have multiple steep segments which correspond to the peaks in probability density (modes). An interesting special case arises for iterative improvement algorithms that cannot escape from local minima regions of the given evaluation function. Once they have encountered such a local minima region, these essentially incomplete 164 Chapter 4 Empirical Analysis of SLS Algorithms algorithms are unable to obtain any further improvements in solution quality. Consequently, as the run-time is