A unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, parallel, and distributed metaheuristics Implementing metaheuristics on sequential and parallel machines Using many case studies and treating design and implementation independently, this book gives readers the skills necessary to solve large-scale optimization problems quickly and efficiently. It is a valuable reference for practicing engineers and researchers from diverse areas dealing with optimization or machine learning; and graduate students in computer science, operations research, control, engineering, business and management, and applied mathematics.

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Metaheuristics: From Design to Implementation

This is a survey of "Iterated Local Search", a general purpose metaheuristic for finding good solutions of combinatorial optimization problems. It is based on building a sequence of (locally optimal) solutions by: (1) perturbing the current solution; (2) applying local search to that modified solution. At a high level, the method is simple, yet it allows for a detailed use of problem-specific properties. After giving a general framework, we cover the uses of Iterated Local Search on a number of well studied problems.

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Iterated local search

Functional MRI (fMRI) studies have shown that low-frequency (<0.1 Hz) spontaneous fluctuations of the blood oxygenation level dependent (BOLD) signal during restful wakefulness are coherent within distributed large-scale cortical and subcortical networks (resting state networks, RSNs). The neuronal mechanisms underlying RSNs remain poorly understood. Here, we describe magnetoencephalographic correspondents of two well-characterized RSNs: the dorsal attention and the default mode networks. Seed-based correlation mapping was performed using time-dependent MEG power reconstructed at each voxel within the brain. The topography of RSNs computed on the basis of extended (5 min) epochs was similar to that observed with fMRI but confined to the same hemisphere as the seed region. Analyses taking into account the nonstationarity of MEG activity showed transient formation of more complete RSNs, including nodes in the contralateral hemisphere. Spectral analysis indicated that RSNs manifest in MEG as synchronous modulation of band-limited power primarily within the theta, alpha, and beta bands—that is, in frequencies slower than those associated with the local electrophysiological correlates of event-related BOLD responses.

https://www.pnas.org/content/pnas/107/13/6040.full.pdf

Temporal dynamics of spontaneous MEG activity in brain networks

Metaheuristics are the most exciting development in approximate optimization techniques of the last two decades. They have had widespread successes in attacking a variety of difficult combinatorial optimization problems that arise in many practical areas. This bibliography provides a classification of a comprehensive list of 1380 references on the theory and application of metaheuristics. Metaheuristics include but are not limited to constraint logic programming; greedy random adaptive search procedures; natural evolutionary computation; neural networks; non-monotonic search strategies; space-search methods; simulated annealing; tabu search; threshold algorithms and their hybrids. References are presented in alphabetical order under a number of subheadings.

Metaheuristics: A bibliography

The key idea underlying iterated local search is to focus the search not on the full space of all candidate solutions but on the solutions that are returned by some underlying algorithm, typically a local search heuristic. The resulting search behavior can be characterized as iteratively building a chain of solutions of this embedded algorithm. The result is also a conceptually simple metaheuristic that nevertheless has led to state-of-the-art algorithms for many computationally hard problems. In fact, very good performance is often already obtained by rather straightforward implementations of the metaheuristic. In addition, the modular architecture of iterated local search makes it very suitable for an algorithm engineering approach where, progressively, the algorithms’ performance can be further optimized. Our purpose here is to give an accessible description of the underlying principles of iterated local search and a discussion of the main aspects that need to be taken into account for a successful application of it. In addition, we review the most important applications of this method and discuss its relationship to other metaheuristics.

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Iterated Local Search: Framework and Applications

We study theminimum-cost bounded-skewrouting tree (BST) problem under the linear delay model. This problem captures several engineering tradeoffs in the design of routing topologies with controlled skew. We propose three tradeoff heuristics. (1) For a fixed topology Extended-DME (Ex-DME) extends the DME algorithm for exact zero-skew trees via the concept of a merging region. (2) For arbitrary topology and arbitrary embedding, Extended Greedy-DME (ExG-DME) very closely matches the best known heuristics for the zero-skewcase,and for the infinite-skewcase (i.e., the Steiner minimal tree problem). (3) For arbitrary topology and single-layer (planar) embedding, the Extended Planar-DME (ExP-DME) algorithm exactly matches the best known heuristic for zero-skewplanar routing, and closely approaches the best known performance for the infinite-skewcase. Ourwork provides unifications of the clock routing and Steiner tree heuristic literatures and gives smooth cost-skew tradeoff that enable good engineering solutions.

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On the Bounded-Skew Clock and Steiner Routing Problems

Stochastic hill-climbing algorithms, particularly simulated annealing (SA) and threshold acceptance (TA), have become very popular for global optimization applications. Typical implementations of SA or TA use monotone temperature or threshold schedules, and are not formulated to accommodate practical time limits. We present a new threshold acceptance strategy called Old Bachelor Acceptance (OBA), which has three distinguishing features: (i) it is specifically motivated by the practical requirement of optimization within a prescribed time bound, (ii) the threshold schedule is self-tuning, and (iii) the threshold schedule is non-monotone, with threshold values even allowed to become negative. The standard implementation of the TA method of Dueck and Scheuer is a special case of OBA. Experiments using several classes of symmetric traveling salesman problem instances show that OBA can outperform previous hill-climbing methods for time-critical optimizations. A number of directions for future work are suggeste...

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Old Bachelor Acceptance: A New Class of Non-Monotone Threshold Accepting Methods

This paper presents new single-layer, i.e., planar-embeddable, clock tree constructions with exact zero skew under either the linear or the Elmore delay model. Our method, called Planar-DME, consists of two parts. The first algorithm, called Linear-Planar-DME, guarantees an optimal planar zero-skew clock tree (ZST) under the linear delay model. The second algorithm, called Elmore-Planar-DME, uses the Linear-Planar-DME connection topology in constructing a low-cost ZST according to the Elmore delay model. While a planar ZST under the linear delay model is easily converted to a planar ZST under the Elmore model by elongating tree edges in bottom-up order, our key idea is to avoid unneeded wire elongation by iterating the DME construction of ZST and the bottom-up modification of the resulting nonplanar routing. Costs of our planar ZST solutions are comparable to those of the best previous nonplanar ZST solutions, and substantially improve over previous planar clock routing methods.

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Planar-DME: a single-layer zero-skew clock tree router

Clock routing has become a critical issue in the layout design of high-performance systems. We show that the two passes (bottom-up and top-down) of the DME algorithm [2, 3, 4, 8] can be replaced by a single topdown pass, which yields exactly the same (optimal) solution. From this, we develop a top-down algorithm which dynamically determines and embeds the clock tree topology, such that (i) the embedding is guaranteed to be planar, and (ii) the result has provably minimum total wirelength and minimum pathlength delay for that topology. A simple version of our method produces planar exact zero-skew solutions with total wirelengths that are competitive with the best non-planar exact zero-skew results in the literature.

Planar-DME: improved planar zero-skew clock routing with minimum pathlength delay

We give the first single-layer clock tree construction with exact zero skew according to the Elmore delay model. The previous Linear-Planar-DME method guarantees a planar solution under the linear delay model. In this paper, we use a Linear-Planar-DME variant connection topology to construct a low-cost zero skew tree (ZST) according to the Elmore delay model. While a linear-delay ZST is trivially converted to an Elmore-delay ZST by “detouring” wires, the key idea is to defer this detouring as much as possible to reduce tree cost. Costs of our planar ZST solutions are comparable to those of the best previous non-planar ZST solutions, and substantially improve over previous planar clock routing methods.

Chung-Wen Albert Tsao

Papers

On the Bounded-Skew Clock and Steiner Routing Problems

Old Bachelor Acceptance: A New Class of Non-Monotone Threshold Accepting Methods

Planar-DME: a single-layer zero-skew clock tree router

Planar-DME: improved planar zero-skew clock routing with minimum pathlength delay

Low-cost single-layer clock trees with exact zero Elmore delay skew