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

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

The wireless mobile ad hoc network (MANET) architecture has received a lot of attention recently. This paper considers the access of multiple channels in a MANET with multi-hop communication behavior. We point out several interesting issues when using multiple channels. We then propose a new multi-channel MAC protocol, which is characterized by the following features: (i) it follows an "on-demand" style to assign channels to mobile hosts, (ii) the number of channels required is independent of the network topology and degree, (iii) it flexibly adapts to host mobility and only exchanges few control messages to achieve channel assignment and medium access, and (iv) no clock synchronization is required. Compared to existing protocols, some assign channels to hosts statically (thus a host will occupy a channel even when it has no intention to transmit) some require a number of channels which is a function of the maximum connectivity, and some necessitate a clock synchronization among all hosts in the MANET. Extensive simulations are conducted to evaluate the proposed protocol.

A new multi-channel MAC protocol with on-demand channel assignment for multi-hop mobile ad hoc networks

Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. This survey considers their motivation, complexity, approximation properties, upper and lower bounds, heuristics and probabilistic analysis on random graphs. The result is a complete view of the current state of the art with respect to layout problems from an algorithmic point of view.

A survey of graph layout problems

Two bipartite matching problems arising in Vehicle Scheduling are considered: the capacitated matching and the multicommodity matching. For the former, given a reasonable cost structure, we can exhibit a polynomial time algorithm, while the general case is conjectured to be NP-hard. The latter problem is shown to be NP-hard. A heuristic algorithm based on Lagrangean relaxation for the capacitated version of the multicommodity matching is also presented together with experimental results.

On some matching problems arising in vehicle scheduling models

Hidden terminal interference is caused by the (quasi-) simultaneous transmission of two stations that cannot hear each other, but are both received by the same destination station. This interference lowers the system throughput and increases the average packet delay. Some random access protocols that reduce this interference have been proposed, e.g., BTMA protocol. However, the hidden terminal interference can be totally avoided only by means of code division multiple access (CDMA) schemes. In the paper, the authors investigate the problem of assigning orthogonal codes to stations so as to eliminate the hidden terminal interference. Since the codes share the fixed channel capacity allocated to the network in the design stage, their number must not exceed a given bound. The authors seek assignments that minimize the number of codes used. They show that this problem is NP-complete, and thus computationally intractable, even for very restricted but very realistic network topologies. Then, they present optimal algorithms for further restricted topologies, as well as fast suboptimal centralized and distributed heuristic algorithms. The results of extensive simulation set up to derive the average performance of the proposed heuristics on realistic network topologies are presented. >

Code assignment for hidden terminal interference avoidance in multihop packet radio networks

Dominating sets for split and bipartite graphs

New heuristic algorithms are proposed for the Graph Partitioning problem. A greedy construction scheme with an appropriate tie-breaking rule (MIN-MAX-GREEDY) produces initial assignments in a very fast time. For some classes of graphs, independent repetitions of MIN-MAX-GREEDY are sufficient to reproduce solutions found by more complex techniques. When the method is not competitive, the initial assignments are used as starting points for a prohibition-based scheme, where the prohibition is chosen in a randomized and reactive way, with a bias towards more successful choices in the previous part of the run. The relationship between prohibition-based diversification (Tabu Search) and the variable-depth Kernighan-Lin algorithm is discussed, Detailed experimental results are presented on benchmark suites used in the previous literature, consisting of graphs derived from parametric models (random graphs, geometric graphs, etc.) and of "real-world" graphs of large size. On the first series of graphs, a better performance for equivalent or smaller computing times is obtained, while, on the large "real-world" instances, significantly better results than those of multilevel algorithms are obtained, but for a much larger computational effort.

/pdf/greedy-prohibition-and-reactive-heuristics-for-graph-2r4bjibjif.pdf

Alan A. Bertossi

Papers

On some matching problems arising in vehicle scheduling models

Code assignment for hidden terminal interference avoidance in multihop packet radio networks

Dominating sets for split and bipartite graphs

Greedy, prohibition, and reactive heuristics for graph partitioning

The edge Hamiltonian path problem is NP-complete