The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximum- likelihood principle, which clearly satisfies these requirements. The core of this method is a simple hill-climbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distance-based method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment of the topology and branch lengths, only a few iterations are sufficient to reach an optimum. We used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches. The reduction of computing time is dramatic in comparison with other maximum-likelihood packages, while the likelihood maximization ability tends to be higher. For example, only 12 min were required on a standard personal computer to analyze a data set consisting of 500 rbcL sequences with 1,428 base pairs from plant plastids, thus reaching a speed of the same order as some popular distance-based and parsimony algorithms. This new method is implemented in the PHYML program, which is freely available on our web page: http://www.lirmm.fr/w3ifa/MAAS/. (Algorithm; computer simulations; maximum likelihood; phylogeny; rbcL; RDPII project.) The size of homologous sequence data sets has in- creased dramatically in recent years, and many of these data sets now involve several hundreds of taxa. More- over, current probabilistic sequence evolution models (Swofford et al., 1996 ; Page and Holmes, 1998 ), notably those including rate variation among sites (Uzzell and Corbin, 1971 ; Jin and Nei, 1990 ; Yang, 1996 ), require an increasing number of calculations. Therefore, the speed of phylogeny reconstruction methods is becoming a sig- nificant requirement and good compromises between speed and accuracy must be found. The maximum likelihood (ML) approach is especially accurate for building molecular phylogenies. Felsenstein (1981) brought this framework to nucleotide-based phy- logenetic inference, and it was later also applied to amino acid sequences (Kishino et al., 1990). Several vari- ants were proposed, most notably the Bayesian meth- ods (Rannala and Yang 1996; and see below), and the discrete Fourier analysis of Hendy et al. (1994), for ex- ample. Numerous computer studies (Huelsenbeck and Hillis, 1993; Kuhner and Felsenstein, 1994; Huelsenbeck, 1995; Rosenberg and Kumar, 2001; Ranwez and Gascuel, 2002) have shown that ML programs can recover the cor- rect tree from simulated data sets more frequently than other methods can. Another important advantage of the ML approach is the ability to compare different trees and evolutionary models within a statistical framework (see Whelan et al., 2001, for a review). However, like all optimality criterion-based phylogenetic reconstruction approaches, ML is hampered by computational difficul- ties, making it impossible to obtain the optimal tree with certainty from even moderate data sets (Swofford et al., 1996). Therefore, all practical methods rely on heuristics that obtain near-optimal trees in reasonable computing time. Moreover, the computation problem is especially difficult with ML, because the tree likelihood not only depends on the tree topology but also on numerical pa- rameters, including branch lengths. Even computing the optimal values of these parameters on a single tree is not an easy task, particularly because of possible local optima (Chor et al., 2000). The usual heuristic method, implemented in the pop- ular PHYLIP (Felsenstein, 1993 ) and PAUP ∗ (Swofford, 1999 ) packages, is based on hill climbing. It combines stepwise insertion of taxa in a growing tree and topolog- ical rearrangement. For each possible insertion position and rearrangement, the branch lengths of the resulting tree are optimized and the tree likelihood is computed. When the rearrangement improves the current tree or when the position insertion is the best among all pos- sible positions, the corresponding tree becomes the new current tree. Simple rearrangements are used during tree growing, namely "nearest neighbor interchanges" (see below), while more intense rearrangements can be used once all taxa have been inserted. The procedure stops when no rearrangement improves the current best tree. Despite significant decreases in computing times, no- tably in fastDNAml (Olsen et al., 1994 ), this heuristic becomes impracticable with several hundreds of taxa. This is mainly due to the two-level strategy, which sepa- rates branch lengths and tree topology optimization. In- deed, most calculations are done to optimize the branch lengths and evaluate the likelihood of trees that are finally rejected. New methods have thus been proposed. Strimmer and von Haeseler (1996) and others have assembled four- taxon (quartet) trees inferred by ML, in order to recon- struct a complete tree. However, the results of this ap- proach have not been very satisfactory to date (Ranwez and Gascuel, 2001 ). Ota and Li (2000, 2001) described

A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood.

https://leeds-faculty.colorado.edu/glover/TS%20-%20Future%20Paths%20for%20Integer%20Programming.pdf

Future paths for integer programming and links to artificial intelligence

The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

/pdf/metaheuristics-in-combinatorial-optimization-overview-and-menr0q3bxw.pdf

Metaheuristics in combinatorial optimization: Overview and conceptual comparison

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.

/pdf/metaheuristics-from-design-to-implementation-1vqdfv8nk9.pdf

Metaheuristics: From Design to Implementation

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

/pdf/branch-and-price-column-generation-for-solving-huge-integer-4jvlny6blr.pdf

Branch-And-Price: Column Generation for Solving Huge Integer Programs

computational bounds for local search in combinatorial local search algorithms for combinatorial problems local search algorithms for solving the combinatorial a dual local search framework for combinatorial the max-min ant system and local search for combinatorial a framework for local combinatorial optimization problems local search in combinatorial optimization mifou local search in combinatorial optimization radarx heuristics and local search paginas.fe.up local search in combinatorial optimization banani local search in combinatorial optimization integrating interval estimates of global optima and local local search in combinatorial optimization holbarto a fuzzy valuation-based local search framework for local search in combinatorial optimization gbv gentle introduction to local search in combinatorial e cient local search for several combinatorial introduction: combinatorial problems and search on application of the local search optimization online local search for combinatorial optimisation problems how to choose solutions for local search in multiobjective a hybrid of inference and local search for distributed on set-based local search for multiobjective combinatorial localsolver: black-box local search for combinatorial on local optima in multiobjective combinatorial sets of interacting scalarization functions in local introduction e r optimization online estimation-based local search for stochastic combinatorial advanced search combinatorial problems sas/or user's guide: local search optimization how easy is local search? univerzita karlova metaheuristic search for combinatorial optimization local search genetic algorithms for the job shop towards a formalization of combinatorial local search dynamic and adaptive neighborhood search in combinatorial global search in combinatorial optimization using a framework for the development of local search heuristics a feasibility-preserving local search operator for hybrid metaheuristics in combinatorial optimization: a survey consultant-guided search algorithms with local search for a new optimization algorithm for combinatorial problems hybrid metaheuristics in combinatorial optimization: a survey network algorithms colorado state university model-based search for combinatorial optimization: a local and global optimization stochastic local search algorithms for multiobjective corso (collaborative reactive search optimization local search in combinatorial optimization zaraa

Local Search in Combinatorial Optimization

We consider the n-period economic lot sizing problem, where the cost coefficients are not restricted in sign. In their seminal paper, H. M. Wagner and T. M. Whitin proposed an O(n2) algorithm for the special case of this problem, where the marginal production costs are equal in all periods and the unit holding costs are nonnegative. It is well known that their approach can also be used to solve the general problem, without affecting the complexity of the algorithm. In this paper, we present an algorithm to solve the economic lot sizing problem in O(n log n) time, and we show how the Wagner-Whitin case can even be solved in linear time. Our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure. Furthermore, we show how Wagner and Whitin's and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem.

/pdf/economic-lot-sizing-an-o-n-log-n-algorithm-that-runs-in-2pj4bj79p9.pdf

Economic lot sizing: an O ( n log n ) algorithm that runs in linear time in the Wagner-Whitin case

In vehicle routing problems with time windows, a fixed fleet of vehicles of limited capacity is available at a depot to serve a set of clients with given demands. Each client must be visited within a given time window. We describe a branch-and-bound method that minimizes the total route length, and present some computational results.

Vehicle routing with time windows

In interval scheduling, not only the processing times of the jobs but also their starting times are given. This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given "maximal" machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/nav.20231

Interval scheduling: A survey

Totally-balanced and greedy matrices are $( 0,1 )$-matrices defined by excluding certain submatrices. For a $n \times m \,( 0,1)$-matrix A we show that the linear programming problem $\max \{ by \mid yA\leqq c,0\leqq y\leqq d \}$ can be solved by a greedy algorithm for all $c\geqq 0$, $d\geqq 0$ and $b_1 \geqq b_2 \geqq \cdots \geqq b_n \geqq 0$, if and only if A is a greedy matrix. Furthermore we show constructively that if b is an integer, then the corresponding primal problem $\min \{ cx + dz \mid Ax + z\geqq b,x\geqq 0,z\geqq 0 \}$ has an integer optimal solution. A polynomial-time algorithm is presented to transform a totally-balanced matrix into a greedy matrix as well as to recognize a totallybalanced matrix. This transformation algorithm together with the result on greedy matrices enables us to solve a class of integer programming problems defined on totally-balanced matrices. Two examples arising in tree location theory are presented.

Antoon W. J. Kolen

Papers

Local Search in Combinatorial Optimization

Economic lot sizing: an O ( n log n ) algorithm that runs in linear time in the Wagner-Whitin case

Vehicle routing with time windows

Interval scheduling: A survey

Totally-Balanced and Greedy Matrices