A comprehensive comparison of metaheuristics for the repetition-free longest common subsequence problem

This paper deals with an NP-hard string problem from the bio-informatics field: the repetition-free longest common subsequence problem. This problem has enjoyed an increasing interest in recent years, which has resulted in the application of several pure as well as hybrid metaheuristics. However, the literature lacks a comprehensive comparison between those approaches. Moreover, it has been shown that general purpose integer linear programming solvers are very efficient for solving many of the problem instances that were used so far in the literature. Therefore, in this work we extend the available benchmark set, adding larger instances to which integer linear programming solvers cannot be applied anymore. Moreover, we provide a comprehensive comparison of the approaches found in the literature. Based on the results we propose a hybrid between two of the best methods which turns out to inherit the complementary strengths of both methods.Peer ReviewedPostprint (author's final draft

On the role of metaheuristic optimization in bioinformatics

Metaheuristic algorithms are employed to solve complex and large-scale optimization problems in many different fields, from transportation and smart cities to finance. This paper discusses how metaheuristic algorithms are being applied to solve different optimization problems in the area of bioinformatics. While the text provides references to many optimization problems in the area, it focuses on those that have attracted more interest from the optimization community. Among the problems analyzed, the paper discusses in more detail the molecular docking problem, the protein structure prediction, phylogenetic inference, and different string problems. In addition, references to other relevant optimization problems are also given, including those related to medical imaging or gene selection for classification. From the previous analysis, the paper generates insights on research opportunities for the Operations Research and Computer Science communities in the field of bioinformatics

Exact algorithms for the repetition-bounded longest common subsequence problem

In this paper, we study exact, exponential-time algorithms for a variant of the classic Longest Common Subsequence problem called the Repetition-Bounded Longest Common Subsequence problem (or RBLCS, for short): Let an alphabet S be a finite set of symbols and an occurrence constraint Cocc be a function Cocc: S → N, assigning an upper bound on the number of occurrences of each symbol in S. Given two sequences X and Y over the alphabet S and an occurrence constraint Cocc, the goal of RBLCS is to find a longest common subsequence of X and Y such that each symbol s ∈ S appears at most Cocc(s) times in the obtained subsequence. The special case where Cocc(s) = 1 for every symbol s ∈ S is known as the Repetition-Free Longest Common Subsequence problem (RFLCS) and has been studied previously; e.g., in [1], Adi et al. presented a simple (exponential-time) exact algorithm for RFLCS. However, they did not analyze its time complexity in detail, and to the best of our knowledge, there are no previous results on the running times of any exact algorithms for this problem. Without loss of generality, we will assume that |X| ≤ |Y | and |X| = n. In this paper, we first propose a simpler algorithm for RFLCS based on the strategy used in [1] and show explicitly that its running time is O(1.44225n). Next, we provide a dynamic programming (DP) based algorithm for RBLCS and prove that its running time is O(1.44225n) for any occurrence constraint Cocc, and even less in certain special cases. In particular, for RFLCS, our DP-based algorithm runs in O(1.41422n) time, which is faster than the previous one. Furthermore, we prove NP-hardness and APX-hardness results for RBLCS on restricted instances

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality

Development of hybrid metaheuristics based on instance reduction for combinatorial optimization problems

113 p.La tesis presentada describe el desarrollo de algoritmos metaheurísticos híbridos, basados en reducción de instancias de problema. Éstos son enfocados en la resolución de problemas de optimización combinatorial. La motivación original de la investigación radicó en lograr, a través de la reducción de instancias de problemas, el uso efectivo de modelos de programación lineal entera (ILP) sobre problemas que dado su tamaño no admiten el uso directo con esta técnica exacta. En este contexto se presenta entre otros desarrollos el framework Construct, Merge, Solve & Adapt (CMSA) para resolución de problemas de optimización combinatorial en general, el cual posteriormente fue adaptado para mejorar el desempeño de otras metaheurísticas sin el uso de modelos ILP. Los algoritmos presentados mostraron resultados que compiten o superan el estado del arte sobre los problemas Minimum Common String Partition (MCSP), Minimum Covering Arborescence (MCA) y Weighted Independent Domination (WID)

A Fitness Function Elimination Theory For Blackbox Optimization And Problem Class Learning

The modern view of optimization is that optimization algorithms are not designed in a vacuum, but can make use of information regarding the broad class of objective functions from which a problem instance is drawn. Using this knowledge, we want to design optimization algorithms that execute quickly (efficiency), solve the objective function with minimal samples (performance), and are applicable over a wide range of problems (abstraction). However, we present a new theory for blackbox optimization from which, we conclude that of these three desired characteristics, only two can be maximized by any algorithm. We put forward an alternate view of optimization where we use knowledge about the problem class and samples from the problem instance to identify which problem instances from the class are being solved. From this Elimination of Fitness Functions approach, an idealized optimization algorithm that minimizes sample counts over any problem class, given complete knowledge about the class, is designed. This theory allows us to learn more about the difficulty of various problems, and we are able to use it to develop problem complexity bounds. We present general methods to model this algorithm over a particular problem class and gain efficiency at the cost of specifically targeting that class. This is demonstrated over the Generalized Leading-Ones problem and a generalization called LO∗∗ , and efficient algorithms with optimal performance are derived and analyzed. We also iii tighten existing bounds for LO∗∗∗. Additionally, we present a probabilistic framework based on our Elimination of Fitness Functions approach that clarifies how one can ideally learn about the problem class we face from the objective functions. This problem learning increases the performance of an optimization algorithm at the cost of abstraction. In the context of this theory, we re-examine the blackbox framework as an algorithm design framework and suggest several improvements to existing methods, including incorporating problem learning, not being restricted to blackbox framework and building parametrized algorithms. We feel that this theory and our recommendations will help a practitioner make substantially better use of all that is available in typical practical optimization algorithm design scenarios

Stochastic Optimisation for Complex Mixed-Integer Programming Problems in Asteroid Tour Missions

Deep space exploration is key to understand the origin of our Solar System and address the Earth impact risk. Space Trajectory Design (STD) has evolved and incremented in complexity due to the interest within the space community to explore multiple celestial bodies in a single mission. This thesis focuses on an Asteroid Tour Trajectory in the context of the CASTAway mission. CASTAway is a mission proposal for European Space Agency’s 5th call of medium-size missions to explore the Asteroid Main Belt. The objective is not to find the global optima but find feasible sequences of asteroid fly-bys, as per feasible tours of 12 asteroids of a total Δv of less than 9 km/s is meant. The complexity of the problem is given by the large number of possible permutations of 12-asteroid tour solutions – even with a reduced catalogue of 158 asteroids – and because of being a Mixed-Integer Non-Linear Programming (MINLP) problem. Because of this, metaheuristics are used to tackle the problem. A novel problem modelling that achieves uniqueness on the cost paths of the Search Space and a novel ACO solver is presented, with the general objective for the whole CASTPath project of finding a robust low computational heuristic. Due to the scientific interest on having diversity in the sequences, a similarity measurement tool is also developed. Several test cases with different ACO tuning parameters are run on a High Performance Computer. Results show that this algorithm outperforms the previous heuristics on CASTPath obtaining the lowest Δv (7.27 km/s) achieved by an heuristic and finding multiple feasible sequences (97 in 1 h). Moreover, the new problem modelling has allowed within the research group, to find the global optima (6.98 km/s) for this asteroid catalogue by Dynamic Programming

Exact and evolutionary algorithms for the score-constrained packing problem

This thesis concerns the Score-Constrained Packing Problem (SCPP), a combinatorial optimisation problem related to the one-dimensional bin packing problem. The aim of the SCPP is to pack a set of rectangular items from left to right into the fewest number of bins such that no bin is overfilled; however, the order and orientation of the items in each bin affects the feasibility of the overall solution. The SCPP has applications in the packaging industry, and obtaining high quality solutions for instances of the SCPP has the ability to reduce the amount of waste material, costs, and time, which motivates the study in this thesis. The minimal existing research on the SCPP leads us to explore a wide range of approaches to the problem in this thesis, implementing ideas from related problems in literature as well as bespoke methods. To begin, we present an exact algorithm that can produce a feasible configuration of a subset of items in a single bin in polynomial-time. We then introduce a range of methods for the SCPP including heuristics, an evolutionary algorithm framework comprising a local search procedure and a choice of three distinct recombination operators, and two algorithms combining metaheuristics with an exact procedure. Each method is investigated to gain more insight into the characteristics that benefit or hinder the improvement of solutions, both theoretically and computationally, using a large number of problem instances with varying parameters. This allows us to determine the specific methods and properties that produce superior solutions depending on the type of problem instance