Fernando Paredes

Parameter tuning of a choice-function based hyperheuristic using Particle Swarm Optimization

A Constraint Satisfaction Problem is defined by a set of variables and a set of constraints, each variable has a nonempty domain of possible values. Each constraint involves some subset of the variables and specifies the allowable combinations of values for that subset. A solution of the problem is defined by an assignment of values to some or all of the variables that does not violate any constraints. To solve an instance, a search tree is created and each node in the tree represents a variable of the instance. The order in which the variables are selected for instantiation changes the form of the search tree and affects the cost of finding a solution. In this paper we explore the use of a Choice Function to dynamically select from a set of variable ordering heuristics the one that best matches the current problem state in order to show an acceptable performance over a wide range of instances. The Choice Function is defined as a weighted sum of process indicators expressing the recent improvement produced by the heuristic recently used. The weights are determined by a Particle Swarm Optimization algorithm in a multilevel approach. We report results where our combination of strategies outperforms the use of individual strategies.

Application of the Artificial Bee Colony Algorithm for Solving the Set Covering Problem

The set covering problem is a formal model for many practical optimization problems. In the set covering problem the goal is to choose a subset of the columns of minimal cost that covers every row. Here, we present a novel application of the artificial bee colony algorithm to solve the non-unicost set covering problem. The artificial bee colony algorithm is a recent swarm metaheuristic technique based on the intelligent foraging behavior of honey bees. Experimental results show that our artificial bee colony algorithm is competitive in terms of solution quality with other recent metaheuristic approaches for the set covering problem.

A Binary Firefly Algorithm for the Set Covering Problem

The set cover problem, belongs to the branch of combinatorial optimization problems, whose complexity is exponential theoretically established as NP-complex problems. Consists in finding a subset of columns in a matrix of zeros and ones such that cover all rows of the matrix at a minimal cost. In this work, the problem is solved by binary Firefly algorithm, based on the flashing behavior of fireflies, using binary representation. A firefly produces a change in brightness based position between the fireflies. The new position is determined by the change in the value of the old position of the firefly, but the number of the new position is a real number, we can solve this problem with the function tanh binarization compared with a random number generated uniformly distributed between 0 and 1. The proposed algorithm has been tested on 65 benchmark instances. The results show that it is capable of producing solutions competitivas. virtualización; ultrasecuenciación genetics.

A reactive and hybrid constraint solver

In Castro et al. [Castro, C., Monfroy, E., Figueroa, C., and Meneses, R. (2005), ‘An Approach for Dynamic Split Strategies in Constraint Solving’, in Proceedings of MICAI 2005 (Vol. 3789), LNAI, Berlin: Springer, pp. 162–174] a framework for adaptive enumeration strategies and meta-backtracks for a propagation-based constraint solver has been studied. Here, we extend this framework in order to trigger some functions of a solver, or of a hybrid solver to respond to some observations of the solving process. We can also simply design adaptive hybridisation strategies by just changing some rules of the update component of our framework. We experiment with this framework on a hybrid Branch and Bound + propagation solver in which propagation can be triggered w.r.t. some observations of the solving process. The results show that some phases of propagation are not only beneficial to the Branch and Bound algorithm, but also that propagation is too costly to be executed at each node of the search tree. The hybridisation strategies are thus crucial in order to decide when to perform the or not propagation.

A hybrid AC3-tabu search algorithm for solving Sudoku puzzles

The Sudoku problem consists in filling a n^2xn^2 grid so that each column, row and each one of the nxn sub-grids contain different digits from 1 to n^2. This is a non-trivial problem, known to be NP-complete. The literature reports different incomplete search methods devoted to tackle this problem, genetic computing being the one exhibiting the best results. In this paper, we propose a new hybrid AC3-tabu search algorithm for Sudoku problems. We merge a classic tabu search procedure with an arc-consistency 3 (AC3) algorithm in order to effectively reduce the combinatorial space. The role of AC3 here is do not only acting as a single pre-processing phase, but as a fully integrated procedure that applies at every iteration of the tabu search. This integration leads to a more effective domain filtering and therefore to a faster resolution process. We illustrate experimental evaluations where our approach outperforms the best results reported by using incomplete search methods.

Cell formation in group technology using constraint programming and Boolean satisfiability

Cell formation consists in organizing a plant as a set of cells, each of them containing machines that process similar types or families of parts. The idea is to minimize the part flow among cells in order to reduce costs and increase productivity. The literature presents different approaches devoted to solve this problem, which are mainly based on mathematical programming and on evolutionary computing. Mathematical programming can guarantee a global optimal solution, however at a higher computational cost than an evolutionary algorithm, which can assure a good enough optimum in a fixed amount of time. In this paper, we model and solve this problem by using state-of-the-art constraint programming (CP) techniques and Boolean satisfiability (SAT) technology. We present different experimental results that demonstrate the efficiency of the proposed optimization models. Indeed, CP and SAT implementations are able to reach the global optima in all tested instances and in competitive runtime.

Flexibility dimensions to control the bullwhip effect in a supply chain

In this paper, we analyse the consequences of two flexibility dimensions proposed in a previous approach—adjustment capability and responsiveness—on the bullwhip effect in a supply-chain model when a stochastic AR(1) demand process is considered. First modelling the managers belief on forecasting in pull, push and hybrid ordering methods, it is revealed that high adjustment capability induces a robust reduction of the bullwhip effect. Secondly, it is found that maximal responsiveness is not always a necessary management strategy. Indeed, we show that these dimensions may be organised in a trade-off, always keeping amplification to acceptable values in the whole supply chain.

A Binary Cat Swarm Optimization Algorithm for the Non-Unicost Set Covering Problem

The Set Covering Problem consists in finding a subset of columns in a zero-one matrix such that they cover all the rows of the matrix at a minimum cost. To solve the Set Covering Problem we use a metaheuristic called Binary Cat Swarm Optimization. This metaheuristic is a recent swarm metaheuristic technique based on the cat behavior. Domestic cats show the ability to hunt and are curious about moving objects. Based on this, the cats have two modes of behavior: seeking mode and tracing mode. We are the first ones to use this metaheuristic to solve this problem; our algorithm solves a set of 65 Set Covering Problem instances from OR-Library.

Putting Continuous Metaheuristics to Work in Binary Search Spaces

In the real world, there are a number of optimization problems whose search space is restricted to take binary values; however, there are many continuous metaheuristics with good results in continuous search spaces. These algorithms must be adapted to solve binary problems. This paper surveys articles focused on the binarization of metaheuristics designed for continuous optimization.

A Binary Cuckoo Search Algorithm for Solving the Set Covering Problem

The non-unicost set covering problem is a classical optimization benchmark that belongs to the Karp’s 21 NP-complete problems. In this paper, we present a new approach based on cuckoo search for solving such problem. Cuckoo search is a modern nature-inspired metaheuristic that has attracted much attention due to its rapid convergence and easy implementation. We illustrate interesting experimental results where the proposed cuckoo search algorithm reaches several global optimums for the non-unicost instances from the OR-Library.