Ignacio Araya

Adaptive constructive interval disjunction: algorithms and experiments

An operator called CID and an efficient variant 3BCID were proposed in 2007. For the numerical CSP handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for the discrete CSP. In addition to the constraint propagation procedure used to refute a given subproblem, the main two parameters of CID are the number of times the main CID procedure is called and the maximum number of sub-intervals treated by the procedure. The 3BCID operator is state-of-the-art in numerical CSP, but not in constrained global optimization, for which it is generally too costly. This paper proposes an adaptive variant of 3BCID called ACID. The number of variables handled is auto-adapted during the search, the other parameters are fixed and robust to modifications. On a representative sample of instances, ACID appears to work efficiently, both with the HC4 constraint propagation algorithm and with the state-of-the-art Mohc algorithm. Experiments also highlight that it is relevant to auto-adapt only a number of handled variables, instead of a specific set of selected variables. Finally, ACID appears to be the best interval constraint programming operator for solving and optimization, and has been therefore added to the default strategies of the Ibex interval solver.

Interval Branch-and-Bound algorithms for optimization and constraint satisfaction: a survey and prospects

Interval Branch and Bound algorithms are used to solve rigorously continuous constraint satisfaction and constrained global optimization problems. In this paper, we explain the basic principles behind interval Branch and Bound algorithms. We detail the main components and describe issues that should be considered to improve the efficiency of the algorithms.

Solving Manufacturing Cell Design Problems by Using a Dolphin Echolocation Algorithm

The Manufacturing Cell Design is a problem that consist in organize machines in cells to increase productivity, i.e., minimize the movement of parts for a given product between machines. In order to solve this problem we use a Dolphin Echolocation algorithm, a recent bio-inspired metaheuristic based on a dolphin feature, the echolocation. This feature is used by the dolphin to search all around the search space for a target, then the dolphin exploits the surround area in order to find promising solutions. Our approach has been tested by using a set of 10 benchmark instances with several configurations, reaching to optimal values for all of them.

Node selection strategies in interval Branch and Bound algorithms

We present in this article new strategies for selecting nodes in interval Branch and Bound algorithms for constrained global optimization. For a minimization problem the standard best-first strategy selects a node with the smallest lower bound of the objective function estimate. We first propose new node selection policies where an upper bound of each node/box is also taken into account. The good accuracy of this upper bound achieved by several contracting operators leads to a good performance of the node selection rule based on this criterion. We propose another strategy that also makes a tradeoff between diversification and intensification by greedily diving into potential feasible regions at each node of the best-first search. These new strategies obtain better experimental results than classical best-first search on difficult constrained global optimization instances.

VCS: A new heuristic function for selecting boxes in the single container loading problem

Abstract The single container loading problem consists of a container that has to be filled with a set of boxes. The objective of the problem is to maximize the total volume of the loaded boxes. For solving the problem, constructive approaches are the most successful. A key element of these approaches is related to the selection of the box to load next. In this work, we propose a new evaluation function for ranking boxes. Our function rewards boxes that fit well in the container, taking into account the previously placed ones. To construct a more robust function, we consider some other well-known evaluation criteria such as the volume of the block and the estimated wasted volume in the free space of the container. Our approach shows promising results when compared with other state-of-the-art algorithms on a set of 1600 well-known benchmark instances.

Adaptive filtering strategy for numerical constraint satisfaction problems

Adaptive mechanism for controlling filtering in branch and bound solvers.The mechanism is based on monitoring and clustering exploitation.Monitoring: periodic application of filtering algorithms for extracting information.Clustering exploitation: consecutive application of filtering algorithms. The reliability and increasing performance of search-tree-based interval solvers for solving numerical systems of constraints make them applicable to various expert system domains. Filtering methods are applied in each node of the search tree to reduce the variable domains without the loss of solutions. Current interval-based solvers generally leave it up to the solver designer to decide which set of filtering methods to apply to solve a particular problem. In this work, we propose an adaptive strategy to dynamically determine the set of filtering methods that will be applied in each node of the search tree. Our goal is twofold: first, we want to simplify the task of the solver designer, and second, we believe that an adaptive strategy may improve the average performance of the current state-of-the-art strategies.The proposed adaptive mechanism attempts to avoid calling costly filtering methods when their probability of filtering domains is low. We assume that fruitful filtering occurs in nearby revisions or clusters. Thus, the decision about whether or not to apply a filtering method is based on a cluster detection mechanism. When a cluster is detected, the associated methods are consecutively applied in order to exploit the cluster. Alternately, in zones without clusters, only a cheap method is applied, thus reducing the filtering effort in large portions of the search. We compare our approach with state-of-the-art strategies, demonstrating its effectiveness.

Solving Manufacturing Cell Design Problems Using the Black Hole Algorithm.

In this paper we solve the Manufacturing Cell Design Problem. This problem considers the grouping of different machines into sets or cells with the objective of minimizing the movement of material. To solve this problem we use the Black Hole algorithm, a modern population-based metaheuristic that is inspired by the phenomenon of the same name. At each iteration of the search, the best candidate solution is selected to be the black hole and other candidate solutions, known as stars, are attracted by the black hole. If one of these stars get too close to the black hole it disappears, generating a new random star (solution). Our approach has been tested by using a well-known set of benchmark instances, reaching optimal values in all of them.

Solving Manufacturing Cell Design Problems by Using a Bat Algorithm Approach

Manufacturing Cell Design is a problem that consist in distributing machines in cells, in such a way productivity is improved. The idea is that a product, build up by using different parts, has the least amount of travel on its manufacturing process. To solve the MCDP we use the Bat Algorithm, a metaheuristic inspired by a feature of the microbats, the echolocation. This feature allows an automatic exploration and exploitation balance, by controlling the rate of volume and emission pulses during the search. Our approach has been tested by using a well-known set of benchmark instances, reaching optimal values for most of them.

A Beam-Search Approach to the Set Covering Problem

In this work we present a beam-search approach applied to the Set Covering Problem. The goal of this problem is to choose a subset of columns of minimal cost covering every row. Beam Search constructs a search tree by using a breadth-first search strategy, however only a fixed number of nodes are kept and the rest are discarded. Even though original beam search has a deterministic nature, our proposal has some elements that makes it stochastic. This approach has been tested with a well-known set of 45 SCP benchmark instances from OR-Library showing promising results.