Rodrigo Olivares

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.

Solving the non-unicost set covering problem by using cuckoo search and black hole optimization

The set covering problem is a classical optimization benchmark that finds application in several real-world domains, particularly in line balancing production, crew scheduling, and service installation. The 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. In this paper, we present two new approaches for efficiently solving this problem, the first one based on cuckoo search and the second one on black hole optimization. Both are relatively modern bio-inspired metaheuristics that have attracted much attention due to their rapid convergence, easy implementation, and encouraging obtained results. We integrate to the core of both metaheuristics an effective pre-processing phase as well as multiple transfer functions and discretization methods. Pre-processing is employed for filtering the values from domains leading to infeasible solutions, while transfers function and discretization methods are used for efficiently handling the binary nature of the problem. We illustrate interesting experimental results where the two proposed approaches are able to obtain various global optimums for a set of well-known set covering problem instances, outperforming also several recently reported techniques.

Using autonomous search for solving constraint satisfaction problems via new modern approaches

Abstract Constraint Programming is a powerful paradigm which allows the resolution of many complex problems, such as scheduling, planning, and configuration. These problems are defined by a set of variables and a set of constraints. Each variable has non-empty domain of possible value and each constraint involves some subset of the variables and specifies the allowable combinations of values for that subset. The resolution of these problems is carried out by a constraint satisfaction solver which explores a search tree of potential solutions. This exploration is controlled by the enumeration strategy, which is responsible for choosing the order in which variables and values are selected to generate the potential solution. There exist different ways to perform this selection, and depending on the quality of this decision, the efficiency of the solving process may dramatically vary. Autonomous search is a particular case of adaptive systems that aims at improving its solving performance by adapting itself to the problem at hand without manual configuration of an expert user. The goal is to improve their solving performance by modifying and adjusting themselves, either by self-adaptation or by supervised adaptation. This approach has been effectively applied to different optimization and satisfaction techniques such as constraint programming, metaheuristics, and SAT. In this paper, we present a new Autonomous Search approach for constraint programming based on four modern bio-inspired metaheuristics. The goal of those metaheuristics is to optimize the self-tuning phase of the constraint programming search process. We illustrate promising results, where the proposed approach is able to efficiently solve several well-known constraint satisfaction problems.

Online control of enumeration strategies via bat algorithm and black hole optimization

Constraint programming is an efficient and powerful paradigm for solving constraint satisfaction and optimization problems. Under this paradigm, problems are modeled as a sequence of variables and a set of constraints. The variables have a non-empty domain of candidate values and constraints restrict the values that variables can adopt. The solving process operates by assigning values to variables in order to produce potential solutions which are then evaluated. A main component in this process is the enumeration strategy, which decides the order in which variables and values are chosen to produce such potential solutions. There exist different ways to perform this selection, and depending on the quality of this decision, the efficiency of the solving process may dramatically vary. Unfortunately, selecting the proper strategy is known to be a hard task, as its behavior during search is generally unpredictable and certainly depends on the problem at hand. A recent trend to handle this concern, is to interleave a set of different strategies instead of using a single one during the whole process. The strategies are evaluated according to process indicators in order to use the most promising one on each part of the search process. This process is known as online control of enumeration strategies and its correct configuration can be seen itself as an optimization problem. In this paper, we present two new systems for online control of enumeration strategies based on recent nature-inspired metaheuristics: bat algorithm and black hole optimization. The bat algorithm mimics the location capabilities of bats that employ echoes to identify the objects in their surrounding areas, while black hole optimization inspires its behavior on the gravitational pull of black holes in space. We perform different experimental results by using different enumeration strategies and well-known benchmarks, where the proposed approaches are able to noticeably outperform previous work on online control.

Online Control of Enumeration Strategies via Bat-Inspired Optimization

Constraint programming allows to solve constraint satisfaction and optimization problems by building and then exploring a search tree of potential solutions. Potential solutions are generated by firstly selecting a variable and then a value from the given problem. The enumeration strategy is responsible for selecting the order in which those variables and values are selected to produce a potential solution. There exist different ways to perform this selection, and depending on the quality of this decision, the efficiency of the solving process may dramatically vary. A modern idea to handle this concern, is to interleave during solving time a set of different strategies instead of using a single one. The strategies are evaluated according to process indicators in order to use the most promising one on each part of the search process. This process is known as online control of enumeration strategies and its correct configuration can be seen itself as an optimization problem. In this paper, we present a new system for online control of enumeration strategies based on bat-inspired optimization. The bat algorithm is a relatively modern metaheuristic based on the location behavior of bats that employ echoes to identify the objects in their surrounding area. We illustrate, promising results where the proposed bat algorithm is able to outperform previously reported metaheuristic-based approaches for online control of enumeration strategies.

Top- Based Adaptive Enumeration in Constraint Programming

Constraint programming effectively solves constraint satisfaction and optimization problems by basically building, pruning, and exploring a search tree of potential solutions. In this context, a main component is the enumeration strategy, which is responsible for selecting the order in which variables and values are selected to build a possible solution. This process is known to be quite important; indeed a correct selection can reach a solution without failed explorations. However, it is well known that selecting the right strategy is quite challenging as their performance is notably hard to predict. During the last years, adaptive enumeration appeared as a proper solution to this problem. Adaptive enumeration allows the solving algorithm being able to autonomously modifying its strategies in solving time depending on performance information. In this way, the most suitable order for variables and values is employed along the search. In this paper, we present a new and more lightweight approach for performing adaptive enumeration. We incorporate a powerful classification technique named Top- in order to adaptively select strategies along the resolution. We report results on a set of well-known benchmarks where the proposed approach noticeably competes with classical and modern adaptive enumeration methods for constraint satisfaction.

Autonomous Search in Constraint Satisfaction via Black Hole: A Performance Evaluation Using Different Choice Functions

Autonomous Search is a modern technique aimed at introducing self-adjusting features to problem-solvers. In the context of constraint satisfaction, the idea is to let the solver engine to autonomously replace its solving strategies by more promising ones when poor performances are identified. The replacement is controlled by a choice function, which takes decisions based on information collected during solving time. However, the design of choice functions can be done in very different ways, leading of course to very different resolution processes. In this paper, we present a performance evaluation of 16 rigorously designed choice functions. Our goal is to provide new and interesting knowledge about the behavior of such functions in autonomous search architectures. To this end, we employ a set of well-known benchmarks that share general features that may be present on most constraint satisfaction and optimization problems. We believe this information will be useful in order to design better autonomous search systems for constraint satisfaction.

WSM Tuning in Autonomous Search via Gravitational Search Algorithms

Autonomous search is a recent approach that allows the solver to adapt their search so as to be more efficient without the manual configuration of an expert user. The goal is to provide more capabilities to the solver in order to improve the search process based on some performance indicators and self-tuning. This approach has effectively been applied to different optimization and satisfaction techniques such as constraint programming, SAT, and various metaheuristics. This paper focuses on automated self-tuning of constraint programming solvers. We employ a classic decision making method called weighted sum model (WSM) to evaluate the search process performance. This evaluation is used by the solver to re-configure its parameters in benefit of reaching a better performance. However, reaching good configurations straightly depends on the correct tuning of the WSM. This is known to be hard as the WSM is problem-dependent and good settings are not commonly stable along the search. To this end, we introduce a gravitational search algorithm (GSA), which is able to find good WSM configurations when solving constraint satisfaction problems. We illustrate experimental results where the GSA-based approach directly competes against previously reported autonomous search methods for constraint programming.

Resolving the Manufacturing Cell Design Problem Using the Flower Pollination Algorithm

The Manufacturing cell design problem focuses on the creation of an optimal distribution of the machinery on a productive plant, through the creation of highly independent cells where the parts of certain products are processed. The main objective is to reduce the movements between this cells, decreasing production times, costs and getting other advantages. To find solutions to this problem, in this paper, the usage of the Flower Pollination Algorithm is proposed, which is one of the many nature-based algorithms, which in this case is inspired in the Pollination of the flowers, and has shown great capacities in the resolution of complex problems. Experimental results are shown, with 90 instances taken from Boctor’s experiments, where the optimum is achieved in all them.

The Impact of Using Different Choice Functions When Solving CSPs with Autonomous Search

Constraint programming is a powerful technology for the efficient solving of optimization and constraint satisfaction problems (CSPs). A main concern of this technology is that the efficient problem resolution usually relies on the employed solving strategy. Unfortunately, selecting the proper one is known to be complex as the behavior of strategies is commonly unpredictable. Recently, Autonomous Search appeared as a new technique to tackle this concern. The idea is to let the solver adapt its strategy during solving time in order to improve performance. This task is controlled by a choice function which decides, based on performance information, how the strategy must be updated. However, choice functions can be constructed in several manners variating the information used to take decisions. Such variations may certainly conduct to very different resolution processes. In this paper, we study the impact on the solving phase of 16 different carefully constructed choice functions. We employ as test bed a set of well-known benchmarks that collect general features present on most CSPs. Interesting experimental results are obtained in order to provide the best-performing choice functions for solving CSPs.