25 research outputs found
Exploring the Impact of Early Decisions in Variable Ordering for Constraint Satisfaction Problems
When solving constraint satisfaction problems (CSPs), it is a common practice to rely on heuristics to decide which variable should be instantiated at each stage of the search. But, this ordering influences the search cost. Even so, and to the best of our knowledge, no earlier work has dealt with how first variable orderings affect the overall cost. In this paper, we explore the cost of finding high-quality orderings of variables within constraint satisfaction problems. We also study differences among the orderings produced by some commonly used heuristics and the way bad first decisions affect the search cost. One of the most important findings of this work confirms the paramount importance of first decisions. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. We propose a simple method to improve early decisions of heuristics. By using it, performance of heuristics increases
Combining Constructive and Perturbative Deep Learning Algorithms for the Capacitated Vehicle Routing Problem
The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that
poses the challenge of finding the optimal route of a vehicle delivering
products to multiple locations. Recently, new efforts have emerged to create
constructive and perturbative heuristics to tackle this problem using Deep
Learning. In this paper, we join these efforts to develop the Combined Deep
Constructor and Perturbator, which combines two powerful constructive and
perturbative Deep Learning-based heuristics, using attention mechanisms at
their core. Furthermore, we improve the Attention Model-Dynamic for the
Capacitated Vehicle Routing Problem by proposing a memory-efficient algorithm
that reduces its memory complexity by a factor of the number of nodes. Our
method shows promising results. It demonstrates a cost improvement in common
datasets when compared against other multiple Deep Learning methods. It also
obtains close results to the state-of-the art heuristics from the Operations
Research field. Additionally, the proposed memory efficient algorithm for the
Attention Model-Dynamic model enables its use in problem instances with more
than 100 nodes
Experimental Matching of Instances to Heuristics for Constraint Satisfaction Problems
Constraint satisfaction problems are of special interest for the artificial intelligence and operations research community due to their many applications. Although heuristics involved in solving these problems have largely been studied in the past, little is known about the relation between instances and the respective performance of the heuristics used to solve them. This paper focuses on both the exploration of the instance space to identify relations between instances and good performing heuristics and how to use such relations to improve the search. Firstly, the document describes a methodology to explore the instance space of constraint satisfaction problems and evaluate the corresponding performance of six variable ordering heuristics for such instances in order to find regions on the instance space where some heuristics outperform the others. Analyzing such regions favors the understanding of how these heuristics work and contribute to their improvement. Secondly, we use the information gathered from the first stage to predict the most suitable heuristic to use according to the features of the instance currently being solved. This approach proved to be competitive when compared against the heuristics applied in isolation on both randomly generated and structured instances of constraint satisfaction problems
Building General Hyper-Heuristics for Multi-Objective Cutting Stock Problems
Abstract: In this article we build multi-objective hyperheuristics (MOHHs) using the multi-objective evolutionary algorithm NSGA-II for solving irregular 2D cutting stock problems under a bi-objective minimization schema, having a trade-off between the number of sheets used to fit a finite number of pieces and the time required to perform the placement of these pieces. We solve this problem using a multiobjective variation of hyper-heuristics called MOHH, whose main idea consists of finding a set of simple
heuristics which can be combined to find a general solution, where a single heuristic is applied depending on the current condition of the problem instead of applying a unique single heuristic during the whole placement process. MOHHs are built after going
through a learning process using the NSGA-II, which evolves combinations of condition-action rules producing at the end a set of Pareto-optimal MOHHs. We test the approximated MOHHs on several sets of benchmark problems and present the results
Experimental Matching of Instances to Heuristics for Constraint Satisfaction Problems
Constraint satisfaction problems are of special interest for the artificial intelligence and operations research community due to their many applications. Although heuristics involved in solving these problems have largely been studied in the past, little is known about the relation between instances and the respective performance of the heuristics used to solve them. This paper focuses on both the exploration of the instance space to identify relations between instances and good performing heuristics and how to use such relations to improve the search. Firstly, the document describes a methodology to explore the instance space of constraint satisfaction problems and evaluate the corresponding performance of six variable ordering heuristics for such instances in order to find regions on the instance space where some heuristics outperform the others. Analyzing such regions favors the understanding of how these heuristics work and contribute to their improvement. Secondly, we use the information gathered from the first stage to predict the most suitable heuristic to use according to the features of the instance currently being solved. This approach proved to be competitive when compared against the heuristics applied in isolation on both randomly generated and structured instances of constraint satisfaction problems. © 2016 Jorge Humberto Moreno-Scott et al