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

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

A Sequence-Based Hyper-Heuristic for Traveling Thieves

A plethora of combinatorial optimization problems can be linked to real-life decision scenarios. Even nowadays, more diverse and complex problems are popping up. One of these problems is the traveling thief problem (TTP), which combines elements from the knapsack and traveling salesperson problems. Hence, it is paramount to keep improving solvers to tackle combinatorial problems. Among recent proposals, hyper-heuristics have proven useful since they seek to combine the strengths of more straightforward solvers. This paper proposes a sequence-based selection hyper-heuristic and assesses its feasibility when solving the TTP. Our proposal can be represented by an array of operators selecting a city or an item. In the first case, the solution moves to a new city and thus advances the tour. In the second one, the thief agent picks an item within the current city and tries to store it in its knapsack. We generate several sets of TTP instances with different parameters to validate our approach and analyze the model’s performance. Our data reveal that the proposed approach outperforms randomly generated sequences. Moreover, our approach finds general sequences that surpass sequences specialized for each instance. We believe this is noteworthy and represents a stepping stone towards achieving a more robust solver for complex problems

Enhancing Hyperheuristics for the Knapsack Problem through Fuzzy Logic

Hyperheuristics rise as powerful techniques that get good results in less computational time than exact methods like dynamic programming or branch and bound. These exact methods promise the global best solution, but with a high computational time. In this matter, hyperheuristics do not promise the global best solution, but they promise a good solution in a lot less computational time. On the contrary, fuzzy logic provides the tools to model complex problems in a more natural way. With this in mind, this paper proposes a fuzzy hyperheuristic approach, which is a combination of a fuzzy inference system with a selection hyperheuristic. The fuzzy system needs the optimization of its fuzzy rules due to the lack of expert knowledge; indeed, traditional hyperheuristics also need an optimization of their rules. The fuzzy rules are optimized by genetic algorithms, and for the rules of the traditional methods, we use particle swarm optimization. The genetic algorithm will also reduce the number of fuzzy rules, in order to find the best minimal fuzzy rules, whereas traditional methods already use very few rules. Experimental results show the advantage of using our approach instead of a traditional selection hyperheuristic in 3200 instances of the 0/1 knapsack problem

Addressing the Algorithm Selection Problem through an Attention-Based Meta-Learner Approach

In the algorithm selection problem, where the task is to identify the most suitable solving technique for a particular situation, most methods used as performance mapping mechanisms have been relatively simple models such as logistic regression or neural networks. In the latter case, most implementations tend to have a shallow and straightforward architecture and, thus, exhibit a limited ability to extract relevant patterns. This research explores the use of attention-based neural networks as meta-learners to improve the performance mapping mechanism in the algorithm selection problem and fully take advantage of the model’s capabilities for pattern extraction. We compare the proposed use of an attention-based meta-learner method as a performance mapping mechanism against five models from the literature: multi-layer perceptron, k-nearest neighbors, softmax regression, support vector machines, and decision trees. We used a meta-data dataset obtained by solving the vehicle routing problem with time window (VRPTW) instances contained in the Solomon benchmark with three different configurations of the simulated annealing meta-heuristic for testing purposes. Overall, the attention-based meta-learner model yields better results when compared to the other benchmark methods in consistently selecting the algorithm that best solves a given VRPTW instance. Moreover, by significantly outperforming the multi-layer perceptron, our findings suggest promising potential in exploring more recent and novel advancements in neural network architectures