Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics

Abstract

Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs) that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-OptimizeExpand (ROE) method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions.

MineReduce: An approach based on data mining for problem size reduction

“…Size reduction is naturally the most crucial procedure in the PSR process since better decisions in this step will produce solutions of better quality in the subsequent stages (Montiel et al, 2013;Montiel & Delgadillo, 2015;Delgadillo et al, 2016). Strategies to make these decisions are highly dependent on the structure and features of the problem, so they vary significantly among distinct classes of COPs.…”

“…Studies found in the literature in which PSR has been successfully applied to routing problems include those by Gavish & Srikanth (1986), Min (1991), Barnhart et al (2002), Fischer & Merz (2007), Ramos & Oliveira (2011), Lin (2011), Montiel et al (2013), Montiel & Delgadillo (2015) and Delgadillo et al (2016).…”

Pose Estimation in Noncontinuous Video Sequences Using Evolutionary Correlation Filtering

“…In this work, we are encouraged finding the optimal solution for 3D pose estimation problem when the target can present abrupt pose changes in the scene, i.e., when the search space of location, orientation, and scaling parameters of the target is very big. This challenge needs to be treated as a combinatorial optimization problem that can become numerically intractable as the number of feasible poses of the target increases [16,17]. From the point of view of computational complexity, this problem is classified as an NPhard problem [18], since it will require an algorithm with the ability to solve problems in nondeterministic polynomial (NP) time, but the solution can be verified in polynomial time.…”