Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

A Fuzzy Simheuristic for the Permutation Flow Shop Problem under Stochastic and Fuzzy Uncertainty

[EN] Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with both stochastic and fuzzy processing times. The main goal is to find the solution (permutation of jobs) that minimizes the expected makespan. However, due to the existence of uncertainty, other characteristics of the solution are also taken into account. In particular, we illustrate how survival analysis can be employed to enrich the probabilistic information given to decision-makers. To solve the aforementioned optimization problem, we extend the concept of a simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated in the PFSP. In order to test our approach, classical PFSP instances have been adapted and extended, so that processing times become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones.This work has been partially supported by the Spanish Ministry of Science (PID2019111100RB-C21/AEI/10.13039/501100011033), as well as by the Barcelona Council and the "la Caixa" Foundation under the framework of the Barcelona Science Plan 2020-2023 (grant 21S09355-001).Castaneda, J.; Martín, XA.; Ammouriova, M.; Panadero, J.; Juan-Pérez, ÁA. (2022). A Fuzzy Simheuristic for the Permutation Flow Shop Problem under Stochastic and Fuzzy Uncertainty. Mathematics. 10(10):1-17. https://doi.org/10.3390/math10101760117101

On Some Optimization Problems on Dynamic Networks

The basic assumption of re-optimization consists in the need of eiciently managing huge quantities of data in order to reduce the waste of resources, both in terms of space and time. Re-optimization refers to a series of computational strategies through which new problem instances are tackled analyzing similar, previously solved, problems, reusing existing useful information stored in memory from past computations. Its natural collocation is in the context of dynamic problems, with these latter accounting for a large share of the themes of interest in the multifaceted scenario of combinatorial optimization, with notable regard to recent applications. Dynamic frameworks are topic of research in classical and new problems spanning from routing, scheduling, shortest paths, graph drawing and many others. Concerning our speciic theme of investigation, we focused on the dynamical characteristics of two problems deined on networks: re-optimization of shortest paths and incremental graph drawing. For the former, we proposed a novel exact algorithm based on an auction approach, while for the latter, we introduced a new constrained formulation, Constrained Incremental Graph Drawing, and several meta-heuristics based prevalently on Tabu Search and GRASP frameworks. Moreover, a parallel branch of our research focused on the design of new GRASP algorithms as eicient solution strategies to address further optimization problems. Speciically, in this research thread, will be presented several GRASP approaches devised to tackle intractable problems such as: the Maximum-Cut Clique, p-Center, and Minimum Cost Satisiability

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

A hybrid GRASP-VNS for Ship Routing and Scheduling Problem with Discretized Time Windows

This paper addresses the Ship Routing and Scheduling Problem with Discretized Time Windows. Being one of the most relevant and challenging problems faced by decision makers from shipping companies, this tramp shipping problem lies in determining the set of contracts that should be served by each ship and the time windows that ships should use to serve each contract, with the aim of minimizing total costs. The use of discretized time windows allows for the consideration of a broad variety of features and practical constraints in a simple way. In order to solve this problem we propose a hybridazation of a Greedy Randomized Adaptive Search Procedure and a Variable Neighborhood Search, which improves previous heuristics results found in literature and requires very short computational time. Moreover, this algorithm is able to achieve the optimal results for many instances, demonstrating its good performance

20 years of Greedy Randomized Adaptive Search Procedures with Path Relinking

This is a comprehensive review of the Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic and its hybridization with Path Relinking (PR) over the past two decades. GRASP with PR has become a widely adopted approach for solving hard optimization problems since its proposal in 1999. The paper covers the historical development of GRASP with PR and its theoretical foundations, as well as recent advances in its implementation and application. The review includes a critical analysis of variants of PR, including memory-based and randomized designs, with a total of ten different implementations. It describes these advanced designs both theoretically and practically on two well-known optimization problems, linear ordering and max-cut. The paper also explores the hybridization of GRASP with PR and other metaheuristics, such as Tabu Search and Scatter Search. Overall, this review provides valuable insights for researchers and practitioners seeking to utilize GRASP with PR for solving optimization problems.Comment: 28 pages, 13 figure

The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems