This paper states a novel hybrid-metaheuristic based on deterministic swapping, evolutionary algorithms and simulated annealing inspired algorithms for the multi-objective optimization of combinatorial problems. The proposed algorithm is named EMSA. It is an improvement of MODS algorithm. Unlike MODS, EMSA works using a search direction given by the assignation of weights to each objective function of the combinatorial problem to optimize. Lastly, EMSA is tested using well know instances of the Bi-Objective Traveling Salesman Problem (BTSP) from TSPLIB. Its results were compared with MODS metaheuristic (its predecessor). The comparison was made using metrics from the specialized literature such as Spacing, Generational Distance, Inverse Generational Distance and Non-Dominated Generation Vectors. In every case, the EMSA results on the metrics were always better and in some of those cases, the superiority was 100%.

A Novel, Evolutionary, Simulated Annealing inspired Algorithm for the Multi-Objective Optimization of Combinatorial Problems

The entire process of extracting knowledge from a database has been a research topic of growing interest in recent decades, because it comprises various stages from obtaining the data to the application of the knowledge acquired in the decisionmaking. Among these stages, is data mining, the most important for the knowledge extraction process. This is vital for obtaining the right results, and depends largely on the learning algorithm used. In recent years, many proposals have been made for modifications to the basic Data Mining algorithms that seek to improve their performance when faced with highdimensional it problems. In this context, research is carried out in data mining, and genetic algorithms are continuously developed, which under acceptable limitations of computational efficiency discover patterns from the data. The pattern search space is usually very large, and the extraction of patterns demands to perform some kind of search on the space. Currently, there are both computational and physical limitations, therefore, it is necessary to restrict this space in specific limits. There are multiple examples of combinatorial optimization, including knowledge extraction, which can be modeled in this way. The modelling of combinatorial optimization is generally characterized by a finite set of admissible solutions, which involves exploring two fundamental fields: the representation of the space of feasible solutions and the metaheuristics for the multi-target optimization. Numerous meta heuristic algorithms have been developed as stated by MerrikhBayat, (2015) the nature has been the source of inspiration for the design of optimization metaheuristics to solve complex problems, in response to the need to find some solution. In fact, the methods currently available for modeling combinatorial optimization problems are indebted to investigations that have been conducted over decades past. See Table 2 for a guide to the main developments made. Many efforts have been devoted to the development of new metaheuristic methods and techniques, instead few efforts have been made to represent the space of feasible solutions to be explored. Some of the research on the subject was carried out by Chaiyaratana (1997) represented the space of feasible solutions of combinatory problems using vectors, each vector represents an encoding (chromosome), later Dorigo (1996) proposed an ant colony algorithm (ACO) based on the natural behavior of the ants to discover food sources, by establishing the shortest path between them and the anthill, and transmitting this information to the rest of their companions. Other ACO-based models can be found in Table 1. Table 1. Classification of ant colony algorithms AUTHOR Algorithm DEVELOPING Dorigo (1996) ACO Shortest route. Eschenauer (1988) algoritmo Bicriterio (BCA) Vehicle routing Morales & Mariano, (1997) MOAQ Water distribution networks Gambardella, Taillard, & Agazzi (1999) MACS-VRPTW Routing of double criteria vehicles Doerner, Hartl & Reimann, (2001) CACompetants Bi-objective problems Iredi, Merkle & Middendorf (2001) ACO Bi-Criterion Multi-objective problems Cardoso, Jesus.&Marquez,(2003) MONA Multi-objetive Network ACO Source: Own collection. Other models that represent the feasible solution space can be seen in Kennedy. & Eberhart. R, (2001) Particle Swarrm optimization (PSO) inspired by the social behavior of bird bands or fish banks represent the space of particle-guided solutions that find the best solution and that makes a leader in the flock; SPEA2 (Kim, Hiroyasu, Miki, & Watanabe, 2010) Strength Pareto Evolutionary Algorithm 2 and NSGAII (Horn, Nafpliotis, & Goldberg, 2002) Niched Pareto Genetic Algorithm allow the optimization of combinatorial problems using elitism techniques with the purpose of elitism rapidly converge to optimal solutions. On the other hand, we cannot fail to mention the classic local search strategy techniques that are still used for multi-target optimization. One of them is AMOSA Bandyopadhyay, Saha, Maulik, & Deb, (2008), ("Multi-objective simulated annealing") avoid as far as possible optimal locals. Other AMOSA-based models such as UMOSA (Ulungu, Teghem, Fortemps, & Tuyttens, 1999), CMOSA (Ulungu et al., 1999), EMOSA (Li & Landa-Silva, 2008). One of the most recent methods in literature is found in Mendoza. M, (2016) ESSA a bio-inspired algorithm of a predator system and a herd of dams to perform an efficient search in a feasible solution region. However, there are various techniques to address the limitations encountered in multi-target combinatory analysis problems, there are predominant gaps in response times. More recent studies to solve optimization problems introduce the concept of finite automata, among the revised studies the authors Niño & Ardila (2009) propose a Finite Determinist Automata de Exchange (AFD-I) which they called MIDA which has proven to be useful in representing the space of feasible solutions for a combinatory problem. However, it is limited to solving single-target combinatorial problems, which does not allow for more complex problems to be solved. However, there are many problems of a combinatorial nature that have more than one target variable. Consequently, the authors Niño, Ardila, Molinares, Barrios, & Yesid (2011), propose a metaheuristic called MODS, inspired by MIDA, used in their structure an elitist search criterion, which allows to explore all the spaces of solutions the application of this model is restricted by reducing the space of feasible solutions to an optimal solution space; Nieto (2011) recognizes the problem in the representation of the model in the procedure proposed by Child et al.,(2011) in response time, increasing the number of objectives and constraints to optimize increases the complexity of finding the optimal solution set, so it proposes an alternative solution route called AERSMIDA the proposed strategy avoids falling into Ideal locals when using two techniques allows a diversification of the population by applying the genetic operator of population recombination (crossing) and the simulated annealing technique. A later study in 2011 Niño, Nieto & Chinchilla, propose metaheuristics that they called EMSA for the optimization of multi-target problems expose a given search direction through the allocation of weights for each function to optimize the problem combinatorial; In a new investigation (Niño. E & Chinchilla. A, 2012), proposes a new Metaheuristic EMODS based on Deterministic Finite Automata (AFDM) for multitarget optimization explores the different regions of the space of feasible solutions and the search for solutions not dominated by search Tabú. In the same year Child proposes metaheuristics SAMODS & SAGAMODS proposes a direction of Search and improves the angle by removing the solutions mastered when he finds solutions not mastered by assigning weights to the objectives of the problem to avoid falling into optimal Local. Although the metaheuristics enunciated allow to solve multi-target combinatory problems prevail the limitations in the response times, given the behavior of the output variables with respect to the parameters of the algorithm, being a key points in achieving the optimal solutions. However, setting the values to the parameters of an algorithm requires deeper analysis to understand the overall behavior of the problem. The different metaheuristics seen, have been used to solve a wide range of combinatorial problems in different areas of industrial processes, such as: Allocation of resources to production processes (Guerra Diego, 2015), selection of the route optimal in the problem of the travel agent TSP (Hincapie, Rios, & Gallego, 2004), the problem of binpacking, (Pérez-Ortega et al., 2016), routing of vehicles from multiple warehouses with weight-related costs (Linfati, Escobar, & Gatica, 2014). (Linfati, Escobar, & Gatica, 2014). In Rocha; González. and Orjuela (2011) present a bibliographic review of the different variants that emerged within Vehicle Routing Problem, such as routing of multi-tank vehicles, problems of routing the delivery vehicle and collection with windows of the problem of street vendors, problem of the street vendor in a mono or multi-target way, among others. As can be seen there are many problems of combinatorial optimization present in reality, and their modeling is defined according to the technique to be adapted. Such is the study carried out by Ruiz, (2013) designed and implemented the metaheuristic ERNEAD based on Finite Determinist Automata Multi-Objective with genetic algorithms (EMODS) allows to solve the problem of neural network trainings with Forward calculation (feedforward) assigning synaptic weights to neurons, applied Framework to problems of diagnosing breast cancer in the area of medicine and classification of flowers in the apothecary area, from the database taken from the MLR. It is another case study of optimization carried out by Hernández Riaño, López Pereira, & Hernández Riaño, (2013a) propose an algorithm called Ebola based on the behavior of the virus to solve the problem of routing in UnicastQoS networks, whose intention is to find an optimal route that allows to offer a better communication service, which depending on some performance criterion "minimize the delay" is seen as an optimization problem to determine the shortest route along the selected route. It is important to note that SCBRD learning methods can be better addressed with optimization techniques. Among the learning methods are stochastic and diffuse techniques: Neural Networks (J. Rua, 2014); Flexible computing: evolutionary and genetic methods (Vaezpour, Dehghan, & Yousefi'zadeh, 2019), (Naghash Asadi, Abdollahi Azgomi, & Entezari-Maleki, 2019); fuzzy logic, Bayesian sorters (Naudin, Tremblais, Guillevin, Guillevin, & Fernandez, 2002); Bayesian techniques: EM algorithm (Simon, Weber, & Evsukoff, 2008); decision tree-based techniques and rule learning sys

Un modelo para la extracción de conocimiento en base de datos, mediante cómputo evolutivo, automátas finitos deterministas y reglas difusas

This paper states a novel hybrid-metaheuristic based on the Theory of Deterministic Swapping, Theory of Evolution and Simulated Annealing Meta-heuristic for ...

Evolutionary algorithm based on simulated annealing for the multi-objective optimization of combinatorial problems

This paper states a novel, Evolutionary Metaheuristic Based on the Automata Theory (EMODS) for the multiobjective optimization of combinatorial problems. The proposed algorithm uses the natural selection theory in order to explore the feasible solutions space of a combinatorial problem. Due to this, local optimums are often avoided. Also, EMODS exploits the optimization process from the Metaheuristic of Deterministic Swapping to avoid finding unfeasible solutions. The proposed algorithm was tested using well known multi-objective TSP instances from the TSPLIB. Its results were compared against others Automata Theory inspired Algorithms using metrics from the specialized literature. In every case, the EMODS results on the metrics were always better and in some of those cases, the distance from the true solutions was 0.89%.

/pdf/evolutionary-algorithm-based-on-the-automata-theory-for-the-1hgeyfpydv.pdf

Evolutionary Algorithm based on the Automata Theory for the Multi-objective Optimization of Combinatorial Problems

This paper states a novel hybrid-metaheuristic based on the Theory of Deterministic Swapping, Theory of Evolution and Simulated Annealing Meta-heuristic for the multi-objective optimization of combinatorial prob- lems. The proposed algorithm is named EMSA. It is an improvement of MODS algorithm. Unlike MODS, EMSA works using a search direction given through the assignation of weights to each function of the com- binatorial problem to optimize. Also, in order to avoid local optimums, EMSA uses crossover strategy of Genetic Algorithm. Lastly, EMSA is tested using well know instances of the Bi-Objective Traveling Sales- man Problem (TSP) from TSPLIB. Its results were compared with MODS Metaheuristic (its precessor). The comparison was made using metrics from the specialized literature such as Spacing, Generational Distance, Inverse Generational Distance and Non-Dominated Generation Vectors. In every case, the EMSA results on the metrics were always better and in some of those cases, the superiority was 100%.

EVOLUTIONARY ALGORITHM BASED ON SIMULATED ANNEALING FOR THE MULTI-OBJECTIVE OPTIMIZATION OF COMBINATORIAL PROBLEMS EMSA: Hybrid Metaheuristic based on Genetic Algorithms, Simulated Annealing and Deterministic Swapping

MODS： A Novel Metaheuristic of Deterministic Swapping for the Multi-Objective Optimization of Combinatorials Problems

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MODS： A Novel Metaheuristic of Deterministic Swapping for the Multi-Objective Optimization of Combinatorials Problems