Optimizing Genetic Algorithm by Implementation of An Enhanced Selection Operator

The probabilistic travelling salesman problem (PTSP) is an extension of the well-known travelling salesman problem (TSP), which has been extensively studied in the field of combinatorial optimization. The goal of the TSP is to find the minimum length of a tour to all customers, given the distances between all pairs of customers whereas the objective of the PTSP is to minimize the expected length of the a priori tour where each customer requires a visit only with a given probability (Bertsimas, 1988; Bertsimas et al., 1990; Jaillet, 1985). The main difference between the PTSP and the TSP is that in the PTSP the probability of each node being visited is between 0.0 and 1.0 while in TSP the probability of each node being visited is 1.0. Due to the fact that the element of uncertainty not only exists, but also significantly affects the system performance in many real-world transportation and logistics applications, the results from the PTSP can provide insights into research in other probabilistic combinatorial optimization problems. Moreover, the PTSP can also be used to model many real-world applications in logistical and transportation planning, such as daily pickup-delivery services with stochastic demand, job sequencing involving changeover cost, design of retrieval sequences in a warehouse or in a cargo terminal operations, meals on wheels in senior citizen services, trip-chaining activities, vehicle routing problem with stochastic demand, and home delivery service under e-commerce (Bartholdi et al., 1983; Bertsimas et al., 1995; Campbell, 2006; Jaillet, 1988; Tang & Miller-Hooks, 2004). Early PTSP computational studies, dating from 1985, adopted heuristic approaches that were modified from the TSP (e.g., nearest neighbor, savings approach, spacefilling curve, radial sorting, 1-shift, and 2-opt exchanges) (Bartholdi & Platzman, 1988; Bertsimas, 1988; Bertsimas & Howell, 1993; Jaillet, 1985, 1987; Rossi & Gavioli, 1987). With its less than satisfactory performance in yielding solution quality, researchers in the recent years switch to metaheuristic methods, such as ant colony optimization (Bianchi, 2006; Branke & Guntsch, 2004), evolutionary algorithm (Liu et al., 2007), simulated annealing (Bowler et al., 2003), threshold accepting (Tang & Miller-Hooks, 2004) and scatter search (Liu, 2006, 2007, 2008). Because the genetic algorithm (GA), a conceptual framework of the population-based metaheuristic method, has been shown to yield promising outcomes for solving various complicated optimization problems in the past three decades (Back et al., 1997; Davis, 1991; O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard combinatorial optimization problems, widely studied due to its numerous industrial applications in logistics, supply chain management, and resource planning. Over the years, various metaheuristic algorithms have been developed to provide near-optimal solutions within a reasonable computational time. While traditional methods such as Genetic Algorithms (GA) and Simulated Annealing (SA) have been applied widely to the TSP, recent developments in metaheuristics have introduced new methods that can ensure improved performance. In this study, we compare three new metaheuristics: Arctic Puffin Optimization (APO), Human Evolutionary Optimization (HEO), and Ship Rescue Optimization (SRO). These methods, inspired by puffin's behavior, human evolutions, and naval rescue, respectively, have demonstrated high optimization capability in various areas. However, these have not been extensively tried on solving the TSP yet. This research seeks to establish the performance of these algorithms by comparing their convergence rate, solution quality, and computational efficiency with well-established metaheuristics. The results of the experiment expose the strengths and weaknesses of such innovative approaches, showing their potential as competitive alternatives to solve complex combinatorial optimization problems

Combinatorial Optimization (CO) problems have been intensively studied for decades with a wide range of applications. For some classic CO problems, e.g., the Traveling Salesman Problem (TSP), both traditional planning algorithms and the emerging reinforcement learning have made solid progress in recent years. However, for CO problems with nested sub-tasks, neither end-to-end reinforcement learning algorithms nor traditional evolutionary methods can obtain satisfactory strategies within a limited time and computational resources. In this paper, we propose an algorithmic framework for solving CO problems with nested sub-tasks, in which learning and planning algorithms can be combined in a modular way. We validate our framework in the Job-Shop Scheduling Problem (JSSP), and the experimental results show that our algorithm has good performance in both solution qualities and model generalizations.

The Traveling Salesman Problem (TSP) is a benchmark NP-hard problem in combinatorial optimization[14]. This paper presents a comparative study of three Genetic Algorithm (GA) variants: (i) Serial GA, (ii) Parallel-Isolated GA (independent subpopulations without migration), and (iii) Parallel-Migrating GA (island model with periodic elite exchange). Experiments on 50-, 100-, and 200-city Euclidean datasets demonstrate that the migrating island GA achieves superior scalability, faster convergence, and improved solution consistency. While the serial GA performs adequately on smaller datasets, its performance degrades significantly at scale, whereas the migrating parallel GA maintains high-quality solutions and reduced runtime. We expand the classical distance-only objective to a practical multi-objective (distance, traffic, safety, cost) weighted fitness and implement the solver with parallel islands using Python multiprocessing (code and datasets available in the project repository).

The well-known NP-hard traveling salesman problem (TSP) primarily considers distance as its single objective. However, applications modeled from real world systems repeatedly involve more than one objective giving rise to multi-objective optimization. Fusing ideas of dimension reduction, decomposition approaches, and genetic algorithms, this paper presents a multiobjective minimum matrix search algorithm (MOMMS) for the heuristic resolution of the bi-objective TSP (bTSP). The MOMMS uses dimension reduction to obtain a reduce matrix network that is used to obtain or to approximate the set of efficient solutions. The reduce matrix network aids in the decomposition of a multiobjective combinatorial optimization (MOCO) problem into a single objective combinatorial optimization problem. Moreover, using the reduce matrix network MOMMS introduces a population generator that creates an initial population composed of an approximation to the extreme supported efficient solutions. The MOMMS does not use any numerical parameter. Also, MOMMS uses family competitive metamorphosis and short-term memory selection to maintain population diversity in MOCO problems. The proposed algorithm showed respectable results in testing on well-known benchmark problems of the bTSP. Comparisons are performed with the results of state-of-the-art algorithms from the literature. Moreover, the MOMMS is tested on largescale instances of the bTSP. The computational study shows that the proposed algorithm is able to solve large-scale instances in reasonable time. Therefore, the MOMMS is a competitive tool for solving the bTSP.

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, for example, algebraic connectivity, permutation matrices, and association schemes. The main results of this paper are twofold. First, de Klerk and Sotirov [de Klerk E, Sotirov R (2012) Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Math. Programming 133(1):75–91.] present a semidefinite program (SDP) based on permutation matrices and symmetry reduction; they show that it is incomparable to the subtour elimination linear program but generally dominates it on small instances. We provide a family of simplicial TSP instances that shows that the integrality gap of this SDP is unbounded. Second, we show that these simplicial TSP instances imply the unbounded integrality gap of every SDP relaxation of the TSP mentioned in the survey on SDP relaxations of the TSP in section 2 of Sotirov [Sotirov R (2012) SDP relaxations for some combinatorial optimization problems. Anjos MF, Lasserre JB, eds., Handbook on Semidefinite, Conic and Polynomial Optimization (Springer, New York), 795–819.]. In contrast, the subtour linear program performs perfectly on simplicial instances. The simplicial instances thus form a natural litmus test for future SDP relaxations of the TSP.

The Meta heuristic algorithms are the higher level technique which helps to find the best feasible solution out of all possible solution of an optimization problem. There are various different types of meta heuristic algorithms like Ant Colony Optimization (ACO), Genetic Algorithm, Simulated Annealing, Particle Swarm Optimization, etc. Genetic Algorithm is a search-based optimization technique based on the biological principle of Genetics and adaptation. It is a meta-heuristic approach which is used to solve complex combinatorial problem. The integration of Genetic algorithm with machine learning will be helpful in solving unconstrained and constrained optimization problem. The various genetic operator like selection operator, mutation and cross-over are discussed which will be helpful in knowing how these operators significantly improves State Space search. In this paper the various applications of Genetic algorithms which can be used in machine learning has been discussed. In this paper the author discussed how the significance of Genetic algorithm will be improved while solving complex optimization problem in machine learning. In this paper, flow diagram of Genetic Algorithms has been discussed which will ease the understanding of complex optimization problem like 0–1 Knapsack, Traveling Salesman Problem, etc. In this paper a comparative analysis between traditional algorithm and genetic algorithm has been done on the basis of parameters like flow of control, state space search, Complication, Preconditions, CPU utilization etc. The various limitations of Genetic Algorithms in solving problems with optimal solutions has also been discussed.

A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.

The canonical genetic algorithm (CGA) applies selection, crossover and mutation operators to solve difficult optimization problems. This paper introduces a new approach to CGA. It applies only mutation and selection operators. It is a non-crossover genetic algorithm (NCGA). The proof of global convergence of NCGA is presented in this paper. The simulation on the NP-complete traveling salesman problem (TSP) shows that NCGA is much faster than the CGA. In terms of computation efficiency, NCGA is a very promising approach. This paper casts doubt on the need of the crossover operator in GAs.

III.4 - Hopfield Model and Optimization Problems

Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search

The traveling salesman problem (TSP), a typical non-deterministic polynomial (NP) hard problem, has been used in many engineering applications. Genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. However, it has some issues for solving TSP, including quickly falling into the local optimum and an insufficient optimization precision. To address TSP effectively, this paper proposes a hybrid Cellular Genetic Algorithm with Simulated Annealing (SA) Algorithm (SCGA). Firstly, SCGA is an improved Genetic Algorithm (GA) based on the Cellular Automata (CA). The selection operation in SCGA is performed according to the state of the cell. Secondly, SCGA, combined with SA, introduces an elitist strategy to improve the speed of the convergence. Finally, the proposed algorithm is tested against 13 standard benchmark instances from the TSPLIB to confirm the performance of the three cellular automata rules. The experimental results show that, in most instances, the results obtained by SCGA using rule 2 are better and more stable than the results of using rule 1 and rule 3. At the same time, we compared the experimental results with GA, SA, and Cellular Genetic Algorithm (CGA) to verify the performance of SCGA. The comparison results show that the distance obtained by the proposed algorithm is shortened by a mean of 7% compared with the other three algorithms, which is closer to the theoretical optimal value and has good robustness.

Parallel techniques for solving large scale travelling salesperson problems

The Traveling Salesman Problem (TSP) is a well-known problem in computer science that requires finding the shortest possible route that visits every city exactly once. TSP has broad applications in logistics, routing, and supply chain management, where finding optimal or near-optimal solutions efficiently can lead to substantial cost and time reductions. However, traditional solvers rely on iterative processes that can be computationally expensive and time-consuming for large-scale instances. This research proposes a novel deep learning architecture designed to predict optimal or near-optimal TSP tours directly from the problem’s distance matrix, eliminating the need for extensive iterations to save total solving time. The proposed model leverages the attention mechanism to effectively focus on the most relevant parts of the network, ensuring accurate and efficient tour predictions. It has been tested on the TSPLIB benchmark dataset and observed significant improvements in both solution quality and computational speed compared to traditional solvers such as Gurobi and Genetic Algorithm. This method presents a scalable and efficient solution for large-scale TSP instances, making it a promising approach for real-world traveling salesman applications.

The classical travelling salesperson problem (TSP) models the movements of a salesperson travelling through a number of cities. The optimization problem is to choose the sequence in which to visit the cities in order to minimize the total distance travelled. This paper presents a generalized point-to-point motion-planning technique for multi-robot assemblysystems modelled as TSP-type optimization problems. However, in these augmented TSPs (TSP+), both the 'salesperson' (a robot with a tool) as well as the 'cities' (another robot with a workpiece) move. In addition to the sequencing of tasks, further planning is required to choose where the 'salesperson' (i.e., the tool) should rendezvous with each 'city' (i.e. the workpiece). The use of a genetic algorithm (GA) is chosen as the search engine for the solution of this TSP+ optimization problem. As an example area, the optimization of the electronic-component placement process is addressed. The simulation tools developed have been tested on five different component-placement system configurations. In the most generalized configuration, the placement robot meets the component delivery system at an optimal rendezvous location for the pick-up of the component and subsequently meets the printed-cirucit-board (on a mobile XY-table) at an optimal rendezvous location. In addition to the solution of the component-placement sequencing problem and the rendezvous-point planning problem, the collision-avoidance issue is addressed.