An Experimental Comparison of Algebraic Crossover Operators for Permutation Problems

2020 ◽  
Vol 174 (3-4) ◽  
pp. 201-228
Author(s):  
Marco Baioletti ◽  
Gabriele Di Bari ◽  
Alfredo Milani ◽  
Valentino Santucci
Keyword(s):  
Optimization Problems ◽  
Experimental Comparison ◽  
Lattice Structures ◽  
Flowshop Scheduling ◽  
Permutation Flowshop ◽  
Combinatorial Optimization Problems ◽  
Algebraic Properties ◽  
The Traveling Salesman Problem ◽  
Permutation Problems ◽  
Semantic Properties

Crossover operators are very important components in Evolutionary Computation. Here we are interested in crossovers for the permutation representation that find applications in combinatorial optimization problems such as the permutation flowshop scheduling and the traveling salesman problem. We introduce three families of permutation crossovers based on algebraic properties of the permutation space. In particular, we exploit the group and lattice structures of the space. A total of 34 new crossovers is provided. Algebraic and semantic properties of the operators are discussed, while their performances are investigated by experimentally comparing them with known permutation crossovers on standard benchmarks from four popular permutation problems. Three different experimental scenarios are considered and the results clearly validate our proposals.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

A Research on Flowshop Scheduling Problems With Column Generation

2012 ◽  
Author(s):  
H. Tanohata ◽  
T. Kaihara ◽  
N. Fujii
Keyword(s):  
Combinatorial Optimization ◽  
Local Search ◽  
Column Generation ◽  
Optimization Problems ◽  
New Method ◽  
Duality Gap ◽  
Scheduling Problems ◽  
Flowshop Scheduling ◽  
Feasible Schedule ◽  
Combinatorial Optimization Problems

Column generation is a method to calculate lowerbound for combinatorial optimization problems, although a feasible schedule is generally obtained with the upperbound. Therefore, in this paper, a new method is proposed to solve the flowshop scheduling problems with column generation, which is composed of the local search and duality gap termination condition. The neighborhood of the local search is composed of columns, and the method is applied in column generation to improve the upperbound and lowerbound. The effectiveness of the proposed method is verified by computational experiments.

Microcanonical Optimization Applied to the Traveling Salesman Problem

1998 ◽  
Vol 09 (01) ◽  
pp. 133-146 ◽  
Author(s):  
Alexandre Linhares ◽  
José R. A. Torreão
Keyword(s):  
Simulated Annealing ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Physics ◽  
Traveling Salesman ◽  
Tabu Search Algorithm ◽  
Combinatorial Optimization Problems ◽  
Microcanonical Annealing ◽  
The Traveling Salesman Problem

Optimization strategies based on simulated annealing and its variants have been extensively applied to the traveling salesman problem (TSP). Recently, there has appeared a new physics-based metaheuristic, called the microcanonical optimization algorithm (μO), which does not resort to annealing, and which has proven a superior alternative to the annealing procedures in various applications. Here we present the first performance evaluation of μO as applied to the TSP. When compared to three annealing strategies (simulated annealing, microcanonical annealing and Tsallis annealing), and to a tabu search algorithm, the microcanonical optimization has yielded the best overall results for several instances of the euclidean TSP. This confirms μO as a competitive approach for the solution of general combinatorial optimization problems.

scholarly journals Synergy of Genetic Algorithm with Extensive Neighborhood Search for the Permutation Flowshop Scheduling Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Rong-Chang Chen ◽  
Jeanne Chen ◽  
Tung-Shou Chen ◽  
Chien-Che Huang ◽  
Li-Chiu Chen
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Neighborhood Search ◽  
Local Optimum ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Permutation Flowshop ◽  
Hybrid Genetic Algorithms ◽  
Combinatorial Optimization Problems ◽  
Flowshop Scheduling Problem

The permutation flowshop scheduling problem (PFSP) is an important issue in the manufacturing industry. The objective of this study is to minimize the total completion time of scheduling for minimum makespan. Although the hybrid genetic algorithms are popular for resolving PFSP, their local search methods were compromised by the local optimum which has poorer solutions. This study proposed a new hybrid genetic algorithm for PFSP which makes use of the extensive neighborhood search method. For evaluating the performance, results of this study were compared against other state-of-the-art hybrid genetic algorithms. The comparisons showed that the proposed algorithm outperformed the other algorithms. A significant 50% test instances achieved the known optimal solutions. The proposed algorithm is simple and easy to implement. It can be extended easily to apply to similar combinatorial optimization problems.

scholarly journals Computation Results of Finding All Efficient Points in Multiobjective Combinatorial Optimization

2008 ◽  
Vol 3 (4) ◽  
pp. 374 ◽  
Author(s):  
Milan Stanojevic ◽  
Mirko Vujoševic ◽  
Bogdana Stanojevic
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Efficient Points ◽  
Steiner Tree Problem ◽  
Pareto Optimal Solutions ◽  
Problem Size ◽  
Original Algorithm ◽  
Multiobjective Combinatorial Optimization ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The number of efficient points in criteria space of multiple objective combinatorial optimization problems is considered in this paper. It is concluded that under certain assumptions, that number grows polynomially although the number of Pareto optimal solutions grows exponentially with the problem size. In order to perform experiments, an original algorithm for obtaining all efficient points was formulated and implemented for three classical multiobjective combinatorial optimization problems. Experimental results with the shortest path problem, the Steiner tree problem on graphs and the traveling salesman problem show that the number of efficient points is much lower than a polynomial upper bound.

VRoptBees

2018 ◽  
Vol 7 (1) ◽  
pp. 32-56
Author(s):  
Thiago A.S. Masutti ◽  
Leandro Nunes de Castro
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Optimization Problems ◽  
The Other ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Biological Phenomena ◽  
The Traveling Salesman Problem

Combinatorial optimization problems are broadly studied in the literature. On the one hand, their challenging characteristics, such as the constraints and number of potential solutions, inspires their use to test new solution techniques. On the other hand, the practical application of these problems provides support of daily tasks of people and companies. Vehicle routing problems constitute a well-known class of combinatorial optimization problems, from which the Traveling Salesman Problem (TSP) is one of the most elementary ones. TSP corresponds to finding the shortest route that visits all cities within a path returning to the start city. Despite its simplicity, the difficulty in finding its exact solution and its direct application in practical problems in multiple areas make it one of the most studied problems in the literature. Algorithms inspired by biological phenomena are being successfully applied to solve optimization tasks, mainly combinatorial optimization problems. Those inspired by the collective behavior of insects produce good results for solving such problems. This article proposes the VRoptBees, a framework inspired by honeybee behavior to tackle vehicle routing problems. The framework provides a flexible and modular tool to easily build solutions to vehicle routing problems. Together with the framework, two examples of implementation are described, one to solve the TSP and the other to solve the Capacitated Vehicle Routing Problem (CVRP). Tests were conducted with benchmark instances from the literature, showing competitive results.

Omicron ACO. A New Ant Colony Optimization Algorithm

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Benjamın Baran ◽  
Osvaldo Gomez
Keyword(s):  
Ant Colony Optimization ◽  
Optimization Problems ◽  
Population Based ◽  
Analytical Tool ◽  
Traveling Salesman ◽  
Ant Colony ◽  
Ant Colony Optimization Algorithm ◽  
Ant Colonies ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

Ant Colony Optimization (ACO) is a metaheuristic inspired by the foraging behavior of ant colonies that has been successful in the resolution of hard combinatorial optimization problems like the Traveling Salesman Problem (TSP). This paper proposes the Omicron ACO (OA), a novel population-based ACO alternative originally designed as an analytical tool. To experimentally prove OA advantages, this work compares the behavior between the OA and the MMAS as a function of time in two well-known TSP problems. A simple study of the behavior of OA as a function of its parameters shows its robustness.

Unit Commitment by Evolving Ant Colony Optimization

2010 ◽  
Vol 1 (3) ◽  
pp. 67-77 ◽  
Author(s):  
K. Vaisakh ◽  
L. R. Srinivas
Keyword(s):  
Ant Colony Optimization ◽  
Unit Commitment ◽  
Optimization Problems ◽  
Problem Formulation ◽  
Ant Colony ◽  
Spinning Reserve ◽  
Combinatorial Optimization Problems ◽  
Start Up ◽  
The Traveling Salesman Problem ◽  
Optimal Set

Ant Colony Optimization is more suitable for combinatorial optimization problems. ACO is successfully applied to the traveling salesman problem, and multistage decision making of ACO has an edge over other conventional methods. In this paper, the authors propose the Evolving Ant Colony Optimization (EACO) method for solving unit commitment (UC) problem. The EACO employs Genetic Algorithm (GA) for finding optimal set of ACO parameters, while ACO solves the UC problem. Problem formulation takes into consideration the minimum up and down time constraints, start up cost, spinning reserve, and generation limit constraints. The feasibility of the proposed approach is demonstrated on the systems with number of generating units in the range of 10 to 60. The test results are encouraging and compared with those obtained by other methods.

Research on MPI-Based Parallel Max-Min Ant System

2012 ◽  
Vol 198-199 ◽  
pp. 1321-1326 ◽  
Author(s):  
Yu Liu ◽  
Guo Dong Wu
Keyword(s):  
Combinatorial Optimization ◽  
Numerical Experiments ◽  
Large Scale ◽  
Optimization Problems ◽  
Computation Time ◽  
Traveling Salesman ◽  
Ant System ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

When solving large scale combinatorial optimization problems, Max-Min Ant System requires long computation time. MPI-based Parallel Max-Min Ant System described in this paper can ensure the quality of the solution, as well as reduce the computation time. Numerical experiments on the multi-node cluster system show that when solving the traveling salesman problem, MPI-based Parallel Max-Min Ant System can get better computational efficiency.

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