Symbiotic Organisms Search (SOS) algorithm is an effective new metaheuristic search algorithm, which has recently recorded wider application in solving complex optimization problems. SOS mimics the symbiotic relationship strategies adopted by organisms in the ecosystem for survival. This paper, presents a study on the application of SOS with Simulated Annealing (SA) to solve the well-known traveling salesman problems (TSPs). The TSP is known to be NP-hard, which consist of a set of (n1)!/2 feasible solutions. The intent of the proposed hybrid method is to evaluate the convergence behaviour and scalability of the symbiotic organism's search with simulated annealing to solve both small and large-scale travelling salesman problems. The implementation of the SA based SOS (SOS-SA) algorithm was done in the MATLAB environment. To inspect the performance of the proposed hybrid optimization method, experiments on the solution convergence, average execution time, and percentage deviations of both the best and average solutions to the best known solution were conducted. Similarly, in order to obtain unbiased and comprehensive comparisons, descriptive statistics such as mean, standard deviation, minimum, maximum and range were used to describe each of the algorithms, in the analysis section. The Friedman's Test (with post hoc tests) was further used to compare the significant difference in performance between SOS-SA and the other selected state-of-the-art algorithms. The performances of SOS-SA and SOS are evaluated on different sets of TSP benchmarks obtained from TSPLIB (a library containing samples of TSP instances). The empirical analysis results show that the quality of the final results as well as the convergence rate of the new algorithm in some cases produced even more superior solutions than the best known TSP benchmarked results.

Simulated annealing based symbiotic organisms search optimization algorithm for traveling salesman problem

A Discrete Symbiotic Organisms Search (DSOS) algorithm for finding a near optimal solution for the Travelling Salesman Problem (TSP) is proposed. The SOS is a metaheuristic search optimization algorithm, inspired by the symbiotic interaction strategies often adopted by organisms in the ecosystem for survival and propagation. This new optimization algorithm has been proven to be very effective and robust in solving numerical optimization and engineering design problems. In this paper, the SOS is improved and extended by using three mutation-based local search operators to reconstruct its population, improve its exploration and exploitation capability, and accelerate the convergence speed. To prove that the proposed solution approach of the DSOS is a promising technique for solving combinatorial problems like the TSPs, a set of benchmarks of symmetric TSP instances selected from the TSPLIB library are used to evaluate its performance against other heuristic algorithms. Numerical results obtained show that the proposed optimization method can achieve results close to the theoretical best known solutions within a reasonable time frame.

Discrete symbiotic organisms search algorithm for travelling salesman problem

A discrete water cycle algorithm for solving the symmetric and asymmetric traveling salesman problem

An intelligent/cognitive model of task scheduling for IoT applications in cloud computing environment

The Travelling Salesman Problem (TSP) is an NP-hard problem with high number of possible solutions. The complexity increases with the factorial of n nodes in each specific problem. Meta-heuristic algorithms are an optimization algorithm that able to solve TSP problem towards a satisfactory solution. To date, there are many meta-heuristic algorithms introduced in literatures which consist of different philosophies of intensification and diversification. This paper focuses on 6 heuristic algorithms: Nearest Neighbor, Genetic Algorithm, Simulated Annealing, Tabu Search, Ant Colony Optimization and Tree Physiology Optimization. The study in this paper includes comparison of computation, accuracy and convergence.

Combinatorial Optimization: Comparison of Heuristic Algorithms in Travelling Salesman Problem

Simulated annealing SA algorithm is a popular intelligent optimization algorithm which has been successfully applied in many fields. Parameters’ setting is a key factor for its performance, but it is also a tedious work. To simplify parameters setting, we present a list-based simulated annealing LBSA algorithm to solve traveling salesman problem TSP. LBSA algorithm uses a novel list-based cooling schedule to control the decrease of temperature. Specifically, a list of temperatures is created first, and then the maximum temperature in list is used by Metropolis acceptance criterion to decide whether to accept a candidate solution. The temperature list is adapted iteratively according to the topology of the solution space of the problem. The effectiveness and the parameter sensitivity of the list-based cooling schedule are illustrated through benchmark TSP problems. The LBSA algorithm, whose performance is robust on a wide range of parameter values, shows competitive performance compared with some other state-of-the-art algorithms.

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List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

List-based simulated annealing (LBSA) algorithm, which uses list-based cooling scheme to control the change of parameter temperature, was first proposed for traveling salesman problem. This paper extends the application of LBSA algorithm for 0–1 knapsack problem (0-1 KP). A hybrid greedy repair and optimization operator, which combines density-based and value-based greedy repair and optimization operators, is designed to get better balance between intensification and diversification. Extensive experiments were performed to show the effectiveness and parameter robustness of a list-based cooling scheme and to verify the advantage of using hybrid greedy repair and optimization operator. Comparing experiments, which were conducted on small-scale, medium-scale, and large-scale 0–1 KP instances, have shown that LBSA algorithm is better than or competitive with other state-of-the-art metaheuristics.

List-Based Simulated Annealing Algorithm With Hybrid Greedy Repair and Optimization Operator for 0–1 Knapsack Problem

Noising methods (NMs) include a set of local search methods and can be considered as simulated annealing algorithm or threshold accepting (TA) method when its components are properly chosen. This paper studies how to utilize NMs for solving the 0–1 knapsack problem (0–1 KP). Two noising strategies, noising variation of objective function and noising data, are used to help NMs escape from local optima. When noising variation of objective function is used, probabilistic acceptance or deterministic acceptance is used to decide whether to accept neighbor solutions. Two decreasing strategies, arithmetical decreasing and geometrical decreasing, are used to control the change of parameter noise-rate. In total, six variants of NMs including two TAs are designed to solve the 0–1 KP. In those variants, a hybrid greedy repair operator, which combines density-based and value-based greedy drop and add operators, is designed to get better balance between intensification and diversification. Extensive experiments were performed to compare the performances of the six variants of NMs. The performances of the six variants of NMs were also compared with some state-of-the-art metaheuristics on a wide range of small size, medium size, and large size 0–1 KP instances. Simulation results show that NMs are better than or competitive with other state-of-the-art metaheuristics.

Noising methods with hybrid greedy repair operator for 0–1 knapsack problem

Artificial bee colony (ABC) algorithm, which has explicit strategies to balance intensification and diversification, is a simple and effective swarm intelligence algorithm for both continuous and combinatorial optimisation problems. Selection scheme, which is used by onlooker bees to select employed bees to follow, is an important factor for ABC algorithm to keep good balance between intensification and diversification. In this paper, a normalised fitness function for minimisation problem is first proposed for roulette wheel selection, so ABC can still have enough selection pressure in late stage. And then, aim to analyse the effect of different selection schemes, systematic experiments were carried for roulette wheel selection, rank selection, tournament selection, and disruptive selection on a set of test functions with different dimensions and different computation resources. Simulation results show that the suitability of a selection scheme depends not only on the features of test functions and but also on the computation resources used. No selection scheme can always outperform other selection schemes on all test functions.

Zejun Zhang

Papers

List-Based Simulated Annealing Algorithm for Traveling Salesman Problem

List-Based Simulated Annealing Algorithm With Hybrid Greedy Repair and Optimization Operator for 0–1 Knapsack Problem

Noising methods with hybrid greedy repair operator for 0–1 knapsack problem

Comparative analysis of selection schemes used in artificial bee colony algorithm