Clique Finder

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

Clique Finder

The Maximum Clique Problem (MCP) is a classical NP-hard problem that has gained considerable attention due to its numerous real-world applications and theoretical complexity. It is inherently computationally complex, and so exact methods may require prohibitive computing time. Nature-inspired meta-heuristics have proven their utility in solving many NP-hard problems. In this research, we propose a simulated annealing-based algorithm that we call Clique Finder algorithm to solve the MCP. Our algorithm uses a logarithmic cooling schedule and two moves that are selected in an adaptive manner. The objective (error) function is the total number of missing links in the clique, which is to be minimized. The proposed algorithm was evaluated using benchmark graphs from the open-source library DIMACS, and results show that the proposed algorithm had a high success rate.

Multiple-Try Simulated Annealing Algorithm for Global Optimization

Simulated annealing is a widely used algorithm for the computation of global optimization problems in computational chemistry and industrial engineering. However, global optimum values cannot always be reached by simulated annealing without a logarithmic cooling schedule. In this study, we propose a new stochastic optimization algorithm, i.e., simulated annealing based on the multiple-try Metropolis method, which combines simulated annealing and the multiple-try Metropolis algorithm. The proposed algorithm functions with a rapidly decreasing schedule, while guaranteeing global optimum values. Simulated and real data experiments including a mixture normal model and nonlinear Bayesian model indicate that the proposed algorithm can significantly outperform other approximated algorithms, including simulated annealing and the quasi-Newton method.

Insights Into Simulated Annealing

Simulated annealing is a probabilistic local search method for global combinatorial optimisation problems allowing gradual convergence to a near-optimal solution. It consists of a sequence of moves from a current solution to a better one according to certain transition rules while accepting occasionally some uphill solutions in order to guarantee diversity in the domain exploration and to avoid getting caught at local optima. The process is managed by a certain static or dynamic cooling schedule that controls the number of iterations. This meta-heuristic provides several advantages that include the ability of escaping local optima and the use of small amount of short-term memory. A wide range of applications and variants have hitherto emerged as a consequence of its adaptability to many combinatorial as well as continuous optimisation cases, and also its guaranteed asymptotic convergence to the global optimum.

Constructal Design of Double-T Shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.

List-Based Simulated Annealing Algorithm for Traveling 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.