Performance analysis of the n-queen problem using a simulated annealing optimization approach

Optimization of process parameters in the abrasive waterjet machining using integrated SA–GA

This paper explores the potential of quantum computing on a WCET(Worst-Case Execution Time (of a program).)-related combinatorial optimization problem applied to a set of several polynomial special cases. We consider the maximization problem of determining the most expensive path in a control flow graph. In these graphs, vertices represent blocks of code whose execution times are fixed and known in advance. We port the considered optimization problem to the quantum framework by expressing it as a QUBO. We then experimentally compare the performances in solving the problem of classic Simulated Annealing (SA), Quantum Annealing (QA), and Quantum Approximate Optimization Algorithm (QAOA). Our experiments suggest that QA represents a fast equivalent of simulated annealing. Indeed, we measured the approximation ratio on the results of QA and SA, showing that their performances are comparable, at least on our set of simplified problems.KeywordsWCETsQuantum computingQUBOCombinatorial optimizationQuantum annealingQAOA

Traditional Hopfield networking has been widely used to solve combinatorial optimization problems. However, high order Hopfiled networks, as an expansion of traditional Hopfield networks, are seldom used to solve combinatorial optimization problems. In theory, compared with low order networks, high order networks have better properties, such as stronger approximations and faster convergence rates. In this chapter, the authors focus on how to use high order networks to model combinatorial optimization problems. Firstly, the high order discrete Hopfield Network is introduced, then the authors discuss how to find the high order inputs of a neuron. Finally, the construction method of energy function and the neural computing algorithm are presented. In this chapter, the N queens problem and the crossbar switch problem, which are NP-complete problems, are used as examples to illustrate how to model practical problems using high order neural networks. The authors also discuss the performance of high order networks for modeling the two combinatorial optimization problems.

Researchers have utilised nature-inspired metaheuristic algorithms to find solutions for complex combinatorial optimisation problems and Non-deterministic polynomial (NP) problems. The N-queens problem is categorised as an NP-Hard problem as it becomes insurmountable for large N. This paper proposed a solution for the N-queens problem based on the Apiary Organisational-Based Optimisation Algorithm (AOOA). AOOA is a nature-inspired metaheuristic optimisation algorithm for NP-Hard problems comprised of multiple beehives inside the apiary, each with its population. In contrast to the backtracking method, AOOA employs a fitness function and randomisation techniques through seven stages to approach the optimal distributions of queens so they don’t attack each other. Experiments were carried out for different values of N ranging from 4 to 10. All solutions were found for Ns (4–8), which comprised 100% of the total solutions. At the same time, 97.7272% of total solutions were found for N = 9 and 98.6187% for N = 10. Moreover, several metaheuristic algorithms have been implemented to solve the N-queens problem, and the average number of 100 iterations has been compared. The results reflect the superiority of AOOA over the competing algorithms in finding the possible number of solutions in earlier iterations and consequently reducing the computational cost of further iterations.

Editorial

Dual-mode dynamics neural network for combinatorial optimization

In this paper, we propose a saturation computation method of neural networks for efficiently solving combinatorial optimization problems. In this computation method, once the neuron is in excitatory state, then its input potential is considered to be in positive saturation where the input potential can only be reduced but cannot be increased, and once the neuron is in inhibitory state, then its input potential is considered to be in negative saturation where the input potential can only be increased but cannot be reduced. The proposed method is applied to N-Queens problem. The performance is evaluated through simulations where the results show that the saturation method improves the searching capability of neural networks and shortens the computation time. Particularly, the simulation results show that the performance of the proposed method surpasses the exiting methods for N-queens problem in synchronous parallel model.

In this paper the influence of using heuristic functions to initialize the population of a classic genetic algorithm (GA) applied to the N-Queens Problem (NQP) is analyzed. The aim of this work is to evaluate the impact of the heuristic initialization phase on the results of the classic GA. In order to probe this, several experiments using two different initialization functions have been carried out. In this paper, the well-known NQP has been used as benchmark problem, but the objective of the authors is to contrast the findings of this study with other combinatorial optimization problems.

The Differential Evolution (DE) algorithm was initially proposed for continuous numerical optimization, but it has been applied with success in many combinatorial optimization problems, particularly permutation-based integer combinatorial problems. In this paper, a new and general approach for combinatorial optimization is proposed using the Differential Evolution algorithm. The proposed approach aims at preserving its interesting search mechanism for discrete domains, by defining the difference between two candidate solutions as a differential list of movements in the search space. Thus, a more meaningful and general differential mutation operator for the context of combinatorial optimization problems can be produced. We discuss three alternatives for using the differential list of movements within the differential mutation operation. We present results on instances of the Traveling Salesman Problem (TSP) and the N-Queen Problem (NQP) to illustrate the adequacy of the proposed approach for combinatorial optimization.

Constraint programming offers a declarative approach to solving problems modeled as constraint satisfaction problems (CSPs). However, the precise specification of a set of constraints is sometimes not available, but may have to be learned, for instance, from a set of examples of its solutions and non-solutions. In general, one may wish to learn generalized CSPs involving classical, fuzzy, weighted or probabilistic constraints, for example. This paper introduces a unifying framework for CSP learning. The framework is generic in that it can be instantiated to obtain specific formulations for learning classical, fuzzy, weighted or probabilistic CSPs. In particular, a new formulation for classical CSP learning, which minimizes the number of examples violated by candidate CSPs, is obtained by instantiating the framework. This formulation is equivalent to a simple pseudo-boolean optimization problem, thus being efficiently solvable using many optimization tools.

An adaptive control scheme of simulated annealing (SA) parameters derived from the polynomial-time cooling schedule is presented in terms of the efficiency enhancement of the SA algorithm. The parallel computing adaptive SA optimization scheme, which incorporates the optimization-layer-by-layer (OLL) neutronics evaluation model is then applied to determining the optimum fuel assembly (FA) loading pattern (LP) in the Korea Nuclear Unit 2 pressurized water reactor (PWR) using seven Pentium personal computers (three 266-MHz Pentium II and four 200-MHz Pentium Pro computers). It is shown that the parallel scheme enhances the efficiency of the SA optimization computation significantly but that it can get trapped in local optimum LPs more frequently than the single-processor SA scheme unless one takes preventive steps. As a way to prevent trapping of the parallel scheme in local optima, using multiple seed LPs is proposed instead of a single LP with which the individual processors start each stage, and how to determine the multiple seed LPs is discussed. Because of the high efficiency of the parallel scheme, the acceptability of a hybrid neutronics evaluation model, which is slower but more accurate than the OLL model, in the parallel optimization calculation is examined from the standpoint of computing time. By demonstrating that the FA LP optimization calculation for the equilibrium cycle core of the KNU-2 PWR can be completed in <1 h on seven Pentiums, we justify the routine utilization of the hybrid model in the parallel SA optimization scheme.

A new search method for combinatorial optimization problem inspired by the spin glass system

Artificial Intelligence: Search

The impact of neighbourhood size on the process of simulated annealing: Computational experiments on the flowshop scheduling problem

Feature selection is performed to eliminate irrelevant features to reduce computational overheads. Metaheuristic algorithms have become popular for the task of feature selection due to their effectiveness and flexibility. Hybridization of two or more such metaheuristics has become popular in solving optimization problems. In this paper, we propose a hybrid wrapper feature selection technique based on binary butterfly optimization algorithm (bBOA) and Simulated Annealing (SA). The SA is combined with the bBOA in a pipeline fashion such that the best solution obtained by the bBOA is passed on to the SA for further improvement. The SA solution improves the best solution obtained so far by searching in its neighborhood. Thus the SA tries to enhance the exploitation property of the bBOA. The proposed method is tested on twenty datasets from the UCI repository and the results are compared with five popular algorithms for feature selection. The results confirm the effectiveness of the hybrid approach in improving the classification accuracy and selecting the optimal feature subset.