Novel algorithms of particle swarm optimisation with decision criteria

The particle swarm optimisation (PSO) is a stochastic, optimisation technique based on the movement and intelligence of swarms. In this paper, three new effective optimisation algorithms BPSO, HPSO and WPSO, by incorporating some decision criteria into PSO, have been proposed and analysed both in terms of their efficiency, resistance to the problem of premature convergence and the ability to avoid local optima. In the new algorithms, for each particle except position, two sets of velocities are generated and the profit matrix is constructed. Using the decision criteria the best strategy is selected. Simulations for benchmark test nonlinear function show that the algorithms in which the decision criteria have been applied, are beneficial over classical PSO in terms of their performance and efficiency.     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

A genetic algorithm for combined topology and shape optimisations

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coordinates of the keypoints of changeable boundaries constituted by curves. In both the steps the aim is that to find the variable sets producing the maximum stiffness of the structure, respecting an upper limit on the employed mass. The structural evaluations are carried out with a FEM commercial code, linked to the algorithm. Some applications have been performed and results compared with solutions reported in literature.     

A learning approach to the bandwidth multicolouring problem

In this article, a generalisation of the vertex colouring problem known as bandwidth multicolouring problem (BMCP), in which a set of colours is assigned to each vertex such that the difference between the colours, assigned to each vertex and its neighbours, is by no means less than a predefined threshold, is considered. It is shown that the proposed method can be applied to solve the bandwidth colouring problem (BCP) as well. BMCP is known to be NP-hard in graph theory, and so a large number of approximation solutions, as well as exact algorithms, have been proposed to solve it. In this article, two learning automata-based approximation algorithms are proposed for estimating a near-optimal solution to the BMCP. We show, for the first proposed algorithm, that by choosing a proper learning rate, the algorithm finds the optimal solution with a probability close enough to unity. Moreover, we compute the worst-case time complexity of the first algorithm for finding a 1/(1–?) optimal solution to the given problem. The main advantage of this method is that a trade-off between the running time of algorithm and the colour set size (colouring optimality) can be made, by a proper choice of the learning rate also. Finally, it is shown that the running time of the proposed algorithm is independent of the graph size, and so it is a scalable algorithm for large graphs. The second proposed algorithm is compared with some well-known colouring algorithms and the results show the efficiency of the proposed algorithm in terms of the colour set size and running time of algorithm.     

Model review and algorithm comparison on multi-objective disassembly line balancing

As the disassembly of end-of-life products is affected by several dynamic and uncertain issues, many mathematical models and solution approaches have been established. However, with more extended objectives, constraints and different methods of disassembly, inconsistent models relating to product representations and types of disassembly lines have become the main barriers for the transfer of research to practise. In this paper, a systematic overview of recent models to summarise the input data, parameters, decision variables, constraints and objectives of disassembly line balancing are presented. After discussing the adaptation and extensibility of these models for different environments, a unified encoding scheme is designed to apply typical multi-objective evolutionary algorithms on this problem with extensive decision variables and seven significant objectives. Algorithm comparison on four typical cases is then carried out based on seven commonly used products to verify the optimisation process for the integrated version of existing models and demonstrate the overall performance of the typical multi-objective evolutionary algorithms on this problem. Experimental results can be a baseline for further algorithm design and practical algorithm selection on these disassembly line balancing scenarios.     

Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem

Hyper heuristics is a relatively new optimisation algorithm. Numerous studies have reported that hyper heuristics are well applied in combinatorial optimisation problems. As a classic combinatorial optimisation problem, the row layout problem has not been publicly reported on applying hyper heuristics to its various sub-problems. To fill this gap, this study proposes a parallel hyper-heuristic approach based on reinforcement learning for corridor allocation problems and parallel row ordering problems. For the proposed algorithm, an outer layer parallel computing framework was constructed based on the encoding of the problem. The simulated annealing, tabu search, and variable neighbourhood algorithms were used in the algorithm as low-level heuristic operations, and Q-learning in reinforcement learning was used as a high-level strategy. A state space containing sequences and fitness values was designed. The algorithm performance was then evaluated for benchmark instances of the corridor allocation problem (37 groups) and parallel row ordering problem (80 groups). The results showed that, in most cases, the proposed algorithm provided a better solution than the best-known solutions in the literature. Finally, the meta-heuristic algorithm applied to three low-level heuristic operations is taken as three independent algorithms and compared with the proposed hyper-heuristic algorithm on four groups of parallel row ordering problem instances. The effectiveness of Q-learning in selection is illustrated by analysing the comparison results of the four algorithms and the number of calls of the three low-level heuristic operations in the proposed method.     

Multi-objective ACO algorithms to minimise the makespan and the total rejection cost on BPMs with arbitrary job weights

In this paper, we investigate the batch-scheduling problem with rejection on parallel machines with non-identical job sizes and arbitrary job-rejected weights. If a job is rejected, the corresponding penalty has to be paid. Our objective is to minimise the makespan of the processed jobs and the total rejection cost of the rejected jobs. Based on the selected multi-objective optimisation approaches, two problems, P1 and P2, are considered. In P1, the two objectives are linearly combined into one single objective. In P2, the two objectives are simultaneously minimised and the Pareto non-dominated solution set is to be found. Based on the ant colony optimisation (ACO), two algorithms, called LACO and PACO, are proposed to address the two problems, respectively. Two different objective-oriented pheromone matrices and heuristic information are designed. Additionally, a local optimisation algorithm is adopted to improve the solution quality. Finally, simulated experiments are conducted, and the comparative results verify the effectiveness and efficiency of the proposed algorithms, especially on large-scale instances.     

An iterated greedy algorithm for the large-scale unrelated parallel machines scheduling problem

In this work, we tackle the problem of scheduling a set of jobs on a set of unrelated parallel machines with minimising the total weighted completion times as performance criteria. The iterated greedy metaheuristic generates a sequence of solutions by iterating over a constructive heuristic using destruction and construction phases. In the last few years, iterated greedy has been employed to solve a considerable number of problems. This is because it is based on a very simple principle, it is easy to implement, and it often exhibits an excellent performance. Moreover, scalability for high-dimensional problems becomes an essential requirement for modern optimisation algorithms. This paper proposes an iterated greedy model for the above-mentioned scheduling problem to tackle large-size instances. The benefits of our proposal in comparison to existing metaheuristics proposed in the literature are experimentally shown.     

Particle swarm optimisation in designing parameters of manufacturing processes: A review (2008–2018)

The evolutionary optimisation algorithms appeared as an effective alternative to conventional statistical methods that have certain limitations in optimising complex manufacturing processes. Considering works published in the last decade, this paper presents an analysis of the particle swarm optimisation (PSO) implementation in designing parameters of heterogeneous manufacturing processes, both conventional and emerging, new processes. The literature review and analysis was structured according to the complexity of the optimisation problem (single response and multiresponse problems), and the development of an objective function for PSO. The tuning of the PSO algorithm-specific parameters was analysed in detail. The PSO algorithm performance was benchmarked with the results of other methods, including evolutionary algorithms, in designing process parameters. The concerns in applying PSO for multiresponse manufacturing problems were highlighted, and recommendations for future research were drawn. Such a comprehensive review on the PSO application in optimising manufacturing processes, including the detailed discussion on the algorithm characteristics and benchmark with other optimisation procedures, has not been pursued so far. Therefore, this review analysis provides hands on information for researchers and engineers at one place, and it is believed that the findings could serve as a basis for the future research and implementation directions.     

Randomised Local Search Algorithm for the Clustering Problem

We consider clustering as a combinatorial optimisation problem. Local search provides a simple and effective approach to many other combinatorial optimisation problems. It is therefore surprising how seldom it has been applied to the clustering problem. Instead, the best clustering results have been obtained by more complex techniques such as tabu search and genetic algorithms at the cost of high run time. We introduce a new randomised local search algorithm for the clustering problem. The algorithm is easy to implement, sufficiently fast, and competitive with the best clustering methods. The ease of implementation makes it possible to tailor the algorithm for various clustering applications with different distance metrics and evaluation criteria.