Inherent in model selection is the problem of simultaneously optimizing multiple performance metrics. Some of these metrics express potentially conflicting criteria, like accuracy and simplicity. Pareto optimization is a branch of mathematical optimization that deals precisely with problems involving conflicting objective functions. In this article, an algorithm was developed that searches automatically for Pareto optimal linear regression models given a dataset and a set of performance metrics. The optimization task was framed as one of sequential variable selection on a graph. A search strategy was proposed that draws on ant colony optimization, a probabilistic technique well suited for graph-based problems. Experiments were run in which the metrics to be minimized were the root-mean-square error, expressing accuracy, and the number of coefficients, expressing simplicity. To substantiate the usefulness of our algorithm, cases were presented in which it outperformed AIC-based stepwise regression. Results suggested that our algorithm copes well with small datasets and correlated predictors, that it is efficient and that it informs model selection. Key properties of our algorithm were discussed and areas of improvement highlighted.
A combination of the two most important problems in logistics called the capacitated vehicle routing problem with two-dimensional loading constraint is studied in this article. It aims in designing the most appropriate pathways, starting and terminating at a central depot, minimising the total transportation cost with a homogenous fleet of vehicles. Items loaded in each vehicle's trip must satisfy the two-dimensional of orthogonal packing constraint. Since the problem is an NP-hard optimisation problem, a large number of approaches have been proposed. Whereas, finding the exact solution via optimisation is still a challenging problem due to their complexity. In order to increase the exploration in the solution space, we propose the parallel variable neighbourhood search algorithm. It is tested with 180 benchmark instances and compared with state-of-the-art approaches. The results showed that our approach is competitive in terms of the quality of solutions found.
General solvers exist for several types of optimisation problems, with the commercially available solvers for mixed integer programming (MIP) being a prime example. Although binary integer programming (BIP) can be used to model a wide variety of important combinatorial optimisation problems, relatively few contributions have been made to develop heuristic algorithms for BIP. This paper examines whether variable neighbourhood search can be successfully used to tackle BIP instances, when avoiding very large neighbourhoods explored by the means of external MIP solvers. The results indicate that methods based on variable neighbourhood search are more successful than exact and heuristic commercial solvers on certain types of instances, while the opposite holds true on others. A general variable neighbourhood search proves very effective on instances with up to 200 variables, in particular some instances that are tightly constrained.
K nearest neighbours algorithm is a classic, well studied yet a promising classification technique with high accuracy and best learning time compared to other classification algorithms. The goal is to overcome its slow classification time using instance selection by eliminating redundant and erroneous data. The instance selection problem has been classified as a non-deterministic polynomial time hard problem. In this article, the aim is to keep up with real time applications such as robotics with limited memory, while maintaining the fast-learning speed and high classification accuracy. We introduce a new multistage genetic algorithm for instance selection consisting of successive genetic instance selection stages with iterative search space reduction. The results witnessed an extreme reduction in classification time, reaching 99% without any significant penalty in the accuracy. It has been tested successfully using real traces of robot wall following navigation datasets and favourably compared to other approaches using various datasets.
This work considers the periodic open arc routing problem (POCARP) that models the meter reader application. This application is very interesting when the routes are planned on horizon of several periods. We develop two approaches to solve the problem under study: the first one is based on hybrid genetic algorithm with a specific crossover and the second one on hybrid ant colony method combined with an insertion heuristic. The two proposed algorithms are hybridised with a local search procedure that exploits several moves (relocate, swap, 2-opt and change combination). The objective of the problem is to find a combination of service periods for each task as well as the feasible routes of each period by using a predefined number of available vehicles that minimise the total travelling distance over the multi-period horizon. We extended the optimal splitting procedure to generate and evaluate solutions. We compared our approaches with one of the most important insertion heuristics adapted to this problem. Computational experiments are conducted on a set of generated benchmark instances and indicate that the proposed metaheuristics dominate the good insertion heuristic.
This paper presents a comparison of metaheuristics algorithms for solving crew rostering problem in airline company. Many optimisation methods have been developed to improve both roster quality and computational time. This paper proposes simple iterative mutation (SIMA) method to solve airline crew rostering problem. The proposed method is originated from genetic algorithm. Unlike genetics algorithm which is commonly used, the proposed simple iterative method consists of only three steps including initialisation, selection, and mutation. The method is applied to the datasets from Indonesia airline company, Merpati Nusantara Airline (MNA). To evaluate the performance of the proposed method, the results are compared to those of cross entropy, differential evolution, column generation and MOSI (method used by the airline) in minimising number of assigned crews to cover all of scheduled flights. From the experiments, SIMA method produced better result in term of roster quality and computational time.
In this paper, we study the performance of five population-based metaheuristics to solve a large 393 number of comprehensive problem instances from the literature for the important NP-Hard multiple choice multidimensional knapsack problem MMKP. The five metaheuristics are: teaching-learning-based optimisation TLBO, artificial bee colony ABC, genetic algorithm GA, criss-cross optimisation algorithm COA, and binary bat algorithm BBA. All five of these metaheuristics are similar in that they transform a population of solutions in an effort to improve the solutions in the population and they are all implemented in a straightforward manner. Statistically over all 393 problem instances, we show that COA, GA, and TLBO give similar results which are better than other published solution approaches for the MMKP. However, if we incorporate a simple neighbourhood search into each of these five metaheuristics, in addition to improved solution quality, there is now no statistically significant difference among the results for these five metaheuristics.
The problem under study is the minimum broadcast time. Given an undirected connected graph and a singleton that owns a message, the goal is to broadcast this message as soon as possible, where the communication takes place between neighbouring-nodes in a selective fashion and each forwarding takes one time-slot. Historically, this problem finds applications in telephonic services; however, it serves as an inspirational problem for the design of current delay-tolerant forwarding schemes in modern communication systems like content delivery networks and peer-to-peer networks. The problem belongs to the NP -complete class. As a consequence, the literature offers heuristics, approximation algorithms and exact exponential-time solutions. The contributions of this paper are two-fold. First, an efficient integer linear programming formulation for the problem is provided. Second, a competitive heuristic called TreeBlock , is developed. A fair comparison between TreeBlock and previous heuristics highlights the effectiveness of our proposal.
This paper aims to analyse the influence of parameter setup over a set of five heuristic methods applied to the graph colouring problem. Each heuristic is applied to a considerable set of problem instances, using a range of different parameter values. Multidimensional analysis is applied to extract and express knowledge about the performance of heuristic methods according to problem instance feature values, highlighting the effect of different parameter setups. The dynamic behaviour of the heuristics is also evaluated at different stages of execution (runtime), providing additional knowledge about speed of convergence/stagnation. Results demonstrate that it is possible to associate regions of the instance space in which problem instances exhibit particular features with specific parameter values yielding superior performance. Information relating runtime with average rate of solution improvement also suggests that certain instance features can be used to determine for how long the heuristics need to run before they converge or stagnate.
This paper addresses the problem of computational and networking resources embedding across multiple independent cloud providers (CPs). We focus on the splitting phase problem by proposing a virtual network requests (VNRs) splitting strategy, which aims at improving the performance and the quality of service (QoS) of resulting mapped VNR segments. We formalise our splitting strategy as a mathematical maximisation problem with constraints by using an integer linear program (ILP). Since the VNRs splitting process is classified as an NP-hard problem, we propose a metaheuristic approach based on the Tabu search (TS), in order to find good feasible solutions in polynomial solving time. The simulations results obtained show the efficiency of the proposed algorithm, in comparison with the exact method and an other baseline approach. Solution costs are on average close to the upper bounds, with an average gap ranging from 0% to a maximum of 2.97%, performed in a highly reduced computing time.
To evade the big and destructive obstacles in the real world scenario, such as bomb blast, nuclear activities, and fire breakdowns, robots are necessary. Robot path planning (RPP) problem is one of the interesting NP-hard problems in the world of robotics. The RPP problem can be dealt with, using swarm intelligence (SI) based optimisation algorithms. Teaching learning based optimisation (TLBO) algorithm is a very efficient and reliable swarm intelligence based algorithm in the history of optimisation. This paper proposed a hybridised version of TLBO with shuffled frog leaping algorithm (SFLA) to improve the efficiency in terms of exploitation and to overcome the slow convergence rate. The proposed variant is named as shuffled teaching learning-based optimisation (STLBO) algorithm. For checking the efficiency and accuracy of the proposed STLBO, it is applied to 12 continuous benchmark functions and compared with different nature inspired algorithms (NIA). To check the robustness of the propounded STLBO, it is implemented to solve the problem of RPP. Through simulation results and statistical analyses, the effectiveness of the proposed STLBO is proved.
This paper presents a comparison between three new hybridisations using three particle swarm optimisation (PSO) variants: The Barebones PSO (BPSO), the comprehensive learning PSO (CLPSO) and the cooperative learning PSO (CoLPSO). The goal of these hybridisations is to improve the exploration and the exploitation of the search space from these three variants and contributes to PSO on high scale continuous optimisation problems. The performance of these three new hybrids, named HCLBPSO-Half, HBPSO+CL and HCoCLPSO, are compared with the original methods on which they are based. The comparison is done using six classical continuous optimisation functions with dimensions set to 50, 100 and 200, and all 15 continuous optimisation functions from the CEC'15 benchmark with dimensions set to 10, 30, 50 and 100. The results are compared using the mean and median of executions.
Whale optimisation algorithm (WOA) is a new bio-inspired algorithm which mimics the hunting behaviour of humpback whale in nature. Standard WOA is easily trapped in local optima, provide slow convergence rate and lack of diversity, as the dimension of the search space expansion. In this paper, modified whale optimisation algorithm (MWOA) is proposed to improve the quality of standard WOA algorithm performance. Moreover, an adaptive optimisation algorithm based on modified whale optimisation algorithm and Laplace crossover (ALMWOA) is presented in this paper to increase the diversity of search space and enhance the capability to avoid local optimal solutions. The proposed MWOA and ALMWOA algorithms are tested on a set of 23 benchmark functions and the results are compared with standard WOA and other well-known meta-heuristic optimisation algorithms. Experimental results show that MWOA and ALMWOA can significantly outperform other optimisation algorithms in most of benchmark functions.
Metaheuristic search algorithms have become ubiquitous in the applied optimisation world. Various works have appeared classifying and improving these algorithms and the particular processes embedded within the algorithms. Successful metaheuristic approaches have a common general structure to their search processes. To this end, we offer a structural taxonomy of metaheuristic search methods. This taxonomy serves as a framework for constructing and evaluating metaheuristic approaches from a general structural perspective as well as for conducting empirical research regarding the effectiveness of more detailed structural components. Implementation mechanisms of the detailed components within each structural component are left for future taxonomy research and development.
A hybrid algorithm for the maximum clique problem is presented. A heuristic is used to generate cliques and these are improved by some simple optimisations and Tabu search. All components of the algorithm make use of an exact algorithm or a pseudoexact algorithm, which is an exact algorithm with some specialised pruning. Pre-processing is useful for some instances. The algorithm is shown to be successful using standard and new benchmarks.
This paper is the second part of our study. In the first part, we introduced the concept of solution attractor of local search system for the travelling salesman problem (TSP), described a procedure for constructing the solution attractor, and presented an attractor-based search system to solve the dynamic multi-objective TSP. In this paper, we report the results of our recent empirical study on some important properties of the solution attractor of local search system for the TSP. These properties include the nature of convergence of local search trajectories, the size of the constructed solution attractor, the relationship between the size of the problem and the size of the constructed solution attractor, the best tour in the solution attractor, and computational complexity in the attractor-based search system.
We investigate a new variant of network design problems (NDPs) called the generalised discrete cost multicommodity network design problem (GDCMNDP) that arises in a wide variety of real-life situations such as transportation, telecommunication and logistics. The problem consists on identifying the optimal capacitated network by choosing the connections to be installed in order to satisfy partially or totally the multicommodity demands. The objective is to minimise the sum of installation costs and penalty costs due to the unrouted demands. For the GDCMNDP, we propose three basic greedy heuristics and three bio-inspired metaheuristics: a basic genetic algorithm, a hybrid genetic algorithm via a variable neighbourhood search procedure and a biogeography-based optimisation heuristic. To assess the performance of the proposed approaches, computational results are reported using real-world and benchmark instances from the literature. Computational results show that our hybrid genetic algorithm performs well by obtaining very good final solutions in reasonable times.
The use of the Flying Elephants Method engenders a simple one-level completely differentiable optimisation problem and allows overcoming the main difficulties presented by the original one. Computational results obtained for the covering of some solid body test instances show the good performance of the proposed methodology.
The comparison between metaheuristics has been frequently addressed and, in a certain way, there is some controversy regarding the techniques to be employed in such comparison. In a multimodal problem, the capability of the algorithm to identify more than one solution must be considered. Computation time and/or the number of objective-function evaluations are possible metrics to be compared. The robustness and the accuracy of the methodologies are also fundamental quantities. In this work, we present a scenario of comparisons between two metaheuristics – the differential evolution (DE) and the symbiotic organisms search (SOS). This scenario consisted of a problem characterised by a nonlinear algebraic system (converted into an optimisation problem): the double azeotrope in the system ammonia + R-125. The results indicate that DE and SOS exhibit similar performances in the search for the first minimum. Nevertheless, the DE outperformed the SOS with respect to the capability to identify both minima.
