Metaheuristic Framework Research Articles

Metaheuristic Framework Introducing the Concept of Reinforcement Learning for Combinatorial Optimization Problems

Metaheuristic Framework Introducing the Concept of Reinforcement Learning for Combinatorial Optimization Problems

Framework for treating non-Linear multi-term fractional differential equations with reasonable spectrum of two-point boundary conditions

In this work, a novel bio-inspired meta-heuristic framework is presented for the assessment of linear and non-linear multi-term fractional differential equations (MFDEs) based on the idea of residual power series method (RPSM) in amalgamation with the bat algorithm (BATA) which, mimics the echolocation behavior of the foraging bats. The bat-inspired based methodology has been implemented to solve MFDEs with different possible variants of two point boundary conditions. The BATA is utilized in the recommended new residual optimization technique (NROT) for the minimization of the energy function attained by the spirit of RPSM. Moreover, to ratify the correctness and accuracy of the deliberated technique the results are evaluated by using two other meta-heuristic optimization techniques i.e., differential evolution algorithm (DEA) and the accelerated particle swarm optimization algorithm (APSOA) for the learning of unknown weights in the derived fitness function. The accuracy and competency of the NROT is validated by comparing the BATA computed results with the exact solution and the corresponding data acquired by the DEA and APSOA. Furthermore, detailed performance analysis is performed through statistical inference based on the large number of independent runs.

An iterated greedy algorithm with variable neighborhood descent for the planning of specialized diagnostic services in a segmented healthcare system

In this paper, a problem arising in the planning of specialized diagnostic services in a segmented public healthcare system is addressed. The problem consists of deciding which hospitals will provide the service and their capacity levels, the allocation of demand in each institution, and the reallocation of uncovered demand to other institutions or private providers, while minimizing the total equivalent annual cost of investment and operating cost required to satisfy all the demand. An associated mixed-integer linear programming model can be solved by conventional branch and bound for relatively small instances; however, for larger instances the problem becomes intractable. To effectively address larger instances, a hybrid metaheuristic framework combining iterated greedy (IGA) and variable neighborhood descent (VND) components for this problem is proposed. Two greedy construction heuristics are developed, one starting with an infeasible solution and iteratively adding capacity and the other starting with a feasible, but expensive, solution and iteratively decrease capacity. The iterated greedy algorithm includes destruction and reconstruction procedures. Four different neighborhood structures are designed and tested within a VND procedure. In addition, the computation of local search components benefit from an intelligent exploitation of problem structure since, when the first-level location variables (hospital location and capacity) are fixed, the remaining subproblem can be solved efficiently as it is very close to a transshipment problem. All components and different strategies were empirically assessed both individually and within the IGA-VND framework. The resulting metaheuristic is able to obtain near optimal solutions, within 3% of optimality, when tested over a data base of 60- to 300-hospital instances.

A meta-heuristic framework based on clustering and preprocessed datasets for solving the link prediction problem

This study presents a solution to a problem commonly known as link prediction problem. Link prediction problem interests in predicting the possibility of appearing a connection between two nodes of a network, while there is no connection between these nodes in the present state of the network. Finding a solution to link prediction problem attracts variety of computer science fields such as data mining and machine learning. This attraction is due to its importance for many applications such as social networks, bioinformatics and co-authorship networks. Towards solving this problem, Evolutionary Link Prediction (EVO-LP) framework is proposed, presented, analysed and tested. EVO-LP is a framework that includes dataset preprocessing approach and a meta-heuristic algorithm based on clustering for prediction. EVO-LP is divided into preprocessing stage and link prediction stage. Feature extraction, data under-sampling and feature selection are utilised in the preprocessing stage, while in the prediction stage, a meta-heuristic algorithm based on clustering is used as an optimiser. Experimental results on a number of real networks show that EVO-LP improves the prediction quality with low time complexity.

On the Use of Learnheuristics in Vehicle Routing Optimization Problems with Dynamic Inputs

Freight transportation is becoming an increasingly critical activity for enterprises in a global world. Moreover, the distribution activities have a non-negligible impact on the environment, as well as on the citizens’ welfare. The classical vehicle routing problem (VRP) aims at designing routes that minimize the cost of serving customers using a given set of capacitated vehicles. Some VRP variants consider traveling times, either in the objective function (e.g., including the goal of minimizing total traveling time or designing balanced routes) or as constraints (e.g., the setting of time windows or a maximum time per route). Typically, the traveling time between two customers or between one customer and the depot is assumed to be both known in advance and static. However, in real life, there are plenty of factors (predictable or not) that may affect these traveling times, e.g., traffic jams, accidents, road works, or even the weather. In this work, we analyze the VRP with dynamic traveling times. Our work assumes not only that these inputs are dynamic in nature, but also that they are a function of the structure of the emerging routing plan. In other words, these traveling times need to be dynamically re-evaluated as the solution is being constructed. In order to solve this dynamic optimization problem, a learnheuristic-based approach is proposed. Our approach integrates statistical learning techniques within a metaheuristic framework. A number of computational experiments are carried out in order to illustrate our approach and discuss its effectiveness.

Gnowee: A Hybrid Metaheuristic Optimization Algorithm for Constrained, Black Box, Combinatorial Mixed-Integer Design

This paper introduces Gnowee, a modular, Python-based, open-source hybrid metaheuristic optimization algorithm (available from https://github.com/SlaybaughLab/Gnowee). Gnowee is designed for rapid convergence to nearly globally optimum solutions for complex, constrained nuclear engineering problems with mixed-integer (MI) and combinatorial design vectors and high-cost, noisy, discontinuous, black box objective function evaluations. Gnowee’s hybrid metaheuristic framework is a new combination of a set of diverse, robust heuristics that appropriately balance diversification and intensification strategies across a wide range of optimization problems. There are many potential applications for this novel algorithm both within the nuclear community and beyond. Given that a set of well-known and studied nuclear benchmarks does not exist for the purpose of testing optimization algorithms, comparisons between Gnowee and several well-established metaheuristic algorithms are made for a set of 18 established continuous, MI, and combinatorial benchmarks representing a wide range of types of engineering problems and solution space behaviors. These results demonstrate Gnoweee to have superior flexibility and convergence characteristics over this diverse set of design spaces. We anticipate this wide range of applicability will make this algorithm desirable for many complex engineering applications.

A novel metaheuristic framework for the scheduling of multipurpose batch plants

A genetic algorithm (GA) is proposed along with a general framework for the scheduling of a typical multipurpose/product batch plant. The majority of literature regarding these problems make use of mathematical programming methods. Modelling problems in this manner leads to numerous binary variables relating to material balance and sequence of batches along long time horizons, thus resulting in large computational time. The proposed GA does not suffer the same scalability issues of mathematical programming approaches. The GA makes use of a coupled chromosome system with specific crossover and mutation functions utilised with the purpose of profit maximisation. Results show that optimal or close-to-optimal solutions can be achieved with a reduction of up to 98.53% computational time in certain cases.

Proteomics Versus Clinical Data and Stochastic Local Search Based Feature Selection for Acute Myeloid Leukemia Patients' Classification.

The use of data issued from high throughput technologies in drug target problems is widely widespread during the last decades. This study proposes a meta-heuristic framework using stochastic local search (SLS) combined with random forest (RF) where the aim is to specify the most important genes and proteins leading to the best classification of Acute Myeloid Leukemia (AML) patients. First we use a stochastic local search meta-heuristic as a feature selection technique to select the most significant proteins to be used in the classification task step. Then we apply RF to classify new patients into their corresponding classes. The evaluation technique is to run the RF classifier on the training data to get a model. Then, we apply this model on the test data to find the appropriate class. We use as metrics the balanced accuracy (BAC) and the area under the receiver operating characteristic curve (AUROC) to measure the performance of our model. The proposed method is evaluated on the dataset issued from DREAM 9 challenge. The comparison is done with a pure random forest (without feature selection), and with the two best ranked results of the DREAM 9 challenge. We used three types of data: only clinical data, only proteomics data, and finally clinical and proteomics data combined. The numerical results show that the highest scores are obtained when using clinical data alone, and the lowest is obtained when using proteomics data alone. Further, our method succeeds in finding promising results compared to the methods presented in the DREAM challenge.

A new cooperative framework for parallel trajectory-based metaheuristics

In this paper, we propose the Parallel Elite Biased framework (PEB framework) for parallel trajectory-based metaheuristics. In the PEB framework, multiple search processes are executed concurrently. During the search, each process sends its best found solutions to its neighboring processes and uses the received solutions to guide its search. Using the PEB framework, we design a parallel variant of Guided Local Search (GLS) called PEBGLS. Extensive experiments have been conducted on the Tianhe-2 supercomputer to study the performance of PEBGLS on the Traveling Salesman Problem (TSP). The experimental results show that PEBGLS is a competitive parallel metaheuristic for the TSP, which confirms that the PEB framework is useful for designing parallel trajectory-based metaheuristics.

Software framework for optimization problems and meta-heuristics based on scripting language

Since most researchers working in meta-heuristics fields are required to develop their own algorithm for their specific optimization problem, the task of selecting, modifying and extending codes from rapid software framework is very likely to occur. Software framework enables design and codes reuses to allow faster programming development of the meta-heuristics. This paper presents a review of the available rapid software framework for meta-heuristics and summarize some important features of the rapid software. A description about a new software framework based on scripting language is given. Furthermore, the scripting language that was used to develop a meta-heuristics algorithm of PSO-GA hybridization is evaluated according to the conciseness aspects. This results has clearly indicate that the program codes with scripting language has more conciseness that the main JAVA codes.

Informative Gene Selection for Cancer Classification with Microarray Data Using a Metaheuristic Framework

Objective:Cancer diagnosis is one of the most vital emerging clinical applications of microarray data. Due to the high dimensionality, gene selection is an important step for improving expression data classification performance. There is therefore a need for effective methods to select informative genes for prediction and diagnosis of cancer. The main objective of this research was to derive a heuristic approach to select highly informative genes.Methods:A metaheuristic approach with a Genetic Algorithm with Levy Flight (GA-LV) was applied for classification of cancer genes in microarrays. The experimental results were analyzed with five major cancer gene expression benchmark datasets.Result:GA-LV proved superior to GA and statistical approaches, with 100% accuracy for the dataset for Leukemia, Lung and Lymphoma. For Prostate and Colon datasets the GA-LV was 99.5% and 99.2% accurate, respectively.Conclusion:The experimental results show that the proposed approach is suitable for effective gene selection with all benchmark datasets, removing irrelevant and redundant genes to improve classification accuracy.

Deterministic Blockmodeling of Two-Mode Binary Networks Using a Two-Mode KL-Median Heuristic

Abstract Deterministic blockmodeling of a two-mode binary network matrix based on structural equivalence is a well-known problem in the social network literature. Whether implemented in a standalone fashion, or embedded within a metaheuristic framework, a popular relocation heuristic (RH) has served as the principal solution tool for this problem. In this paper, we establish that a two-mode KL-median heuristic (TMKLMedH) seeks to optimize the same criterion as the RH for deterministic blockmodeling. The TMKLMedH runs much faster than the RH, so many more restarts of the TMKLMedH can be accomplished when the two methods are constrained to the same time limit. Three computational comparisons of RH and TMKLMedH were conducted using both synthetic and real-world networks. In all three comparisons, the superiority of TMKLMedH was unequivocal.

Design of Novel Metaheuristic Techniques for Clustering

One of the major drawbacks of clustering techniques utilizing a predetermined number of clusters is that it does not guarantee convergence to the global optimum. Evolutionary algorithms are one of the most powerful general search techniques that can guarantee, if well designed, to converge to the global optimum. In this paper, a novel metaheuristic framework capable of identifying the optimum number of clusters will be proposed. In the proposed framework, an edge-recombination crossover operator, along with a redesigned chromosome architecture, is implemented to help in obtaining the optimum number of clusters. A genetic algorithm (GA)-based technique, an artificial immune system centralized on clonal selection algorithm, and immuno-GA will be designed and implemented. The proposed techniques will be tested on different real-world data sets with various sizes and dimensions. The obtained results are then used in a comparative study between all the proposed techniques to determine and select the best solution. Further investigation for the effectiveness of the results and the verification of the statistical validity for the number of clusters is carried out using Mann–Whitney–Wilcoxon rank-sum test.

A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems

This work proposes a unified heuristic algorithm for a large class of earliness–tardiness (E–T) scheduling problems. We consider single/parallel machine E–T problems that may or may not consider some additional features such as idle time, setup times and release dates. In addition, we also consider those problems whose objective is to minimize either the total (average) weighted completion time or the total (average) weighted flow time, which arise as particular cases when the due dates of all jobs are either set to zero or to their associated release dates, respectively. The developed local search-based metaheuristic framework is quite simple, but at the same time relies on sophisticated procedures for efficiently performing local search according to the characteristics of the problem. We present efficient move evaluation approaches for some parallel machine problems that generalize the existing ones for single machine problems. The algorithm was tested in thousands of instances of several E–T problems and particular cases. The results obtained show that our unified heuristic is capable of producing high-quality solutions when compared to the best ones available in the literature that were obtained by specific methods. Moreover, we provide an extensive annotated bibliography on the problems related to those considered in this work, where we not only indicate the approach(es) used in each publication, but we also point out the characteristics of the problem(s) considered. Beyond that, we classify the existing methods in different categories so as to have a better idea of the popularity of each type of solution procedure.

Solving the deterministic and stochastic uncapacitated facility location problem: from a heuristic to a simheuristic

The uncapacitated facility location problem (UFLP) is a popular combinatorial optimization problem with practical applications in different areas, from logistics to telecommunication networks. While most of the existing work in the literature focuses on minimizing total cost for the deterministic version of the problem, some degree of uncertainty (e.g., in the customers’ demands or in the service costs) should be expected in real-life applications. Accordingly, this paper proposes a simheuristic algorithm for solving the stochastic UFLP (SUFLP), where optimization goals other than the minimum expected cost can be considered. The development of this simheuristic is structured in three stages: (i) first, an extremely fast savings-based heuristic is introduced; (ii) next, the heuristic is integrated into a metaheuristic framework, and the resulting algorithm is tested against the optimal values for the UFLP; and (iii) finally, the algorithm is extended by integrating it with simulation techniques, and the resulting simheuristic is employed to solve the SUFLP. Some numerical experiments contribute to illustrate the potential uses of each of these solving methods, depending on the version of the problem (deterministic or stochastic) as well as on whether or not a real-time solution is required.

Stochastic Project Scheduling with Hierarchical Alternatives

In this paper, a resource constrained project scheduling problem with hierarchical alternatives and stochastic activity durations is studied. A stochastic chance constraint is introduced to formulate this problem. A metaheuristic framework called SAA/DAAA through integrating the sampling average approximation (SAA) with the population-based evolutionary artificial algae algorithm (AAA) is developed to solve the problem due to the NP-hardness nature of the problem. The priority-selection list (PSL) and schedule generation scheme (SGS) are introduced for local search. Experiments with different sizes (50-scale, 100-scale, 150-scale) as well as different uncertainty levels (moderate, medium, high) are used as examples to illustrate and validate the proposed method. The influences of sample size, sampling times and confidence level are also analyzed during experiments. In addition, the proposed discrete AAA (DAAA) is compared with classic GA and numerical experiments show that the SAA/DAAA outperforms the SAA/GA in terms of both objectives and solving time.

A biased-randomized simheuristic for the distributed assembly permutation flowshop problem with stochastic processing times

Modern manufacturing systems are composed of several stages. We consider a manufacturing environment in which different parts of a product are completed in a first stage by a set of distributed flowshop lines, and then assembled in a second stage. This is known as the distributed assembly permutation flowshop problem (DAPFSP). This paper studies the stochastic version of the DAPFSP, in which processing and assembly times are random variables. Besides minimizing the expected makespan, we also discuss the need for considering other measures of statistical dispersion in order to account for risk. A hybrid algorithm is proposed for solving this NP-hard and stochastic problem. Our approach integrates biased randomization and simulation techniques inside a metaheuristic framework. A series of computational experiments contribute to illustrate the effectiveness of our approach.

Meta-heuristic framework: Quantum inspired binary grey wolf optimizer for unit commitment problem

This paper proposes a quantum inspired binary grey wolf optimizer (QI-BGWO) to solve unit commitment (UC) problem. The QI-BGWO integrates quantum computing concepts with BGWO to improve the hunting process of the wolf pack. The inherent properties of Q-bit and Q-gate concepts in quantum computing help in achieving better balance between exploration and exploitation properties of the search process. The position update processes of wolves at different hierarchy levels are replaced by Q-bit's individual probabilistic representation along with dynamic rotation angle and coordinate rotation gate. Therefore, solution approaches exploit the search properties of GWO and quantum computing using quantum bits, gates, superposition principle etc., to solve the unit commitment schedule efficiently. The results and statistical analysis demonstrates the effectiveness of proposed approaches in solving the UC problem and establishes the significance of proposed approaches among existing binary and quantum computing based heuristic approaches.

A problem evolution algorithm with linear programming for the dynamic facility layout problem—A general layout formulation

Facility layout problems (FLPs) are quite common and important in many industries. This paper presents a mixed integer linear programming (MILP) model for the dynamic facility layout problem, which is a generalization of several special cases of FLPs studied in recent years. A new evolutionary meta-heuristic framework, named as the problem evolution algorithm (PEA), is developed as a general solution approach for FLPs. Computational experiments show that the PEA combined with the linear programming (LP), called PEA-LP in short, performs well in various types of FLPs. In addition, a new polyhedral inner-approximation method is proposed based on secant lines for the linearization of the non-linear constraint for department area requirements. This new method guarantees that the actual department area is always greater than or equal to the required area within a given maximum deviation error. Furthermore, two new symmetry-breaking constraints which help to improve the computational efficiency of the MILP model are also introduced. Computational experiments on several well-known problem instances from the literature are carried out to test the DFLP-FZ and the PEA-LP with promising results.

Effective local search algorithms for high school timetabling problems

This paper addresses the high school timetabling problem. The problem consists in building weekly timetables for meetings between classes and teachers with the goal of minimizing violations of specific requirements. In the last decades, several mixed-integer programs have been proposed and tested for this family of problems. However, medium and large size instances are still not effectively solved by these programs using state-of-the-art solvers and the scientific community has given special attention to the devising of alternative soft computing algorithms. In this paper, we propose a soft computing approach based on Iterated Local Search and Variable Neighborhood Search metaheuristic frameworks. Our algorithms incorporate new neighborhood structures and local search routines to perform an effective search. We validated the proposed algorithms on variants of the problem using seven public instances and a new dataset with 34 real-world instances including large cases. The results demonstrate that the proposed algorithms outperform the state-of-the-art approaches in both cases, finding the best solutions in 38 out of the 41 tested instances.