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In recent years, grey models based on fractional-order accumulation and/or derivatives have attracted considerable research interest because they offer better performance in handling limited samples with uncertainty than integer-order grey models; however, there remains room for improvement. This paper considers a more flexible and general structure for the fractional grey model by incorporating a generalized fractional-order derivative (GFOD) that complies by memory effects, resulting in the development of a generalized fractional grey model (denoted as GFGM(1,1)). Specifically, we comprehensively analyse the modelling mechanism of the proposed GFGM(1,1) model, involving model parameter estimation and time response function derivation, and discuss the link between the proposed approach and existing special cases. Then, to further improve the efficacy of the proposed approach, four mainstream metaheuristic algorithms are employed to ascertain the orders of fractional accumulation and derivatives. Finally, we carry out a series of simulation studies and a real-world application case to demonstrate the applicability and advantage of the our approach. The numerical results show that GFGM(1,1) outperforms other benchmarks, and some significant insights are obtained from the numerical experiments.

Task scheduling is one of the major issues in cloud computing environment. Efficient task scheduling is substantial to attain cost-effective execution and improve resource utilization. The task scheduling problem is classified to be a nondeterministic polynomial time (NP)-hard problem. This feature attracts researchers to utilize nature inspired metaheuristic algorithms. Initializing searching solutions randomly is one of the key features in such optimization algorithms. However, assisting metaheuristic algorithms with effective initialized solutions can significantly improve its performance. In this paper, an improved initialization of particle swarm optimization (PSO) using heuristic algorithms is proposed. Longest job to fastest processor (LJFP) and minimum completion time (MCT) algorithms are used to initialize the PSO. The performance of the proposed LJFP-PSO and MCT-PSO algorithms are evaluated in minimizing the makespan, total execution time, degree of imbalance, and total energy consumption metrices. Moreover, the performance of the proposed algorithms is compared with recent task scheduling methods. Simulation results revealed the effectiveness and superiority of the proposed LJFP-PSO and MCT-PSO compared to the conventional PSO and comparative algorithms.

Considering ergonomic factors in assembly line balancing problems can significantly improve human ergonomic conditions. In this study, a two-stage framework is developed to balance a mixed-model parallel U-shaped assembly line by considering ergonomic risks. In the first stage, according to various ergonomic standards and using the best-worst method and ELECTRE TRI, ergonomic risks of each task are identified and each task is classified into hard, normal, or easy class. In the second stage, a mathematical model of the problem is developed by considering a new objective function to level the number of tasks of each class between stations. This objective ensures that the tasks of each class are distributed equally among stations, resulting in having a roughly equal number of hard, normal, and easy tasks in each station. To solve the problem, a constraint programming model and a heuristic algorithm are developed. Numerical results show that the proposed objective function can level ergonomic risks well. The performance of the proposed solution approaches is examined against six different metaheuristic algorithms. Numerical results indicate the superiority of the constraint programming model for small and medium-size problems and that of the heuristic algorithm for large-size problems.

Support Vector Regression (SVR) is often used in forecasting. Adjustment of parameters in the SVR affects the results of forecasting. This study aims to analyze the SVR method that is optimized using Harris Hawks Optimization (HHO), hereinafter referred to as HHO-SVR. The HHO-SVR was evaluated using five benchmark datasets to determine the performance of this method. The HHO process is also compared based on the type of kernel and other metaheuristic algorithms. The results showed that the HHO-SVR has almost the same performance as other methods but is less efficient in terms of time. In addition, the type of kernel also affects the process and results.

Modified Adaptive Weight Approach (MAWA) is one of the simplest methods used for solving time-cost optimization problems. This type of optimization problem, categorized as multi-objective optimization, can be solved with metaheuristic algorithms. Here, metaheuristic algorithms evaluate a randomly generated solution set, referred to as population, within the boundary condition of a solution space. The weight factor values determined by MAWA are applied to all solutions in the population without distinguishing the solutions in that population. However, the potential solutions in the population indicate different fitness properties concerning solution space. In this paper to solve time-cost optimization problems, new adaptive weight formulations are proposed. In contrast to MAWA, the novelty of this study’s formulations is to adaptively detect the weight factor value, depending on the solution‘s fitness in the population. The results obtained from the numerical experiments examined in this study show that the proposed formulations can improve the performance of MAWA and can find identical or slightly different Pareto results for investigated multi-objective optimization problems.

The design of efficient routes for vehicles visiting a significant number of destinations is a critical factor for the competitiveness of many companies. The design of such routes is known as the vehicle routing problem. Indeed, efficient vehicle routing is one of the most studied problems in the areas of logistics and combinatorial optimization. The present study presents a memetic algorithm that evolves using a mechanism inspired by virus mutations. Additionally, the algorithm uses Taboo Search as an intensification mechanism.

Hybrid metaheuristics have proven to be effective at solving complex real-world problems. However, designing hybrid metaheuristics is extremely time consuming and requires expert knowledge of the different metaheuristics that are hybridized. In previous work, the effectiveness of automating the design of relay hybrid metaheuristics has been established. A genetic algorithm was used to determine the sequence of hybridized metaheuristics and the parameters of the metaheuristics in the hybrid. This study extends this idea by automating the design of each metaheuristic involved in the hybridization in addition to automating the design of the hybridization. A template is specified for each metaheuristic, defining the metaheuristic in terms of components. Manual design of metaheuristics usually involves determining the components of the metaheuristic. In this study, a genetic algorithm is employed to determine the components and parameters for each metaheuristic as well as the sequence of hybridized metaheuristics. The proposed genetic algorithm approach was evaluated by using it to automatically design hybrid metaheuristics for two problem domains, namely, the aircraft landing problem and the two-dimensional bin packing problem. The automatically designed hybrid metaheuristics were found to perform competitively to state-of-the-art hybridized metaheuristics for both problems. Future research will extend these ideas by looking at automating the derivation of metaheuristic algorithms without predefined structures specified by the templates.

Moth-flame optimization algorithm (MFO) is a new nature-inspired meta-heuristic based on the navigation routine of moths in the environment known as transverse orientation. For some complex optimization tasks, especially high dimensional and multimodal problems, the conventional MFO may face problems in the convergence trends or be trapped into the local and deceptive optima. Therefore, in this study, two strategies have been introduced into the conventional MFO to get a more stable sense of balance between the exploration and exploitation propensities. First, Gaussian mutation is employed to increase the population diversity of MFO. Then, a chaotic local search is applied to the flame updating process of MFO for better exploiting the locality of the solutions. The proposed CLSGMFO approach was compared against a wide range of well-known classical metaheuristic algorithms (MAs) and various advanced MAs using 23 classical benchmark functions. It was shown that the designed CLSGMFO can outperform most of the popular MAs in terms of solution quality and convergence speed. Moreover, based on CLSGMFO, a hybrid kernel extreme learning machine model, which is called CLSGMFO-KELM, is established to deal with financial stress prediction scenarios. To investigate the effectiveness of the CLSGMFO-KELM model, the proposed hybrid system was tested on two widely used financial datasets and compared against a broad array of popular classifiers. The results demonstrate that the proposed learning scheme can offer a superior kernel extreme learning machine model with excellent predictive performance. Accordingly, the proposed CLSGMFO can serve as an effective and efficient computer-aided tool for financial prediction.

This paper presents two metaheuristic algorithms for the solution of the p-next center problem: a Greedy Randomized Adaptive Search Procedure and a Variable Neighborhood Search algorithm, that will be subsequently hybridized. The p-next center problem is a variation of the p-center problem, which consists of locating p out of n centers and assigning them to users in order to minimize the maximum, over all users, of the distance of each user to its corresponding center plus the distance between this center to its closest alternative center. This problem emerges from the need to reach a secondary help center in the case of a natural disaster, when the closest center may become unavailable.

This paper presents the congested location-pricing problem under customers’ choice behavior. In the choice-based congested location-pricing problem (CCLPP), the appropriate facilities are selected for offering service by deciding about their fare classes during consecutive time periods. The customer choosing behavior is captured by the discrete choice models. The dominant factors in the customers' decision are proximity and service fare classes offered by the facilities. In the congested systems with immobile facilities, customer waiting time for getting service is important and the M / M / 1 / k queuing system is used for capturing facilities queue in this paper. Customers can choose the competitors for getting service according to the no-service utility. The obtained mathematical model for solving this problem is a nonlinear mixed integer model which is extremely hard to solve and therefore, the alternative modeling approach is developed for solving the problem by the column generation algorithm. The subproblem in this approach determines configurations including open facilities and their fare classes and the master problem specifies the number of time periods for offering each configuration. We also develop a hybrid heuristic including greedy and metaheuristic algorithms for solving the subproblem. The numerical experiments and sensitivity analysis are carried out for demonstrating the efficiency of the proposed algorithm. This analysis indicates that the total profit is the most sensitive to the offering fare classes and available resources.

Production distribution network (PDN) planning problems in multi echelon status are commonly complex with dynamic relationships that cause several uncertainties in different parameters of the network. In this paper, we formulate a multi echelon PDN to deliver products to customers with uncertain demand in the least time with uncertain delivery lead time. The proposed network is including multi supplier, producer, potential depot, retailer and inland and outland customer in multi time period horizon. A stochastic multi objective model with maximizing total profit of the system and minimizing total delivery lead time is designed. We apply chance constraints approach to cover the uncertainty of the model and introduce two heuristic methods named selective firefly algorithm (SFA) and ranking genetic algorithm (RGA) in order to solve several sized especially real world instances. Finally, the performance of two proposed algorithms is examined with solving several sized instances. The results indicate average improvement 6.12% and 8.93% with applying SFA and RGA, respectively.

Metaheuristic algorithms usually aim to solve nonconvex optimization problems in black-box and high-dimensional scenarios. Characterizing and understanding the properties of nonconvex problems is therefore important for effectively analyzing metaheuristic algorithms and their development, improvement and selection for problem solving. This paper establishes a novel analysis framework called nonconvex ratio analysis, which can characterize nonconvex continuous functions by measuring the degree of nonconvexity of a problem. This analysis uses two quantitative measures: the nonconvex ratio for global characterization and the local nonconvex ratio for detailed characterization. Midpoint convexity and Monte Carlo integral are important methods for constructing the measures. Furthermore, as a practical feature, we suggest a rapid characterization measure that uses the local nonconvex ratio and can characterize certain black-box high-dimensional functions using a much smaller sample. Throughout this paper, the effectiveness of the proposed measures is confirmed by numerical experiments using the COCO function set.

The impact of the horizontal collaboration of logistic providers as upstream supply chain elements is studied in this paper. The logistic providers can be considered as different players and, in order to analyze different types of coalitions by computing the synergy between the players in each cooperative structure, we developed a mixed integer programming (MIP) formulation for a cooperative inventory routing problem (Co-IRP). In this paper, each player has one depot and some retailers, which are considered as its available market. The model will have a many-to-many network structure once a coalition is formed, where a single product from different depots will be delivered to different retailers. We establish a robust version of Co-IRP, which is called Co-RIRP, considering uncertainty in the network. We developed a few metaheuristic algorithms to promote the gained results once MIP is solved. Finally, in order to share the possible cost saving between players and compare the assignments, we applied a few payoff distribution methods. In addition, a comprehensive analysis of example results and some important managerial insights are presented.

The paper studies a generalized mixed-integer linear production planning problem with multi-period and multi-item specification in a make-to-order manufacturing system. In this system, a holding company assigns the customers’ orders to its subsidiary companies in a way to minimize the total cost as well as minimizing the maximal production utilization which consequently leads to the fair allocations of production loads. Moreover, order splitting and assignment are allowed and production time windows and capacities are taken to account. Because of the complexity of the NP-hard problem, a ɛ-constraint method is firstly performed for small-sized problems and then three metaheuristic algorithms including NSGA-II, SPEA2, and MOPSO are applied for large-sized problems in order to find the set of Pareto optimization solutions. Numerous computational experiments illustrate that all algorithms evolve reasonably distributed fronts. The results prove the validity of the proposed model and also the efficiency of the proposed solution methods. Finally, the managerial insights are figured out and conclusions and future research directions are applied.

In this study, a workforce scheduling and balancing problem is solved in unpaced sub-assembly lines with buffers feeding the paced body assembly line of a car manufacturer. The goal is to determine the minimum workforce required to process split lots at sub-assembly stations to feed the paced line over a periodic time window. Limited by a given buffer capacity at each station but with flexible start times for each split lot, an efficient workforce scheduling is possible to prevent shortages in downstream stations. Therefore, a stock-continuity equation has been proposed yielding the size of those split lots. Next, a single-objective Mixed Integer Programming (MIP) model is formulated for the problem as a combination of two implicitly weighted goals to minimise the workforce and the unbalanced workloads. The problem is a variant of workforce scheduling and routing problem with time windows and negligible walking distances. Due to the non-deterministic polynomial-time -hardness of the problem, we proposed an improved Artificial Bee Colony (ABC) algorithm named as discrete ABC with solution acceptance rule and multi-search (SAMSABC). The proposed algorithm is compared with different variants of ABC and other well-known metaheuristic algorithms such as Particle Swarm Optimisation and Differential Evolution on generated test cases. The computational results demonstrate the superiority of the proposed ABC algorithm and reveal that the SAMSABC can achieve accurate results within short computational times.

Oil Spills are one the major environmental hazards in modern era. It needs to be understood; its origin and trajectory duly analyzed and tracked; so as to confine it in a limited spatial domain of least contamination. In this study, we propose a Modified Firefly Algorithm (PropFA) which is closely based on Firefly Algorithm (Yang, 2008). Unlike Firefly Algorithm, no parameter tuning is required in PropFA as all parameters are dynamically calculated based on present, past and expected objective function values; thus maintaining a proper balance between “exploration” and “exploitation”. The proposed algorithm is evaluated over 18 Classical Benchmark Functions, 14 Benchmark Functions of CEC-2005 (Real-Parameter Optimization) and 28 Benchmark Functions of CEC-2013 (Special Session on Real-Parameter Optimization). PropFA is compared to modern evolutionary and metaheuristic algorithms like PSO, CMA-ES, RC-MEMETIC, EDA etc. The numerical results show that the PropFA enhances the performance of Firefly Algorithm; successfully avoids local minima across dimensions and has a fast convergence. PropFA is then used to model a system for distributed control of swarm UAVs (UnManned Aerial Vehicles) to efficiently search, confine and track the shape and area of irregular dynamic oil spills for fast containment and trajectory estimation. The proposed method is also used to predict boom placement locations around the spill for its efficient confinement. Experimental results revealed that the proposed method as applied on a swarm UAV size of 30 was able to search, fully confine and track an expanding oil spill as large as 16 km 2 for 9 min.

ParamILS, I-Race and Evoca are well-known tuning methods designed to search quality parameter calibrations for metaheuristic algorithms. The set-up of parameter search space can strongly affect the performance of tuning methods. In this work we study how the parameter search definitions affect the quality of parameter calibrations delivered by these tuners. An experimental evaluation using two well known metaheuristic algorithms and a real life case is presented. We also provide some guidelines to consider when defining parameters search spaces according to the tuner used in order to obtain the best performance they can find.

The study considers a parallel machine scheduling (PMS) problem with time-dependent deterioration and multiple rate-modifying activities (RMAs). The objective of the problem is to simultaneously determine the number and positions of RMAs and a schedule of jobs on parallel machines to minimize the makespan. In order to determine an optimal solution, a mixed integer linear programming (MILP) model for the PMS problem is introduced. Subsequently, novel metaheuristic algorithms embedding a mathematical model are developed based on matheuristic approaches to effectively handle large-sized problems. The matheuristic approaches decompose the original problem into sub-problems by determining partial decision variables from each iteration in simulated annealing (SA) and genetic algorithm (GA). Subsequently, the rest of the decision variables are optimally determined by using a mathematical model for the sub-problems with partial decision variables predetermined. In order to enhance the performance of SA and GA, an adjustment heuristic is proposed based on an optimality property for the problem. The performance of the proposed algorithms is evaluated by conducting numerical experiments based on randomly generated examples, and subsequently the behavior of the algorithms is discussed.

This paper proposes a multi-objective version of recently developed Spotted Hyena Optimizer (SHO) called Multi-objective Spotted Hyena Optimizer (MOSHO). It is used to optimize the multiple objectives problems. In the proposed algorithm, a fixed-sized archive is employed for storing the non-dominated Pareto optimal solutions. The roulette wheel mechanism is used to select the effective solutions from archive to simulate the social and hunting behaviors of spotted hyenas. The proposed algorithm is tested on 24 benchmark test functions and compared with six recently developed metaheuristic algorithms. The proposed algorithm is then applied on six constrained engineering design problems to demonstrate its applicability on real-life problems. The experimental results reveal that the proposed algorithm performs better than the others and produces the Pareto optimal solutions with high convergence.

This paper proposes a new metaheuristic routing algorithm for the minimization of the travel distance of pickers in manual warehouses. The algorithm is based on the ant colony optimization (ACO) metaheuristic, which is combined and integrated with the Floyd–Warshall (FW) algorithm, and is therefore referred to as FW–ACO. To assess the performance of the FW–ACO algorithm, two sets of analyses are carried out. Firstly, the capability of the algorithm to provide effective solutions for the picking problem is analyzed as a function of the settings of the main ACO parameters. Secondly, the performance of the FW–ACO algorithm is compared with that of six algorithms typically used to optimize the travel distance of pickers, including exact algorithms for the solution of the travelling salesman problem (where available), two heuristic routing strategies (i.e. S-shape and largest gap) and two metaheuristic algorithms (i.e. the MIN–MAX ant system and Combined+). The comparison is made considering different warehouse layouts and problem complexities. The outcomes obtained suggest that the FW–ACO is a promising algorithm generally able to provide better results than the heuristic and metaheuristic algorithms, and often able to find an exact solution. The FW–ACO algorithm also shows a very efficient computational time, which makes it suitable for defining the route of pickers in real time. The FW–ACO algorithm is finally implemented in a real case study, where constraints exist on the order in which items should be picked, to show its practical usefulness and quantify the resulting savings.

For a hybrid system with manufacturing and remanufacturing, a variant of dynamic lot sizing problem is addressed in this study. In the system, manufactured and remanufactured products are produced on separate lines and sold in segmented markets. In addition to these two types of products, there are also hybrid products produced in the system. Hybrids are used to meet the excess manufactured product demand and integrate the two distinct lines. Therefore, this study investigates the profitability conditions for producing the hybrid products. Using a variant of dynamic lot sizing problem, called dynamic lot sizing problem with returns and hybrids (DLSPRH), which is a constrained mixed-integer nonlinear programming problem, the performance of the system with hybrids is compared to the same system with no hybrids. The DLSPRH is a NP-hard problem. A Genetic Algorithm based heuristic (GA_H) has been proposed to solve the DLSPRH and its capacitated version from the literature. The performance of the algorithm is tested by comparing its results with Simulated Annealing (SA), Variable Neighborhood Search (VNS) and Simulated Annealing with Neighborhood List (SA_NL). Numerical experiments show that GA_H significantly outperforms the other metaheuristic algorithms. On average, GA_H performs 2.51%, 2.24% and 2.06% better than SA, VNS and SA_NL algorithms, respectively. Another finding is that the system with hybrids performs well at medium–high holding cost environments especially when remanufacturing demand is low. Additional managerial insights are also presented.

We present in this study an algorithmic framework of an intelligent scheduling system that aims to provide an optimum planning for the production process of cutting tools taking into consideration the constraining conditions such as production characteristics, capacity, and performance criteria. Once blunt, cutting tools are sent to the sharpening service composed of parallel machines capable of sharpening more than one tool at the same time. After sharpening, tools are sent back to the departments of origins to be used in other production processes. Thus, any delay in the sharpening service provokes delays in other departments. We develop first a genetic algorithm enhanced by a dynamic programming procedure capable of optimally scheduling a given job sequence. Then we develop a branch and bound method that emulates at each node possible decisions based on a postpone or schedule strategy. Numerical results show that both methods give high quality solutions for the scheduling of tool sharpening operations. Beside the minimization of total tardiness, many other types of decision making related to minimal operation time of a sharpening service, minimal amount of cutting tool inventory and the number of required sharpening machines can be deduced thanks to applying our models.

Optimal design and control of industrially important chemical processes rely on dynamic optimization. However, because of the highly constrained, nonlinear, and sometimes discontinuous nature that is inherent in chemical processes, solving dynamic optimization problems (DOPs) is still a challenging task. Teaching-learning-based optimization (TLBO) is a relative new metaheuristic algorithm based on the philosophy of teaching and learning. In this paper, we propose an improved TLBO called quadratic interpolation based TLBO (QITLBO) for handling DOPs efficiently. In the QITLBO, two modifications, namely diversity enhanced teaching strategy and quadratic interpolation operator, are introduced into the basic TLBO. The diversity enhanced teaching strategy is employed to improve the exploration ability, and the quadratic interpolation operator is used to enhance the exploitation ability; therefore, the ensemble of these two components can establish a better balance between exploration and exploitation. To test the performance of the proposed method, QITLBO is applied to solve six chemical DOPs include three parameter estimation problems and three optimal control problems, and compared with eleven well-established metaheuristic algorithms. Computational results reveal that QITLBO has the best precision and reliability among the compared algorithms for most of the test problems.

Parameters estimation of photovoltaic (PV) model based on experimental data plays an important role in the simulation, evaluation, control, and optimization of PV systems. In the past decade, many metaheuristic algorithms have been used to extract the PV parameters; however, developing hybrid algorithms based on two or more metaheuristic algorithms may further improve the accuracy and reliability of single metaheuristic algorithms. In this paper, by combining teaching-learning-based optimization (TLBO) and artificial bee colony (ABC), we propose a new hybrid teaching-learning-based artificial bee colony (TLABC) for the solar PV parameter estimation problems. The proposed TLABC employs three hybrid search phases, namely teaching-based employed bee phase, learning-based on looker bee phase, and generalized oppositional scout bee phase to efficiently search the optimization parameters. TLABC is applied to identify parameters of different PV models, including single diode, double diode, and PV module, and the results of TLABC are compared with well-established TLBO and ABC algorithms, as well as those results reported in the literature. Experimental results show that TLABC can achieve superior performance in terms of accuracy and reliability for different PV parameter estimation problems.

In this paper, we analyze single machine scheduling problems under the following minimization objectives: the maximum completion time (makespan), the total completion time and the maximum lateness, including fundamental practical aspects, which often occur in industrial or manufacturing reality: release dates, due dates, setup times, precedence constraints, deterioration (aging) of machines, as well as maintenance activities. To solve the problems, we propose an efficient representation of a solution and a fast neighborhood search technique, which calculates an approximation of criterion values in a constant time per solution in a neighborhood. On this basis, a novel approximate/exact search technique, using exact as well as approximate criterion values during search process, is introduced and used to develop efficient metaheuristic algorithms dedicated to the considered problems. Their efficiency is verified during computational experiments.

In this paper, a new parameter for population management is implemented in the Differential Evolution algorithm. The new scheme integrates a set of operators that analyze the exploration and exploitation effects during its operation. With these operators, the new method obtains important knowledge about its population diversity during its evolution. Under such conditions, the proposed method can reduce its population when the diversity is too low in order to reduce its computational cost and improve its search capacities simultaneously. To test the new additions, the proposed algorithm has been tested in a set of 29 complex functions and two interplanetary trajectory design problems. The outcome of the tests demonstrates a greatly improved performance when compared to the original Differential Evolution algorithm, a few of its most successful variants, and other algorithms.

Optimization algorithms and decision-making techniques are major components of multi-objective optimization. This study evaluated the performance of population-based metaheuristic algorithms and decision-making techniques in optimizing an unconventional building design – a lift-up design – to maximize the areas with wind and thermal comfort in a ‘hot’ and ‘calm’ climate. Four optimization algorithms (GA, PSO, GSA, FA) and three decision-making techniques (LINMAP, TOPSIS, Shannon Entropy) were employed to optimize the lift-up design. The effectiveness and efficiency of algorithms in optimization were measured using six metrics. The evaluation revealed a steady improvement of algorithms' performance as population and number of iterations increased up to the convergence at about 6000 evaluations without excessively increasing computational time. Although no algorithm scored best across all metrics, PSO was superior in many aspects. For the algorithms, the three decision-making techniques chose similar optimum designs with slight differences in a few design parameters. The optimum solution of multi-objective optimization was a better trade-off solution for the two objective functions than that of single-objective optimization. The study recommends conducting convergence tests using the performance metrics before optimization to decide a suitable population size and number of iterations for population-based metaheuristic optimization algorithms.

Permutation flowshop scheduling problem with sequence-dependent setup times (PFSP-SDST) and makespan minimisation is NP-hard. It has important practical applications, for example, in the cider industry and the print industry. There exist several metaheuristic algorithms to solve this problem. However, within practical time limits, those algorithms still either find low quality solutions or struggle with large problems. In this paper, we have proposed a simple but effective local search algorithm, called constraint based local search (CBLS) algorithm, which transforms the SDST constraints into an auxiliary objective function and uses the auxiliary objective function to guide the search towards the optimal value of the actual objective function. Our motivation comes from the constraint optimisation models in artificial intelligence (AI), where constraint-based informed decisions are of particular interest instead of random-based decisions. Our experimental results on well-known 480 instances of PFSP-SDST show that the proposed CBLS algorithm outperforms existing state-of-the-art PFSP-SDST algorithms. Moreover, our algorithm obtains new upper bounds for 204 out of 360 medium- and large-sized problem instances.

This study introduces the extension of currently developed Seagull Optimization Algorithm (SOA) in terms of multi-objective problems, which is entitled as Multi-objective Seagull Optimization Algorithm (MOSOA). In this algorithm, a concept of dynamic archive is introduced, which has the feature to cache the non-dominated Pareto optimal solutions. The roulette wheel selection approach is utilized to choose the effective archived solutions by simulating the migration and attacking behaviors of seagulls. The proposed algorithm is approved by testing it with twenty-four benchmark test functions, and its performance is compared with existing metaheuristic algorithms. The developed algorithm is analyzed on six constrained problems of engineering design to assess its appropriateness for finding the solutions of real-world problems. The outcomes from the empirical analyzes depict that the proposed algorithm is better than other existing algorithms. The proposed algorithm also considers those Pareto optimal solutions, which demonstrate high convergence.

Particle swarm optimization (PSO) is one of the most popular stochastic swarm-based metaheuristic algorithms. Kalman filter principle is introduced to predict the global optimum more accurately to enhance convergence. However, the evolution of particles in current Kalman PSO merely depends on the adjustment based on observation. In this paper, a modified Kalman particle swarm optimization (MKPSO) algorithm is proposed. The population is extended with the estimated optimum based on Kalman filtering, in which the prediction model is formulated as the weighted central optimum. Benchmark functions in the CEC14 test suite are adopted to verify the effectiveness of MKPSO. Numerical results show that MKPSO is more effective in mining capability for high-dimensional problems. Besides, the superiority of MKPSO lies in solving hybrid optimization problems. At last, MKPSO is applied to maximize the attainable moments subset of very flexible aircraft (VFA) on account for redundancy of control surfaces. Simulation results reveal that there is a trade-off between flight and control performance for VFA.

The pickup and delivery problem (PDP) addresses real-world problems in logistics and transportation, and establishes a critical class of vehicle routing problems. This study presents a novel variant of the PDP, called the multi-vehicle selective pickup and delivery problem (MVSPDP), and designs three metaheuristic algorithms for this problem. The MVSPDP aims to find the minimum-cost routes for a fleet of vehicles collecting and supplying commodities, subject to the constraints on vehicle capacity and travel distance. The problem formulation features relaxing the requirement of visiting all pickup nodes and enabling multiple vehicles for achieving transportation efficiency. To solve the MVSPDP, we propose three metaheuristic algorithms: tabu search (TS), genetic algorithm (GA), and scatter search (SS). A fixed-length representation is presented to indicate the varying number of vehicles used and the selection of pickup nodes. Furthermore, we devise four operators for TS, GA, and SS to handle the selection of pickup nodes, number of vehicles used, and their routes. The experimental results indicate that the three metaheuristic algorithms can effectively solve the MVSPDP. In particular, TS outperforms GA and SS in solution quality and convergence speed. In addition, the problem formulation produces substantially lower transportation costs than the PDP does, thus validating the utility of the MVSPDP.

A ternaryintegration jobshop scheduling problem is considered.Employee timetabling is integrated into the scheduling of machines and transporters.The problem is formulated as a mixedinteger linear programming (MILP) model.An algorithm is developed based on the Anarchic Society Optimization (ASO) method.A numerical study is conducted to evaluate the MILP model and ASO algorithm. This paper addresses a ternary-integration scheduling problem that incorporates employee timetabling into the scheduling of machines and transporters in a job-shop environment with a finite number of heterogeneous transporters where the objective is to minimize the completion time of all jobs. The problem is first formulated as a mixed-integer linear programming model. Then, an Anarchic Society Optimization (ASO) algorithm is developed to solve large-sized instances of the problem. The formulation is used to solve small-sized instances and to evaluate the quality of the solutions obtained for instances with larger sizes. A comprehensive numerical study is carried out to assess the performance of the proposed ASO algorithm. The algorithm is compared with three alternative metaheuristic algorithms. It is also compared with several algorithms developed in the literature for the integrated scheduling of machines and transporters. Moreover, the algorithms are tested on a set of adapted benchmark instances for an integrated problem of machine scheduling and employee timetabling. The numerical analysis suggests that the ASO algorithm is both effective and efficient in solving large-sized instances of the proposed integrated job-shop scheduling problem.

We develop a branch-and-price algorithm for the truck and trailer routing problem with time windows.We provide the first optimal solutions to several benchmark instances with 50 and 100 customers.We propose an efficient adaptive large neighborhood search algorithm. Motivated by a situation faced by infrastructure service providers operating in urban areas with accessibility restrictions, we study the truck and trailer routing problem with time windows (TTRPTW). In this problem the vehicle fleet consists of trucks and trailers which may be decoupled. A set of customers has to be served and some of the customers can only be accessed by the truck without the trailer. This gives rise to the planning of truck-and-trailer routes containing truck-only subroutes, in addition to truck-only routes and truck-and-trailer routes without subroutes. We propose a branch-and-price algorithm for the TTRPTW, using problem specific enhancements in the pricing scheme and alternative lower bound computations. We also tailor an adaptive large neighborhood search algorithm to the TTRPTW in order to obtain good initial columns. When compared to existing metaheuristic algorithms we obtain highly competitive results. Some instances with up to 100 customers are solved to optimality with the proposed branch-and-price algorithm.

This paper deals with the backtracking search algorithm (BSA) optimization technique to solve the design problems of multi-machine power system stabilizers (PSSs) in large power system. Power system stability problem is formulated by an optimization problem using the LTI state space model of the power system. To conduct a comprehensive analysis, two test systems (2-AREA and 5-AREA) are considered to explain the variation of design performance with increase in system size. Additionally, two metaheuristic algorithms, namely bacterial foraging optimization algorithm (BFOA) and particle swarm optimization (PSO) are accounted to evaluate the overall design assessment. The obtained results show that BSA is superior to find consistent solution than BFOA and PSO regardless of system size. The damping performance that achieved from both test systems are sufficient to achieve fast system stability. System stability in linearized model is ensured in terms of eigenvalue shifting towards stability regions. On the other hand, damping performance in the non-linear model is evaluated in terms of overshoot and setting times. The obtained damping in both test systems are stable for BSA based design. However, BFOA and PSO based design perform worst in case of large power system. It is also found that the performance of BSA is not affected for large numbers of parameter optimization compared to PSO, and BFOA optimization techniques. This unique feature encourages recommending the developed backtracking search algorithm for PSS design of large multi-machine power system. BSA technique is proposed to alleviate PSS design for large power system.Stability analysis is done based on LTI State Space model of power system.Damping performance is explained in two benchmark systems for BSA, BFOA and PSO.BSA based design shows fast damping while BFOA and PSO perform worst.

We consider a transshipment scheduling problem with identical stations.We consider release date and inventory constraints.We formulate the problem as a mixed integer linear programming model.We developed two constructive heuristic and three metaheuristic algorithms.Using computational results, the performance of all developed algorithms is analyzed. In this paper, we study a transshipment scheduling problem with multiple identical loading/unloading stations and release date and inventory constraints. This problem is similar to the parallel machine scheduling problem where the makespan is to be minimized, which is an NP-hard problem in the scheduling theory. We formulate the problem as an integer linear programming model, which is solvable only for small-size instances by CPLEX solver in reasonable times. Also, we develop two constructive heuristic solution approaches, namely parallel and serial schedule generation schemes. We also develop three metaheuristic methods based on genetic algorithm, particle swarm optimization and cuckoo optimization algorithm. The developed solution methods have been compared using computational studies based upon 870 randomly generated test instances. The experimental results show that the parallel schedule generation scheme outperforms the serial one and the cuckoo optimization algorithm shows the best performance among the developed metaheuristic methods.

Display Omitted An integrated particle swarm optimization algorithm for weight minimization of truss structures with sizing and layout variables is developed;.Optimization problems with frequency constraints and static constraints are solved;.The new algorithm is competitive with other state-of-the-art metaheuristic algorithms. Natural frequencies offer useful knowledge on the dynamic response of the structures. It is possible to avoid from the destructive effects of dynamic loads on the structures by optimizing layout and size of their subject to constraints on natural frequencies. Since optimization problems including frequency constraints are highly nonlinear, this kind of problems forms a challenging area to test the performance of the different optimization techniques. This study tests the performance of an integrated particle swarm optimization algorithm (iPSO), a new particle swarm optimizer integrated with the improved fly-back mechanism and the weighted particle concept, in four weight minimization of truss structures with sizing and layout variables under multiple frequency constraints. Optimization results demonstrate that the new algorithm is competitive with other state-of-the-art metaheuristic algorithms in dynamic and static structural optimization problems.

The influence maximization problem (IMP) is one of the most well-known problems in the research domain of online social networks (OSN) that has attracted the attention of many researchers from different disciplines in recent years. One of the reasons is that the speed of information propagation in the OSN can be increased if we can find out users that have maximum influence on other users. The traditional rule-based and heuristic algorithms may not be able to find useful information out of these data because the data are generally large and complex. Although metaheuristic algorithms can be used to solve the IMP, there is still plenty of room for improvement. That is why an effective and efficient algorithm is presented in this paper. The proposed algorithm, called simulated annealing with search partition (SASP), is based on a search space partitioning mechanism to enhance the search performance of simulated annealing for the IMP. The experimental results show that the proposed algorithm outperforms the other state-of-the-art influence maximization problem algorithms compared in this paper in terms of the quality of the end result and the number of objective function evaluations.

Finding feasible solutions to real-world problems is a crucial task. Metaheuristic algorithms are widely used in many fields due to the variety of solutions they can produce. The grey wolf optimizer (GWO) is a relatively novel population-based metaheuristic algorithm that has been shown to have good optimization performance. However, due to the insufficient diversity of wolves in some cases, this approach can lead to locally optimal situations. Therefore, this paper proposes a grey wolf optimization method based on a beetle antenna strategy (BGWO) that gives the leader wolf a sense of hearing to improve the global search ability and reduce unnecessary searches. In addition, to balance exploration and exploitation, a nonlinear dynamic control parameter update strategy based on the cosine function is proposed. To evaluate the performance of the proposed BGWO, this paper uses 23 standard benchmark functions to test the method in different dimensions. Moreover, four well-known engineering problems are used to evaluate the ability of the proposed algorithm to obtain real-world problem solutions. The experimental results show that BGWO has superior performance and is competitive with many state-of-the-art algorithms in terms of solution accuracy, convergence rate, and stability.

Land Readjustment and redistribution (LR) is a land management tool that helps regular urban development with the contribution of landowners. The main purpose of LR is to transform irregularly developed land parcels into suitable forms. Since it is necessary to handle many criteria simultaneously to solve LR problems, classical mathematical methods can be insufficient due to time limitation. Since LR problems are similar to traveling salesman problems and typical scheduling problems in terms of structure, they are kinds of NP-hard problems in combinatorial optimization. Therefore, metaheuristic algorithms are used in order to solve NP-hard problems instead of classical methods. At first, in this study, an effective problem-specific objective function is proposed to address the main criteria of the problem. In addition, a map-based crossover operator and three different mutation operators are proposed for the LR, and then a hybrid approach is implemented by utilizing those operators together. Furthermore, since the optimal value of the problem handled in real world cannot be exactly estimated, a synthetic dataset is proposed as a benchmarking set in LR which makes the success of algorithms can be objectively evaluated. This dataset consists of 5 different problems according to number of parcel which are 20, 40, 60, 80 and 100. Each problem set consists of 4 sub-problems in terms of number of landowners per-parcel which are 1, 2, 3 and 4. Therefore, the dataset consists of 20 kinds of problems. In this study, artificial bee colony, particle swarm optimization, differential evolution, genetic and tree seed algorithm are used. In the experimental studies, five algorithms are set to run under equal conditions using the proposed synthetic dataset. When the acquired experimental results are examined, genetic algorithm seems to be the most effective algorithm in terms of both speed and performance. Although artificial bee colony has better results from genetic algorithm in a few problems, artificial bee colony is the second most successful algorithm after genetic algorithm in terms of performance. However, in terms of time, artificial bee colony is an algorithm nearly as successful as genetic algorithm. On the other hand, the results of differential evolution, particle swarm optimization and tree seed algorithms are similar to each other in terms of solution quality. In conclusion, the statistical tests clearly show that genetic algorithm is the most effective technique in solving LR problems in terms of speed, performance and robustness.

Recovery of products has received much attention in the last decade due to the increase in both environmental awareness and regulations enacted by governments. In product recovery, disassembly of a product into its constituent parts on a line is one of the most significant operations. This paper deals with a disassembly line balancing and sequencing (DLBS) problem subject to balancing issues, hazardousness of parts, demand quantities and direction changes considered in a lexicographic order. Due to the combinatorial nature of this problem, exact methods, e.g., mixed integer linear programming (MILP), are able to solve only small and medium size problems. Therefore, various metaheuristic algorithms are proposed in literature to find near-optimal solutions. In this paper, constraint programming (CP), which is a suitable technique especially for highly-constrained discrete problems, is used to develop models and solution approaches. To the best of author’s knowledge, this study is the first that uses CP for the disassembly line balancing problems. For the DLBS problem, first, a generic CP model is developed. This CP model provides efficient results for small/medium size disassembly problems and benchmark instances. Observing that the generic CP model could not produce even feasible sequence of tasks for some large-sized benchmark instances, a CP-based solution approach is proposed. This approach generates a feasible sequence subject to a fixed assignment of tasks to the workstations by using a CP model and uses this sequence as an initial feasible solution within a warm-start context in CP sequencing models. The computational results show that the proposed CP model improves the several best solutions of medium-sized benchmark instances, while the proposed CP-based solution approach produces excellent results in all large test instances by either improving the best solutions (found so far) or establishing new benchmark solutions.

Optimization is an essential tool to minimize or maximize functions, obtaining optimal results on costs, mass, energy, gains, among others. Actual problems may be multimodal, nonlinear, and discontinuous and may not be minimized by classical analytical methods that depend on the gradient. In this context, there are metaheuristic algorithms inspired by natural phenomena to optimize real engineering problems. No algorithm is the worst or the best, but more efficient for a given problem. Thus, a new nature-inspired algorithm called Lichtenberg Optimization Algorithm (LA) is applied in this study to solve a complex inverse damage identification problem in mechanical structures built by composite material. To verify the performance of the new algorithm, both LA and Finite Element Method (FEM) were used to identify delamination damage and the results were compared to other algorithms such as Genetic Algorithm (GA) and SunFlower Optimization (SFO). LA was shown to be a powerful damage identification tool since it was able to detect damage even in particular situations like noisy response and low damage severity.

Metaheuristic algorithms are typically used for optimizing a function f : A → R , where A is a subset of R N . Nevertheless, many real-life problems require A to be a set of functions which makes f a functional. In this paper, we present a methodology to address the optimization of functionals by using the evolutionary algorithm known as Differential Evolution. Unlike traditional techniques where continuity and differentiability assumptions are required to solve some associated differential equations—like calculus of variations, Pontryagin’s principle or dynamic programming, the optimization is carried out directly on the functional without the need of any of the assumptions mentioned before. Lagrangians involving derivatives are considered, these derivatives are computed implementing Automatic Differentiation with dual numbers. To the best of our knowledge, this is the first time that a metaheuristic optimization approach has been applied to directly optimize a broad variety of functionals. The effectiveness of our methodology is validated by solving two problems. The first problem is related to the implementation of quarantine and isolation in SARS epidemics and the second validation problem deals with the well-known brachistochrone curve problem. The results of both validation problems are in outstanding agreement with those obtained with the application of traditional techniques, specifically with the Forward–Backward-Sweep method in the first problem, and with the calculus of variations for the latter problem. We also found that interpolation may be employed to solve the large scale global optimization problems arisen in the optimization of functionals.

With the development of powerful computers, some new methods for solving challenging problems are introduced. Some of these methods, which are called metaheuristic algorithms, such as bat algorithm or ant colony algorithm, are inspired by nature and simulate a natural phenomenon for finding the best solution. Today these algorithms with a robust approach can be used to find the solution of a complicated problem very fast although they might be trapped in the local minimums. Rain optimization algorithm (ROA) is a new metaheuristic algorithm that is inspired by the raindrops, which move toward minimum points after getting to the earth. This algorithm can find global extremum as well as local extremums if its parameters are correctly tuned. After the implementation of this algorithm, we compare it with some other existing optimization algorithms such as particle swarm optimization algorithm and bat algorithm by solving 26 benchmarks and three benchmarks in various dimensions as well as a drilling optimization problem. Simulations illustrate the performance and computational time in finding the global minimum. Also, ROA can find local minimum simultaneously and it can be confidently used in optimization problems.

Cell formation, cell scheduling, and group layout are three important problems in designing and configuring a Cellular Manufacturing System (CMS). This paper addresses the integration of these problems in virtual and classical CMSs considering alternative processing routes. The objective is to minimize the total handling costs and cycle time. Due to the computational complexity of the problem, hybrid metaheuristic algorithms are proposed to solve the problem. Depending on the type of cells, which is either classical or virtual, an encoding scheme is proposed to effectively represent candidate solutions. Placement algorithms are developed to obtain the layout from an encoded solution; these algorithms are either based on running a heuristic or a linear program. A computer software, called ICFLSD (Integrated Cell Formation, Layout, and Scheduling Designer) is developed to simplify the problem-solving process from the data entry to getting results. Numerical examples adopted from the literature are solved using the ICFLSD and CPLEX to assess the performance of the metaheuristic algorithms. The comparison results demonstrated the superiority of the simulated annealing to the other solution approaches considered in this study.

This paper addresses a problem regarding the joint decision of process planning and scheduling in the context of a distributed flexible job shop (DFJS). The joint decision is called integrated process planning and scheduling (IPPS). Therefore, the problem is called an IPPS/DFJS problem. This research develops a genetic algorithm (called GA_X) to solve the IPPS/DFJS problem. The GA_X algorithm is meritorious insofar as it entails the development of an incomplete modeling scheme (chromosome Φ s ) to represent an IPPS/DFJS solution. In chromosome Φ s , only some decisions are explicitly modeled, and the remaining decisions are implicitly determined using heuristic rules that ensure load balancing among manufacturing resources. Therefore, GA_X generates load-balanced solutions and is more likely to search effectively. We optimize the genetic parameters of GA_X by conducting a full factorial experiment. Three experiments are conducted to compare GA_X with other algorithms. Experiment I involves two light-loading IPPS/DFJS instances. Experiment II involves 15 light-loading IPPS/flexible job shop (FJS) instances (degenerated cases of IPPS/DFJS problems). Experiment III involves 17 heavy-loading IPPS/DFJS instances. GA_X outperforms benchmark algorithms, and Φ s (the proposed incomplete chromosome representation) has considerable merit. This finding highlights a promising direction in developing “incomplete solution representation schemes” when solving complex space-search problems with genetic or other metaheuristic algorithms.

Metaheuristic algorithms have been successfully used to parameter identification of photovoltaic systems. However, this still faces the following two challenges. Firstly, most of the applied algorithms are complex and need some extra control parameters except the essential population size and stopping criterion, which is against their applications in photovoltaic systems with different characteristics. Secondly, how to obtain model parameters with higher accuracy and reliability has been a very valuable topic. To address the two challenges, this paper presents a new optimization method called backtracking search algorithm with competitive learning (CBSA) for parameter identification of photovoltaic systems. The remarkable features of CBSA are that it has a very simple structure and only needs the essential parameters. The core idea of CBSA is to increase the chance of backtracking search algorithm (BSA) to jump out of the local optimum by the designed competitive learning mechanism. In CBSA, the population is first divided into two subpopulations by built competitive mechanism. Then each subpopulation is optimized by the different search operators with multiple learning strategies. In order to test the performance of CBSA, CBSA is first employed to solve five challenging engineering design optimization problems and then is used to estimate the unknown parameters of three photovoltaic models. Experimental results show the solutions offered by CBSA outperform those of the compared algorithms including BSA, two recently proposed variants of BSA and other some state-of-the-art algorithms on nearly all test problems, which proves the effectiveness of the improved strategies.

To alleviate the shortcomings of the standard Equilibrium Optimizer, a new improved algorithm called Modified Equilibrium Optimizer is proposed in this work. This algorithm utilizes the Gaussian mutation and an additional exploratory search mechanism based on the concept of population division and reconstruction. The population in each iteration of the proposed algorithm is constructed using these mechanisms and standard search procedure of the Equilibrium Optimizer. These strategies attempt to maintain the diversity of solutions during the search, so that the tendency of stagnation towards the sub-optimal solutions can be avoided and the convergence rate can be boosted to obtain more accurate optimal solutions. To validate and analyze the performance of the Modified Equilibrium Optimizer, a collection of 33 benchmark problems and four engineering design problems are adopted. Later, in the paper, the Modified Equilibrium Optimizer has been used to train multilayer perceptrons. The experimental results and comparison based on several metrics such as statistical analysis, scalability test, diversity analysis, performance index analysis and convergence analysis demonstrate that the proposed algorithm can be considered a better metaheuristic optimization approach than other compared algorithms.

This study introduces the extension of currently developed Emperor Penguin Optimizer (EPO) in terms of multi-objective problems solving capability, which is entitled as Multi-objective Emperor Penguin Optimizer (MOEPO) In this algorithm, a concept of dynamic archive is introduced, which has the feature to cache the non-dominated Pareto optimal solutions. Here, the roulette-wheel approach is utilized to choose the effective archived solutions by simulating the huddling behaviors of emperor penguins. The proposed algorithm is approved by testing it with twenty-four well-known benchmark test functions, and its performance is compared with existing metaheuristic algorithms. The developed algorithm is analyzed on seven constrained problems of engineering to assess its appropriateness for finding solutions of real world problems. After, that it is validated on cloud computing application and compared between competitor approaches. By using the proposed algorithm, improvements in tackling the resource scheduling issue in cloud computing have been established. The outcomes from the empirical analyzes depict that the proposed algorithm is better than other existing algorithms.

Due to the continuous growth of Internet traffic, new technologies are proposed to overcome the capacity crunch problem. One of the most promising solutions for optical backbone networks is space division multiplexing (SDM), which allows parallel transmissions in properly designed optical fibers. In SDM, the problem of routing, space, and spectrum allocation (RSSA) emerges. RSSA is more challenging than corresponding optimization problems in optical networks without spatial multiplexing since the additional spatial dimension significantly increases the number of encodable solutions. The exact optimization methods can be used only for small and unrealistic problem instances. Therefore, effective metaheuristics are needed to solve RSSA for larger and practice-based problem instances. In this paper, we propose a new technique of solution encoding in metaheuristic algorithms. The key novelty and contribution is to mix two different solution encoding types to utilize their advantages and improve the overall method performance. The results of experiments conducted on reference optical network topologies using two representative optimization methods (dedicated evolutionary algorithm and tabu search) show that the proposed approach significantly improves the quality of the results for both method types. The proposed encoding technique is generic and applicable to many different metaheuristics employed in solving various optimization problems.

An enhanced version of the Flower Pollination Algorithm (FPA) is proposed.Testing is performed using 23 optimization benchmark problems.The proposed algorithm is compared with five well-known optimization algorithms.Experimental results show the superiority of the proposed algorithm. Expert and intelligent systems try to simulate intelligent human experts in solving complex real-world problems. The domain of problems varies from engineering and industry to medicine and education. In most situations, the system is required to take decisions based on multiple inputs, but the search space is usually very huge so that it will be very hard to use the traditional algorithms to take a decision; at this point, the metaheuristic algorithms can be used as an alternative tool to find near-optimal solutions. Thus, inventing new metaheuristic techniques and enhancing the current algorithms is necessary. In this paper, we introduced an enhanced variant of the Flower Pollination Algorithm (FPA). We hybridized the standard FPA with the Clonal Selection Algorithm (CSA) and tested the new algorithm by applying it to 23 optimization benchmark problems. The proposed algorithm is compared with five famous optimization algorithms, namely, Simulated Annealing, Genetic Algorithm, Flower Pollination Algorithm, Bat Algorithm, and Firefly Algorithm. The results show that the proposed algorithm is able to find more accurate solutions than the standard FPA and the other four techniques. The superiority of the proposed algorithm nominates it for being a part of intelligent and expert systems.