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The set-union knapsack problem is one of the most significant generalizations of the Non-deterministic Polynomial (NP)-hard 0-1 knapsack problem in combinatorial optimization, which has rich application scenarios. Although some researchers performed effective algorithms on normal-sized instances, the authors found these methods deteriorated rapidly as the scale became larger. Therefore, the authors design an efficient yet effective algorithm to solve this large-scale optimization problem, making it applicable to real-world cases under the era of big data.

The authors develop three targeted strategies and adjust them into the adaptive tabu search framework. Specifically, the dynamic item scoring tries to select proper items into the knapsack dynamically to enhance the intensification, while the age-guided perturbation places more emphasis on the diversification of the algorithm. The lightweight neighborhood updating simplifies the neighborhood operators to reduce the algorithm complexity distinctly as well as maintains potential solutions. The authors conduct comparative experiments against currently best solvers to show the performance of the proposed algorithm.

Statistical experiments show that the proposed algorithm can find 18 out of 24 better solutions than other algorithms. For the remaining six instances on which the competitor also achieves the same solutions, ours performs more stably due to its narrow gap between best and mean value. Besides, the convergence time is also verified efficiency against other algorithms.

The authors present the first implementation of heuristic algorithm for solving large-scale set-union knapsack problem and achieve the best results. Also, the authors provide the benchmarks on the website for the first time.

Drugs are strategic products with essential functions in human health. An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health. The vehicle-routing problem, focused on finding the lowest-cost routes with available vehicles and constraints, such as time constraints and road length, is an important aspect of this. In this paper, the vehicle routing problem (VRP) for a pharmaceutical company in Turkey is discussed.

A mixed-integer programming (MIP) model based on the vehicle routing problem with time windows (VRPTW) is presented, aiming to minimize the total route cost with certain constraints. As the model provides an optimum solution for small problem sizes with the GUROBI® solver, for large problem sizes, metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed. A real dataset was used to analyze the effectiveness of the metaheuristic algorithms. The proposed simulated annealing (SA) and adaptive large neighborhood search (ALNS) were evaluated and compared against GUROBI® and each other through a set of real problem instances.

The model is solved optimally for a small-sized dataset with exact algorithms; for solving a larger dataset, however, metaheuristic algorithms require significantly lesser time. For the problem addressed in this study, while the metaheuristic algorithms obtained the optimum solution in less than one minute, the solution in the GUROBI® solver was limited to one hour and three hours, and no solution could be obtained in this time interval.

The VRPTW problem presented in this paper is a real-life problem. The vehicle fleet owned by the factory cannot be transported between certain suppliers, which complicates the solution of the problem.

The proposed algorithm successfully optimizes complex error functions, which are difficult to differentiate, ill conditioned or discontinuous. It is a benchmark to identify initial solutions in artificial neural network (ANN) training.

A multi‐directional ANN training algorithm that needs no derivative information is introduced as constrained one‐dimensional problem. A directional search vector examines the ANN error function in weight parameter space. The search vector moves in all possible directions to find minimum function value. The network weights are increased or decreased depending on the shape of the error function hyper surface such that the search vector finds descent directions. The minimum function value is thus determined. To accelerate the convergence of the algorithm a momentum search is designed. It avoids overshooting the local minimum.

The training algorithm is insensitive to the initial starting weights in comparison with the gradient‐based methods. Therefore, it can locate a relative local minimum from anywhere of the error surface. It is an important property of this training method. The algorithm is suitable for error functions that are discontinuous, ill conditioned or the derivative of the error function is not readily available. It improves over the standard back propagation method in convergence and avoids premature termination near pseudo local minimum.

Classifications problems are efficiently classified when using this method but the complex time series in some instances slows convergence due to complexity of the error surface. Different ANN network structure can further be investigated to find the performance of the algorithm.

The search scheme moves along the valleys and ridges of the error function to trace minimum neighborhood. The algorithm only evaluates the error function. As soon as the algorithm detects flat surface of the error function, care is taken to avoid slow convergence.

The algorithm is efficient due to incorporation of three important methodologies. The first mechanism is the momentum search. The second methodology is the implementation of directional search vector in coordinate directions. The third procedure is the one‐dimensional search in constrained region to identify the self‐adaptive learning rates, to improve convergence.

The purpose of this paper is to present a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations. In this problem, each product is produced by assembling a set of several different parts. At first, the parts are processed in a flexible job shop system, and then at the second stage, the parts are assembled and products are produced.

As the problem is non-deterministic polynomial-time-hard, a new hybrid particle swarm optimization and parallel variable neighborhood search (HPSOPVNS) algorithm is proposed. In this hybrid algorithm, particle swarm optimization (PSO) algorithm is used for global exploration of search space and parallel variable neighborhood search (PVNS) algorithm for local search at vicinity of solutions obtained in each iteration. For parameter tuning of the metaheuristic algorithms, Taguchi approach is used. Also, a statistical test is proposed to compare the ability of metaheuristics at finding the best solution in the medium and large sizes.

Numerical experiments are used to evaluate and validate the performance and effectiveness of HPSOPVNS algorithm with hybrid particle swarm optimization with a variable neighborhood search (HPSOVNS) algorithm, PSO algorithm and hybrid genetic algorithm and Tabu search (HGATS). The computational results show that the HPSOPVNS algorithm achieves better performance than competing algorithms.

Scheduling of manufacturing parts and planning of assembly operations are two steps in production systems that have been studied independently. However, with regard to many manufacturing industries having assembly lines after manufacturing stage, it is necessary to deal with a combination of these problems that is considered in this paper.

This paper proposed a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations.

This paper aims to describe two enhancements of the variable neighbourhood search (VNS) algorithm to solve efficiently the minimum interference frequency assignment problem (MI-FAP) which is a major issue in the radio networks, as well as a well-known NP-hard combinatorial optimisation problem. The challenge is to assign a frequency to each transceiver of the network with limited or no interferences at all. Indeed, considering that the number of radio networks users is ever increasing and that the radio spectrum is a scarce and expensive resource, the latter should be carefully managed to avoid any interference.

The authors suggest two new enhanced VNS variants for MI-FAP, namely, the iterated VNS (It-VNS) and the breakout VNS (BVNS). These two algorithms were designed based on the hybridising and the collaboration approaches that have emerged as two powerful means to solve hard combinatorial optimisation problems. Therefore, these two methods draw their strength from other meta-heuristics. In addition, the authors introduced a new mechanism of perturbation to enhance the performance of VNS. An extensive experiment was conducted to evaluate the performance of the proposed methods on some well-known MI-FAP datasets. Moreover, they carried out a comparative study with other metaheuristics and achieved the Friedman’s non-parametric statistical test to check the actual effect of the proposed enhancements.

The experiments showed that the two enhanced methods (It-VNS) and (BVNS) achieved better results than the VNS method. The comparative study with other meta-heuristics showed that the results are competitive and very encouraging. The Friedman’s non-parametric statistical test reveals clearly that the results of the three methods (It-VNS, BVNS and VNS) are significantly different. The authors therefore carried out the Nemenyi’s post hoc test which allowed us to identify those differences. The impact of the operated change on both the It-VNS and BVNS was thus confirmed. The proposed BVNS is competitive and able to produce good results as compared with both It-VNS and VNS for MI-FAP.

Approached methods and particularly newly designed ones may have some drawbacks that weaken the results, in particular when dealing with extensive data. These limitations should therefore be eliminated through an appropriate approach with a view to design appropriate methods in the case of large-scale data.

The authors designed and implemented two new variants of the VNS algorithm before carrying out an exhaustive experimental study. The findings highlighted the potential opportunities of these two enhanced methods which could be adapted and applied to other combinatorial optimisation problems, real world applications or academic problems.

This paper aims at enhancing the VNS algorithm through two new approaches, namely, the It-VNS and the BVNS. These two methods were applied to the MI-FAP which is a crucial problem arising in a radio network. The numerical results are interesting and demonstrate the benefits of the proposed approaches in particular BVNS for MI-FAP.

This paper aims to address a distributed assembly permutation flow-shop scheduling problem (DAPFSP) considering budget constraints and factory eligibility. The first stage of the considered production system is composed of several non-identical factories with different technology levels and so the factories' performance is different in terms of processing time and cost. The second stage is an assembly stage wherein there are some parallel work stations to assemble the ready parts into the products. The objective function is to minimize the maximum completion time of products (makespan).

First, the problem is formulated as mixed-integer linear programing (MIP) model. In view of the nondeterministic polynomial (NP)-hard nature, three approximate algorithms are adopted based on variable neighborhood search (VNS) and the Johnsons' rule to solve the problem on the practical scales. The proposed algorithms are applied to solve some test instances in different sizes.

Comparison result to mathematical model validates the performance accuracy and efficiency of three proposed methods. In addition, the result demonstrated that the proposed two-level self-adaptive variable neighborhood search (TLSAVNS) algorithm outperforms the other two proposed methods. Moreover, the proposed model highlighted the effects of budget constraints and factory eligibility on the makespan. Supplementary analysis was presented by adjusting different amounts of the budget for controlling the makespan and total expected costs. The proposed solution approach can provide proper alternatives for managers to make a trade-off in different various situations.

The problem of distributed assembly permutation flow-shop scheduling is traditionally studied considering identical factories. However, processing factories as an important element in the supply chain use different technology levels in the real world. The current paper is the first study that investigates that problem under non-identical factories condition. In addition, the impact of different technology levels is investigated in terms of operational costs, quality levels and processing times.

The purpose of this paper is to cut down energy consumption and eliminate production waste on mixed-model assembly lines. Therefore, a supermarket integrated dynamic cyclic kitting system with the application of electric vehicles (EVs) is introduced. The system resorts to just-in-time (JIT) and segmented sub-line assignment strategies, with the objectives of minimizing line-side inventory and energy consumption.

Hybrid opposition-based learning and variable neighborhood search (HOVMQPSO), a multi-objective meta-heuristics algorithm based on quantum particle swarm optimization is proposed, which hybridizes opposition-based learning methodology as well as a variable neighborhood search mechanism. Such algorithm extends the search space and is capable of obtaining more high-quality solutions.

Computational experiments demonstrated the outstanding performance of HOVQMPSO in solving the proposed part-feeding problem over the two benchmark algorithms non-dominated sorting genetic algorithm-II and quantum-behaved multi-objective particle swarm optimization. Additionally, using modified real-life assembly data, case studies are carried out, which imply HOVQMPSO of having good stability and great competitiveness in scheduling problems.

The feeding problem is based on static settings in a stable manufacturing system with determined material requirements, without considering the occurrence of uncertain incidents. Current study contributes to assembly line feeding with EV assignment and could be modified to allow cooperation between EVs.

The dynamic cyclic kitting problem with sub-line assignment applying EVs and supermarkets is solved by an innovative HOVMQPSO, providing both novel part-feeding strategy and effective intelligent algorithm for industrial engineering.

The cross-docking strategy has a significant influence on supply chain and logistics efficiency. This paper aims to investigate the most suitable and efficient way to schedule the transfer of logistics activities and present a meta-heuristic method of the truck scheduling problem in cross-docking logistics. A truck scheduling problem with products time window is investigated with objectives of minimizing the total product transshipment time and earliness and tardiness cost of outbound trucks.

This research proposed a meta-heuristic method for the truck scheduling problem with products time window. To solve the problem, a lower bound of the problem is built through a novel two-stage Lagrangian relaxation problem and on account of the NP-hard nature of the truck scheduling problem, the novel red deer algorithm with the mechanism of the heuristic oscillating local search algorithm, as well as adaptive memory programming was proposed to overcome the inferior capability of the original red deer algorithm in the aspect of local search and run time.

Theory analysis and simulation experiments on an industrial case of a cross-docking center with a product’s time window are conducted in this paper. Satisfactory results show that the performance of the red deer algorithm is enhanced due to the mechanism of heuristic oscillating local search algorithm and adaptive memory programming and the proposed method efficiently solves the real-world size case of truck scheduling problems in cross-docking with product time window.

The consideration of products time window has very realistic significance in different logistics applications such as cold-chain logistics and pharmaceutical supply chain. Furthermore, the novel adaptive memory red deer algorithm could be modified and applied to other complex optimization scheduling problems such as scheduling problems considering energy-efficiency or other logistics strategies.

For the first time in the truck scheduling problem with the cross-docking strategy, the product’s time window is considered. Furthermore, a mathematical model with objectives of minimizing the total product transshipment time and earliness and tardiness cost of outbound trucks is developed. To solve the proposed problem, a novel adaptive memory red deer algorithm with the mechanism of heuristic oscillating local search algorithm was proposed to overcome the inferior capability of genetic algorithm in the aspect of local search and run time.

This research explores mitigating carbon emissions and integrating sustainability in e-commerce logistics by optimizing the multi-depot pollution routing problem with time windows (MDPRPTW). A proposed model contrasts non-collaborative and collaborative decision-making for order assignment among logistics service providers (LSPs), incorporating low-carbon considerations.

The model is substantiated using improved adaptive large neighborhood search (IALNS), tabu search (TS) and oriented ant colony algorithm (OACA) within the context of e-commerce logistics. For model validation, a normal distribution is employed to generate random demand and inputs, derived from the location and requirements files of LSPs.

This research validates the efficacy of e-commerce logistics optimization and IALNS, TS and OACA algorithms, especially when demand follows a normal distribution. It establishes that cooperation among LSPs can substantially reduce carbon emissions and costs, emphasizing the importance of integrating sustainability in e-commerce logistics optimization.

This paper proposes a meta-heuristic algorithm to solve the NP-hard problem. Methodologies such as reinforcement learning can be investigated in future work.

This research can help logistics managers understand the status of sustainable and cost-effective logistics operations and provide a basis for optimal decision-making.

This paper describes the complexity of the MDPRPTW model, which addresses both carbon emissions and cost reduction. Detailed information about the algorithm, methodology and computational studies is investigated. The research problem encompasses various practical aspects related to routing optimization in e-commerce logistics, aiming for sustainable development.

Exact solution of time–cost trade-off problem (TCTP) by the state-of-the-art meta-heuristic algorithms can be obtained for small- and medium-scale problems, while satisfactory results cannot be obtained for large construction projects. In this study, a hybrid heuristic meta-heuristic algorithm that adapts the search domain is developed to solve the large-scale discrete TCTP more efficiently.

Minimum cost slope–based heuristic network analysis algorithm (NAA), which eliminates the unfeasible search domain, is embedded into differential evolution meta-heuristic algorithm. Heuristic NAA narrows the search domain at the initial phase of the optimization. Moreover, activities with float durations higher than the predetermined threshold value are eliminated and then the meta-heuristic algorithm starts and searches the global optimum through the narrowed search space. However, narrowing the search space may increase the probability of obtaining a local optimum. Therefore, adaptive search domain approach is employed to make reintroduction of the eliminated activities to the design variable set possible, which reduces the possibility of converging into local minima.

The developed algorithm is compared with plain meta-heuristic algorithm with two separate analyses. In the first analysis, both algorithms have the same computational demand, and in the latter analysis, the meta-heuristic algorithm has fivefold computational demand. The tests on case study problems reveal that the developed algorithm presents lower total project costs according to the dependent t-test for paired samples with α = 0.0005.

In this study, TCTP is solved without considering quality or restrictions on the resources.

The proposed method enables to adapt the number of parameters, that is, the search domain and provides the opportunity of obtaining significant improvements on the meta-heuristic algorithms for other engineering optimization problems, which is the theoretical contribution of this study. The proposed approach reduces the total construction cost of the large-scale projects, which can be the practical benefit of this study.