Discrete Differential Evolution Algorithm Research Articles

Memetic discrete differential evolution with domain knowledge for blocking scheduling distributed flow shop with lot-streaming constraints

This article addresses the blocking distributed flow shop scheduling problem with lot-streaming (BDFSPL) with the objective of minimizing the maximum completion time, or makespan. In many realistic conditions, a job is divided into multiple continuous processed sublots. This pattern achieves operation overlap on consecutive machines and decreases the completion time of the whole job. Moreover, there are no buffers between machines, potentially causing finished sublots to be blocked on the current machine until the downstream machine is available. This is the first study to consider distributed production, blocking constraints, and lot-streaming together. To address this problem, we formulate a mathematical model for BDFSPL and propose a memetic discrete differential evolution (MDDE) algorithm. First, the MDDE algorithm partitions the entire population into three subpopulations based on solution quality, and each subpopulation evolves independently through adaptive scale and parameter adjustment. Second, four discrete mathematical operators are proposed to generate new individuals, and based on these operators, discrete mutation, crossover, and selection operations of MDDE are designed. Additionally, a crucial path-based local search strategy, informed by the domain knowledge of the best individual, is embedded into MDDE to enhance the exploitation capacity. To validate MDDE’s effectiveness, comprehensive experiments with several related algorithms on extensive testing instances are carried out, and the parameters of the MDDE algorithm are calibrated by employing a design of experiments. The comparison results demonstrate the effectiveness and efficiency of the proposed MDDE algorithm for the BDFSPL.

A novel discrete differential evolution algorithm combining transfer function with modulo operation for solving the multiple knapsack problem

In this paper, an efficient method for solving multiple knapsack problem (MKP) using discrete differential evolution is proposed. Firstly, an integer programming model of MKP suitable for discrete evolutionary algorithm is established. Secondly, a new method for discretizing continuous evolutionary algorithm is proposed based on the combination of transfer function and modulo operation. Therefrom, a new discrete differential evolution algorithm (named TMDDE) is proposed. Thirdly, the algorithm GROA is proposed to eliminate infeasible solutions of MKP. On this basis, a new method for solving MKP using TMDDE is proposed. Finally, the performance of TMDDE using S-shaped, U-shaped, V-shaped, and Taper-shaped transfer functions combined with modulo operation is compared, respectively. It is pointed out that T3-TMDDE which used Taper-shaped transfer function T3 is the best. The comparison results of solving 30 MKP instances show that the performance of T3-TMDDE is better than five advanced evolutionary algorithms. It not only indicates that TMDDE is more competitive for solving MKP, but also demonstrates that the proposed discretization method is an effective method.

Joint Optimization Algorithm for Latency-Energy and Privacy Combining Discrete Differential Evolution and Convex Optimization

A privacy protection task offloading algorithm combining discrete differential evolution and convex optimization is proposed to resolve the new position privacy leakage problem for mobile terminal due to transferring tasks to multiple edge servers for computation via wireless networks. First, the privacy cost of offloading decision is defined for the characteristics of the position privacy problem combined with the standard deviation theory. Second, the objective problem is modeled as a joint optimization of position privacy protection, offloading decision and transmission power, and the total cost of task offloading is an optimization objective. Finally, to handle the objective problem efficiently, offloading decision variable is decoupled from the transmission power variable to decrease the computational complexity of the problem; the discrete differential evolution algorithm is designed to accumulate the approximate optimal offloading decision, and the optimal transmission power is efficiently solved by variable substitution method and subgradient method. Simulations reveal that the algorithm has excellent convergence; it improves the position privacy protection level of mobile terminal and reduces the total cost of task offloading while maintaining lower energy consumption and latency.

A Novel Modified Discrete Differential Evolution Algorithm to Solve the Operations Sequencing Problem in CAPP Systems

Operation Sequencing (OS) is one of the most critical tasks in a CAPP system. This process could be modelled as a combinatorial problem where finding a suitable solution within a reasonable time interval is difficult. This work implements a novel Discrete Differential Evolution Algorithm (DDEA) to solve the OS problem, focusing on parts of up to 76 machining operations; the relationships among operations are represented as a directed graph; the contributions of the DDEA are as follows: (1) operates with a discrete representation in the space of feasible solutions; (2) employs mutation and crossover operators to update solutions and to reduce machining and setup costs, (3) possess a local search strategy to achieve better solutions, and (4) integrates a statistical method based on quantiles to measure the quality and likelihood for an achieving a solution. To demonstrate the efficiency and robustness of the DDEA, five prismatic parts with different numbers of machining operations as benchmarks to address the OS problem were selected. The results generated the same OS for parts with a few machining operations (up to 23 machining operations). Conversely, for parts with more machining operations, the DDEA needs more runs to achieve the best solution.

A multi-objective discrete differential evolution algorithm for energy-efficient distributed blocking flow shop scheduling problem

ABSTRACT The energy problem in green manufacturing has attracted enormous attention from researchers and practitioners in the manufacturing domain with the global energy crisis and the aggravation of environmental pollution. The distributed blocking flow shop scheduling problem (DBFSP) has considerable application scenarios in connection with its widespread application in the industry under the background of intelligent manufacturing. A multi-objective discrete differential evolution (MODE) algorithm is proposed to solve the energy-efficient distributed blocking flow shop scheduling problem (EEDBFSP) with the objectives of the makespan and total energy consumption (TEC) in this paper. The cooperative initialisation strategy is proposed to generate the initial population of the EEDBFSP. The mutation, crossover, and selection operators are redesigned to enable the MODE algorithm as applied to discrete space. A local search strategy based on the knowledge of five operators is introduced to enhance the exploitation capability of the MODE algorithm in the EEDBFSP. The non-critical path energy-efficient strategy is proposed to reduce energy consumption according to the specific constraints in the EEDBFSP. The effectiveness of each strategy in the MODE algorithm is verified and compared with the state-of-the-art algorithms. The numerical results demonstrate that the MODE algorithm is the efficient optimiser for solving the EEDBFSP.

Improved wireless sensor network data collection using discrete differential evolution and ant colony optimization

The main objective of this study is to optimize the performance of a wireless sensor network (WSN) in terms of energy consumption and data routing delay using evolutionary metaheuristics. A WSN mobile sink-based routing method in which the sink moves to certain selected rendezvous nodes for data collection is used to address the hot-spot problem. However, there are two challenges, namely, clustering and mobile sink shortest trajectory traversal, which significantly affect the network energy consumption, lifetime, and delay. To achieve the goal of this study, first, a formal model is presented to solve the optimization problem of determining the optimal number of clusters and corresponding cluster heads, which are taken as rendezvous nodes accessed by the mobile sink considering the network energy consumption, intracluster communication, and transmission delay. Second, a discrete differential evolution algorithm is proposed to solve the formulated optimization problem. Third, an ant colony optimization-based algorithm is proposed to construct the shortest path for the mobile sink to traverse the selected rendezvous nodes. The experimental evaluations show that the proposed strategy significantly improves cluster head selection, balances the cluster members, increases the network lifetime by 54%, decreases the transmission delay by 63%, and reduces energy consumption by 47% compared to several routing strategies in the literature.

A hybrid discrete differential evolution – genetic algorithm approach with a new batch formation mechanism for parallel batch scheduling considering batch delivery

Scheduling is an important decision-making problem in production planning and the resulting decisions have a direct impact on reducing waste, including energy and idle capacity. Batch scheduling problems occur in various industries from automotive to food and energy. This paper introduces the parallel p-batch scheduling problem with batch delivery, content-dependent loading/unloading times and energy-aware objective function. The problem has been motivated by a real system used for freezing products in a food processing company. A mixed-integer linear programming model (MILP) has been developed and explained through a numerical example. As it is not practical to solve large-size instances via a mathematical model, the discrete differential evolution algorithm has been improved (iDDE) and hybridised with the genetic algorithm (GA). A release-oriented vector generation procedure and a heuristic batch formation mechanism have been developed to efficiently solve the problem. The performance of the proposed approach (iDDEGA) has been compared with CPLEX, iDDE and GA through a comprehensive computational study. A case study was conducted based on real data collected from the freezing process of the company, which also verified the practical use and advantages of the proposed methodology.

An artificial immune differential evolution algorithm for scheduling a distributed heterogeneous flexible flowshop

This paper studies a distributed heterogeneous flexible flowshop problem (DHFFP) with sequence-dependent setup and transport times, where each job has a release time and each production stage has multiple unrelated parallel machines. An integer linear programming (ILP) model and a new artificial immune differential evolution (AIDE) algorithm are proposed aiming to minimize the makespan and total tardiness simultaneously. Firstly, the AIDE employs a two-dimensional vector encoding scheme including the information of job permutation and factory allocation for solution representation. In addition, a dynamic decoding scheme is designed to construct a feasible schedule. Secondly, three distributed Nawaz–Enscore–Ham (NEH) based constructive heuristics are presented to provide the initial antibody population. Thirdly, a discrete differential evolution algorithm is introduced to mutate the cloned antibodies. Further, clonal suppression is applied by eliminating the antibodies with lower stimulation values. Simulated annealing (SA) based local search is incorporated with four problem-specific neighborhood structures to enhance the algorithm. Finally, the optimal values of the algorithmic parameters are determined by the orthogonal test. Some numerical experiments of the ILP model on small-scale instances are conducted to show the effectiveness of the proposed AIDE algorithm. The AIDE algorithm is also compared with several existing algorithms for different scale instances. The results demonstrate that the AIDE algorithm generates average relative percentage deviation of 12.51% and 7.99% respectively for small & medium-scale instances and large-scale instances, which is the best-performing among all algorithms.

Mathematical formulation and a novel two-stage algorithm for double-row layout problem with fixed loading and unloading points

Loading and unloading operations are frequent and important in the production workshop. Thus, this paper proposes a novel double-row layout problem, which involves the location planning of material loading and unloading points of the facility in the layout; It needs to solve the sequence and precise coordinates of facilities with safety clearance to ensure the safety of the layout. Subsequently, a mixed-integer programming model and an improved discrete differential evolution algorithm with linear programming are developed to minimize material handling costs. The algorithm includes four efficient operations in optimization: the annealing mechanism, random strategy, variable neighborhood search strategy, and double-threshold termination mode. Thereafter, compared with the computational results of benchmark cases, the validity of the model and the efficiency of the algorithm are verified. In the basic problem, the calculation results of the algorithm are compared with many algorithms in the literature, and the algorithm still performs well. Finally, the algorithm is applied to solve the reducer workshop and provides a better layout scheme.

Modeling and solution for hybrid flow-shop scheduling problem by two-stage stochastic programming

To adapt to the uncertainty of the real environment and solve the problem of high efficiency and high quality, this study comprehensively considers a variety of uncertainty factors, focusing on modeling and solving a hybrid flow-shop scheduling problem by two-stage stochastic programming (HFSP-TSP). First, this paper uses a two-stage scenario tree to describe the uncertain factors, the probabilities and values are obtained under different discrete production scenarios, and stochastic programming theory is used to formulate a mixed-integer linear programming (MILP) model for HFSP-TSP. Second, based on a general discrete optimization algorithm framework, that is, pointer-based discrete differential evolution (PDDE) algorithm, a novel variant (H-PDDE) is proposed for effectively solving the HFSP-TSP. It adopts a permutation scheduling decoding method and introduces three new improvement strategies: the strategy of inconsistent code length of individuals in the population, adding local search in discrete mutation operation, using a heuristic algorithm to generate the initial population. Finally, computational experiments were conducted to illustrate the proposed mathematical model and optimization algorithm. The computational results show that the H-PDDE can solve the HFSP-TSP more effectively than existing algorithms and conventional PDDE variants. The stochastic programming model is increasingly superior to the deterministic model in an uncertain environment. The source code of the H-PDDE algorithm and its data files can be found at https://github.com/huangyiping-ai/H-PDDE-algorithm.git, which is publicly available.

A distributed beamforming interference minimization algorithm based on node selection

Distributed beamforming uses nodes in a wireless sensor network to transmit signals in different phases with controllable delay, to obtain coherent output signals with a gain after superposition. However, a wireless sensor network has a large topological area and wide distribution range, and it is difficult for distributed beamforming to obtain a highly directional beam as centralized beamforming does, which will cause interference to the non-target base stations. To solve this problem, a discrete adaptive dual-population cooperative differential evolution (DPCDE) algorithm is proposed, which can effectively reduce the interference by selecting nodes suitable for participating in distributed beamforming in a wireless sensor network. Simulation results show that the proposed algorithm can optimize the node set participating in distributed beamforming to minimize the interference of the wireless sensor network to the non-target base stations, and the effect is better than other classic intelligent optimization algorithms.

Appling the Roulette Wheel Selection Approach to Address the Issues of Premature Convergence and Stagnation in the Discrete Differential Evolution Algorithm

The discrete differential evolution (DDE) algorithm is an evolutionary algorithm (EA) that has effectively solved challenging optimization problems. However, like many other EAs, it still faces problems such as premature convergence and stagnation during the iterative process. To address these concerns in the DDE algorithm, this work aims to achieve the following objectives: (i) investigate the causes of premature convergence and stagnation in the DDE algorithm; (ii) propose techniques to prevent premature convergence and stagnation in DDE, including a quantitative measurement of premature convergence based on the level of mismatching between the population solutions and then divide the population into individual groups based on the level of mismatching between the population solutions and the best solution; and applying the roulette wheel selection (RWS) approach to determine whether a higher degree of nonmatching is more suitable for choosing a population of separate groups to be able to produce a new solution with more options to prevent the occurrence of premature convergence; (iii) evaluate the effectiveness of the proposed techniques through employing the DDE algorithm to solve the quadratic assignment problem (QAP) as a standard to evaluate our results and their effect on avoiding premature convergence and stagnation issues, which led to the enhancement of the algorithm’s accuracy. Our comparative study based on the statistical analysis shows that the DDE algorithm that uses the proposed techniques is more efficient than the traditional DDE algorithm and the state-of-the-art methods.

A Novel Discrete Differential Evolution with Varying Variables for the Deficiency Number of Mahjong Hand

The deficiency number of one hand, i.e., the number of tiles needed to change in order to win, is an important factor in the game Mahjong, and plays a significant role in the development of artificial intelligence (AI) for Mahjong. However, it is often difficult to compute due to the large amount of possible combinations of tiles. In this paper, a novel discrete differential evolution (DE) algorithm is presented to calculate the deficiency number of the tiles. In detail, to decrease the difficulty of computing the deficiency number, some pretreatment mechanisms are first put forward to convert it into a simple combinatorial optimization problem with varying variables by changing its search space. Subsequently, by means of the superior framework of DE, a novel discrete DE algorithm is specially developed for the simplified problem through devising proper initialization, a mapping solution method, a repairing solution technique, a fitness evaluation approach, and mutation and crossover operations. Finally, several experiments are designed and conducted to evaluate the performance of the proposed algorithm by comparing it with the tree search algorithm and three other kinds of metaheuristic methods on a large number of various test cases. Experimental results indicate that the proposed algorithm is efficient and promising.

Two evolutionary approaches with objective-specific variation operators for vehicle routing problem with time windows and quality of service objectives

This paper addresses a variant of the vehicle routing problem with time windows where the goal is to maximize the quality of service delivered to the customer. In the literature, this problem contains three objectives targeted at improving the quality of service. In this paper, we have proposed two evolutionary approaches, viz., a steady-state grouping genetic algorithm and a discrete differential evolution algorithm, to address this problem. The crossover and mutation operators are designed by considering the characteristics of each objective. The proposed approaches are incorporated with various heuristics that provide a set of better initial solutions in comparison to purely random initial solutions. We have also proposed two bounds for each objective. The approaches presented in this paper are tested on the Solomon instances which are considered as the standard benchmark instances for the vehicle routing problem with time windows in the literature. The proposed approaches are compared with the state-of-the-art approach available in the literature. The computational results demonstrate that our approaches are better in terms of solution quality and execution time than the state-of-the-art approach.

A multi-objective discrete differential evolution algorithm for energy-efficient two-stage flow shop scheduling under time-of-use electricity tariffs

In response to the appeal for environmental protection and the efficient utilization of energy, local governments in China actively promote time-of-use (TOU) electricity tariffs for manufacturing enterprises. Motivated by a real-life industrial scenario of large special-purpose pressure vessel production, this paper addresses an energy-efficient two-stage flow shop scheduling problem under TOU tariffs to minimize the total electricity cost and the mean tardiness. Since the problem is computationally intractable, we focus on developing a multi-objective discrete differential evolution (MDDE) algorithm. Specifically, based on the optimal properties of the problem, we tailor an encoding scheme that consists of two job sequences and an idle time vector. The novel mutation and crossover operators are designed to generate the trail individuals, and the hypervolume contribution indicator is incorporated into the bi-criteria selection operator to measure the quality of the solution. Furthermore, two neighborhood structures are designed to iteratively improve the non-dominated solutions in the external archive set. We evaluate the performance of the MDDE algorithm via extensive computational experiments. The experimental results indicate that the MDDE algorithm can obtain the good approximate Pareto front, and it outperforms the well-known NSGA-II, SPEA2 and MOEA/D algorithms in solution quality.

Hybrid Discrete Differential Evolution and Deep Q-Network for Multimission Selective Maintenance

The multimission selective maintenance problem (MSMP) for repairable systems has received increasing attention in recent years. The problem amounts to selecting a subset of feasible maintenance actions, in view of the resource limitations. For considering the realistic case of the imperfect maintenance, this article introduces a hybrid imperfect maintenance model, which is more realistic to evaluate the system reliability. The challenge of solving such kind of problems lies not only in the reliability estimation, but also in the solution method of the maintenance selection. Such decision-making problem can be effectively formulated using the Markov decision process, but it is difficult to apply current methods for solving the engineering systems with large action decision spaces. In order to solve this issue, this work puts forth a novel hybrid algorithm for the MSMP in a large multicomponent system. In the proposed method, a discrete differential evolution algorithm is developed for searching the optimal maintenance action in large-scale discrete action spaces and the deep Q-network method is utilized to approximate the effectiveness of maintenance actions and facilitate the agent training. The experiments, based on a large-scale coal transportation system, verify the effectiveness of the proposed method compared with LSDQN and differential evolution.

Bi-objective green in-house transportation scheduling and fleet size determination in mixed-model assembly lines with mobile robots

PurposeFacing the challenge of increasing energy cost and requirement of reducing the emissions, identifying the potential factors of them in the manufacturing factories is an important prerequisite to control energy consumption. This paper aims to present a bi-objective green in-house transportation scheduling and fleet size determination problem (BOGIHTS&FSDP) in automobile assembly line to schedule the material delivery tasks, which jointly take the energy consumption into consideration as well.Design/methodology/approachThis research proposes an optimal method for material handling in automobile assembly line. To solve the problem, several properties and definitions are proposed to solve the model more efficiently. Because of the non-deterministic polynomial-time-hard nature of the proposed problem, a Multi-objective Discrete Differential Evolution Algorithm with Variable Neighborhood Search (VNS-MDDE) is developed to solve the multi-objective problem.FindingsThe performances of VNS-MDDE are evaluated in simulation and the results indicate that the proposed algorithm is effective and efficient in solving BOGIHTS&FSDP problem.Originality/valueThis study is the first to take advantage of the robot's interactive functions for part supply in automobile assembly lines, which is both the challenge and trend of future intelligent logistics under the pressure of energy and resource. To solve the problem, a VNS-MDDE is developed to solve the multi-objective problem.

Trust-Based Recommendation for Shared Mobility Systems Based on a Discrete Self-Adaptive Neighborhood Search Differential Evolution Algorithm

Safety is one concern that hinders the acceptance of ridesharing in the general public. Several studies have been conducted on the trust issue in recent years to relieve this concern. The introduction of trust in ridesharing systems provides a pragmatic approach to solving this problem. In this study, we will develop a trust-aware ridesharing recommender system decision model to generate recommendations for drivers and passengers. The requirements of trust for both sides, drivers and passengers, are taken into consideration in the decision model proposed in this paper. The decision model considers the factors in typical ridesharing systems, including vehicle capacities, timing, location and trust requirements, etc. The decision model aims to determine the shared rides that minimize cost while respecting the trust and relevant constraints. As the decision problem is a nonlinear integer programming problem, we combine a self-adaptive neighborhood search with Differential Evolution to develop an algorithm to solve it. To assess the effectiveness of the proposed algorithm, several other evolutionary computation approaches are also applied to solve the same problem. The effectiveness assessment is done based on the performance of applying different algorithms to find solutions for test cases, to provide a guideline for selecting a proper solution approach.

An efficient discrete differential evolution algorithm based on community structure for influence maximization

An efficient discrete differential evolution algorithm based on community structure for influence maximization

Efficient UAV-based mobile edge computing using differential evolution and ant colony optimization.

Internet of Things (IoT) tasks are offloaded to servers located at the edge network for improving the power consumption of IoT devices and the execution times of tasks. However, deploying edge servers could be difficult or even impossible in hostile terrain or emergency areas where the network is down. Therefore, edge servers are mounted on unmanned aerial vehicles (UAVs) to support task offloading in such scenarios. However, the challenge is that the UAV has limited energy, and IoT tasks are delay-sensitive. In this paper, a UAV-based offloading strategy is proposed where first, the IoT devices are dynamically clustered considering the limited energy of UAVs, and task delays, and second, the UAV hovers over each cluster head to process the offloaded tasks. The optimization problem of dynamically determining the optimal number of clusters, specifying the member tasks of each cluster, is modeled as a mixed-integer, nonlinear constraint optimization. A discrete differential evolution (DDE) algorithm with new mutation and crossover operators is proposed for the formulated optimization problem, and compared with the particle swarm optimization (PSO) and genetic algorithm (GA) meta-heuristics. Further, the ant colony optimization (ACO) algorithm is employed to identify the shortest path over the cluster heads for the UAV to traverse. The simulation results validate the effectiveness of the proposed offloading strategy in terms of tasks delays and UAV energy consumption.