Discrete Differential Evolution Research Articles

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 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.

A non-dominated discrete differential evolution for fuel loading pattern optimization of a nuclear research reactor

Abstract This paper presents a detailed description of a new variant of differential evolution for nuclear reactor refueling optimization problem. This variant combines the elitism strategy with a discrete differential evolution. The elitism strategy allows non-dominated solutions found during the search and stored in the archive to participate in the differential evolution operation. The population size is the same as the archive size, and the number of non-dominated solutions participating in the search at a particular generation is controlled by a specific probability. The proposed method is successfully applied to a nuclear research reactor for its first refueling time to search for optimal loading patterns that both maximize the effective multiplication k eff and minimize the power peaking factor PPF of the reactor. The optimal loading patterns can significantly improve the operational time and safety of the reactor compared to the loading pattern used in practice.

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.

Space division and adaptive selection strategy based differential evolution algorithm for multi-objective satellite range scheduling problem

Satellite range scheduling always plays a crucial role in tracking, telemetry, and control of the spacecraft. With the significant increase in the number and type of satellites in orbit, the demands of users for satellite range scheduling are becoming more and more diverse. However, existing studies for the satellite range scheduling problem (SRSP) rarely consider multiple optimization objectives, which is quite significant in practice. Hence, this paper investigates a multi-objective satellite range scheduling problem (MO-SRSP) that optimizes three objectives simultaneously: the overall profits of tasks, load-balance of antennas, and completion timeliness of tasks. To address MO-SRSP, this paper establishes a mathematical model on the basis of analysis of MO-SRSP and proposes a multi-objective evolutionary algorithm, which is called multi-objective differential evolution algorithm based on space division and adaptive selection strategy (MODE-SDAS). The space division strategy will uniformly divide the objective space into a set of subspaces and preserve a set of non-dominated solutions in each subspace during the environmental selection even if some of these solutions are dominated by other solutions in other subspaces, so as to maintain the diversity of the algorithm. The adaptive selection strategy will adaptively allocate computational resources to different subspaces to improve the convergence of the population. Besides, problem-specific designs such as coding and encoding methods, the discrete differential evolution operator, as well as objective-specific individual variation operators are incorporated into the algorithm to enhance the search capability. Finally, extensive experiments based on simulation test cases are carried out to verify the effectiveness and efficiency of MODE-SDAS. The comparison results show that MODE-SDAS significantly outperforms its competitors in terms of three metrics. Meanwhile, knee point analysis, sensitivity analysis, and application insights are presented.

Sequential seeding policy on social influence maximization: a Q-learning-driven discrete differential evolution optimization

Sequential seeding policy on social influence maximization: a Q-learning-driven discrete differential evolution optimization

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.

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.

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.

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.

A discrete differential evolution with local search particle swarm optimization to direct angle and aperture optimization in IMRT treatment planning problem

Intensity-modulated radiation therapy is a well-known technique for treating cancer patients worldwide. A treatment plan in this technique requires decision-making for three main problems: selection of beam angles, intensity map calculation, and leaf sequencing. Previous works investigated these problems sequentially. We present a new integrated framework for simultaneous decision-making of directions, intensities, and aperture shape, called direct angle and aperture optimization, and develop a mixed-integer nonlinear mathematical model for the problem. Due to the nonlinearity and the dimension of the problem, three efficient metaheuristics based on differential evolution (DE) called classic differential evolution (cDE), discrete differential evolution (dDE), and adaptive hybrid discrete differential evolution-particle swarm optimization (ahdDE-PSO) algorithms are designed to solve the problem. Parameters calibration is performed using the Taguchi design of experiments. The performance of the algorithms is evaluated by solving the problem for ten real cases of liver cancer disease from the TROTS data set. The performed ablation study and statistical analysis of computational results demonstrate that ahdDE-PSO is capable of finding high-quality treatment plans.

Discrete region inferred differential evolution feature selection architecture for human face recognition

Face Recognition has received a lot of attention in wide variety of the security application employing face based biometric authentication due to its non intrusive data acquisition. Especially artificial intelligence play important role in face recognition. Numerous researches have been carried out using machine learning technique in order to accuracy of the recognition. In this paper, a novel technique titled as Discrete Differential Evolution (DDE) architecture has been proposed. The proposed architecture will employed after set of the primary image processing steps such as preprocessing, feature extraction and feature selection. Initially preprocessing of the images is performed with image normalization technique and image enhancement technique. Preprocessed image will explored to Linear Discriminant Analysis technique to extract the features of the image. Extracted features will contain some redundant and irrelevant information of the images, it has to eliminate and optimal feature has to be selected to the recognition task. Discrete Region Inferred Differential Evolution architecture is employed to feature selection. Extracted features will be consider as search space, objective function of the DDE generates the optimal features solutions with respect to fitness criteria. Finally recognition task is performed with optimal features using support vector machine.

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.