Multi-objective Optimization Problem Research Articles

Cost-effective task offloading and trajectory optimization in UAV assisted edge networks with DDPG

PurposeUnmanned aerial vehicles (UAVs), known for their exceptional flexibility and maneuverability, have become an integral part of mobile edge computing systems in edge networks. This paper aims to minimize system costs within a communication cycle. To this end, this paper has developed a model for task offloading in UAV-assisted edge networks under dynamic channel conditions. This study seeks to efficiently execute task offloading while satisfying UAV energy constraints, and validates the effectiveness of the proposed method through performance comparisons with other similar algorithms.Design/methodology/approachTo address this issue, this paper proposes a task offloading and trajectory optimization algorithm using deep deterministic policy gradient, which jointly optimizes Internet of Things (IoT) device scheduling, power distribution, task offloading and UAV flight trajectory to minimize system costs.FindingsThe analysis of simulation results indicates that this algorithm achieves lower redundancy compared to others, along with reductions in task size by 22.8%, flight time by 34.5%, number of IoT devices by 11.8%, UAV computing power by 25.35% and the required cycle for per-bit tasks by 33.6%.Originality/valueA multi-objective optimization problem is established under dynamic channel conditions, and the effectiveness of this approach is validated.

A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces

The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696–723, 2021) is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the Clarke subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem.

Multi-objective service composition optimization problem in IoT for agriculture 4.0

Multi-objective service composition optimization problem in IoT for agriculture 4.0

A Two-Stage Robust Optimization for Reliable Logistics Network Design via Evolutionary Computation

This paper presents a novel two-stage robust optimization model for designing a dependable logistics network that integrates evolutionary computation techniques. The proposed model considers both the normal and disrupted states of the logistics network and seeks to reduce the overall network cost and operating time in different disruption situations. The challenge is a multi-objective optimization problem addressed using a hybrid evolutionary method that combines the advantages of the non-dominated sorting genetic algorithm with the large neighborhood search heuristic. Numerical experiments are conducted on various test instances to demonstrate the effectiveness and efficiency of the proposed model and algorithm. The results show that the proposed algorithm can generate robust and reliable logistics network designs resilient to disruptions and uncertainties, leading to significant improvements in logistics performance and cost savings compared to traditional methods.

Novel statistical investigation on performance measures of WEDM: Optimization, microstructure and mechanical properties

A comparative performance analysis has been investigated on wire electrical discharge machining (WEDM) responses while machining a hybrid titanium matrix composite (TMC) varying the key input parameters like power (P), peak current (IP) and time-off (Toff). Two novel multi-objective optimization algorithms are developed namely desirable multi-objective genetic algorithm (DMOGA) and desirable multi-objective giant pacific octopus optimizer (DMOGPOO) for tackling various issues in many industries like automobile valve pins in crank and cam shafts, aerospace propeller and biomedical implants. The principal advantage of DMOGA to other algorithm is accuracy and robustness. The novelty fits in the iterative progression of growth of efficient grandee set, uttered as population congregating to a fitness function. Many techniques frequently encounter substandard solutions when evaluating MOO problems, as opposed to solving properly approximated functions of Pareto optimal solutions in targets. DMOGPOO is an enthralling statistical method which mimics the octopus’s predatory behavior, performs better than other multi-objective optimization (MOO) algorithms, where the desirable objective functions is fetched in python using MOGPOO. In a multi-objective foraging environment, the archive was utilized to imitate octopus predatory behavior and establish social hierarchies. DMOGPOO approach is designed with multi-objective formulations to preserve and guarantee enhanced coverage of optimum solutions across all goals. Experimental investigation is accepted on material removal rate (MRR), surface roughness (SR), kerf width (KW) and over cut (OC). Combined desirability in case of DMOGA is 0.716 which improved to 0.813 when DMOGPOO is proposed. MOO is improved with DMOGPOO of 13.547% when contrasted with DMOGA, with MRR of 3.81 mm3/min, SR of 0.79 µm, KW of 0.349 mm, OC of 0.099 mm, and combined desirability of 0.813. Improved optimality set is obtained when DMOGPOO is used. %improvement of MRR is 5.54%, SR is 75.95%, KW is 0.29%, and OC is 4.21%.

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. The present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

Comparative assessment and performance analysis of interference mitigation techniques for co‐existent non‐geostationary and geostationary satellites

SummaryIn recent years, technological developments with user demands, reduced production, and launch costs have rapidly increased the number of Low Earth Orbit (LEO) satellites in space. Since LEO satellites use the same frequency band as existing Geostationary Earth Orbit (GEO) satellites, the interference coordination between the two satellite networks is vital. In order to minimize the co‐existent interference between these satellite networks, studies perform on different interference mitigation strategies. In this paper, analysis and comparative assessment of these interference mitigation techniques are presented for the co‐existent Non‐Geostationary Earth (NGEO) and GEO systems. More specifically, power control (PC) and spatial isolation‐based link adaptation (SILA) techniques are studied comparatively for the performance evaluation. It is shown that the communication link bandwidth is more efficiently utilized in the SILA technique when compared with the PC technique. Moreover, the multi‐objective optimization problem (MOP) approach in the SILA technique is demonstrated to be more effective when compared with the single‐objective optimization problem (SOP) approach used in the PC technique as the simultaneous prioritizing objective functions outperforms single prioritization. Finally, it is shown that when the PC technique is applied together with the SILA technique, the exclusive angle (EA) can be reduced up to 8% for 100 Mbps, and 8.5% for 200 Mbps transmission bit rates in different operational scenarios. The presented performance evaluation in this paper may help the satellite operator or decision‐maker gain insights on which mitigation technique can be used in the case of a co‐existent interference.

Facilitating Circular Transition in the Construction Industry: Optimizing a Prefabricated Construction Site Layout Using a Novel BIM-Integrated SLP-GA Model

Prefabricated construction is being developed as one of the pathways toward circularity in the construction industry. However, compared to traditional cast-in-place construction methods, the design of prefabricated construction site layouts presents unique challenges, such as managing the space for prefabricated components and lifting equipment, and coordinating the precise timing between off-site fabrication and on-site assembly. Existing research has primarily focused on traditional cast-in-place construction, leaving room for improvement in optimisation models for prefabricated site layouts. This study develops a BIM-based System Layout Planning-Genetic Algorithm (SLP-GA) model specifically tailored for prefabricated construction site optimisation. The proposed model improves the accuracy and visualisation of layout planning through BIM technology, enabling dynamic adjustments and real-time data integration. It also incorporates genetic algorithms to address complex multi-objective optimisation problems, avoiding local optima and overcoming the limitations of traditional SLP methods that rely on subjective judgements. Unlike previous studies that do not consider secondary handling, the optimisation objectives of this study focus on minimising material handling costs associated with secondary handling and maximising comprehensive relationships, including efficiency, safety and space utilisation. The application of this model in a case study shows a reduction in logistics costs of 8.58% and an improvement in comprehensive relationships of 11.61%, indicating significant improvements. This research advances optimisation methods for prefabricated construction site layouts, enriches optimisation objectives by considering secondary handling, and provides practical guidance for improving the efficiency and effectiveness of prefabricated construction projects.

Interval Constrained Multi-Objective Optimization Scheduling Method for Island-Integrated Energy Systems Based on Meta-Learning and Enhanced Proximal Policy Optimization

Multiple uncertainties from source–load and energy conversion significantly impact the real-time dispatch of an island integrated energy system (IIES). This paper addresses the day-ahead scheduling problems of IIES under these conditions, aiming to minimize daily economic costs and maximize the output of renewable energies. We introduce an innovative algorithm for Interval Constrained Multi-objective Optimization Problems (ICMOPs), which incorporates meta-learning and an improved Proximal Policy Optimization with Clipped Objective (PPO-CLIP) approach. This algorithm fills a notable gap in the application of DRL to complex ICMOPs within the field. Initially, the multi-objective problem is decomposed into several single-objective problems using a uniform weight decomposition method. A meta-model trained via meta-learning enables fine-tuning to adapt solutions for subsidiary problems once the initial training is complete. Additionally, we enhance the PPO-CLIP framework with a novel strategy that integrates probability shifts and Generalized Advantage Estimation (GAE). In the final stage of scheduling plan selection, a technique for identifying interval turning points is employed to choose the optimal plan from the Pareto solution set. The results demonstrate that the method not only secures excellent scheduling solutions in complex environments through its robust generalization capabilities but also shows significant improvements over interval-constrained multi-objective evolutionary algorithms, such as IP-MOEA, ICMOABC, and IMOMA-II, across multiple multi-objective evaluation metrics including hypervolume (HV), runtime, and uncertainty.

Coevolutionary multitasking for constrained multiobjective optimization

Addressing the challenges of constrained multiobjective optimization problems (CMOPs) with evolutionary algorithms requires balancing constraint satisfaction and optimization objectives. Coevolutionary multitasking (CEMT) offers a promising strategy by leveraging synergies from distinct, complementary tasks. The primary challenge in CEMT frameworks is constructing suitable auxiliary tasks that effectively complement the main CMOP task. In this paper, we propose an adaptive CEMT framework (ACEMT), which customizes two adaptive auxiliary tasks to enhance CMOP-solving efficiency. The first auxiliary task dynamically narrows constraint boundaries, facilitating exploration in regions with smaller feasible spaces. The second task focuses specifically on individual constraints, continuously adapting to expedite convergence and uncover optimal regions. In solving the main CMOP task, this dual-auxiliary-task strategy not only improves search thoroughness but also clarifies the balance between constraints and objectives. Concretely, ACEMT incorporates an adaptive constraint relaxation technique for the first auxiliary task and a specialized constraint selection strategy for the second. These innovations foster effective knowledge transfer and task synergy, addressing the key challenge of auxiliary task construction in CEMT frameworks. Extensive experiments on three benchmark suites and real-world applications demonstrate ACEMT’s superior performance compared to state-of-the-art constrained evolutionary algorithms. ACEMT sets a new standard in CMOP-solving by strategically constructing and adapting auxiliary tasks, representing a significant advancement in this research direction.

A Novel Resource-Aware Distributed Cooperative Decision-Making Mechanism for Connected Automated Vehicles

<div>This article proposes a new model for a cooperative and distributed decision-making mechanism for an ad hoc network of automated vehicles (AVs). The goal of the model is to ensure safety and reduce energy consumption. The use of centralized computation resource is not suitable for scalable cooperative applications, so the proposed solution takes advantage of the onboard computing resources of the vehicle in an intelligent transportation system (ITS). This leads to the introduction of a distributed decision-making mechanism for connected AVs. The proposed mechanism utilizes a novel implementation of the resource-aware and distributed–vector evaluated genetic algorithm (RAD-VEGA) in the vehicular ad hoc network of connected AVs as a solver to collaborative decision-making problems. In the first step, a collaborative decision-making problem is formulated for connected AVs as a multi-objective optimization problem (MOOP), with a focus on energy consumption and collision risk reduction as example objectives. RAD-VEGA then cooperatively solves this MOOP, taking into account the availability of AV’s onboard resources and the application layer characteristics of today’s ITS communication tools. The performance of the proposed mechanism is evaluated by solving the ZDT1 test problem and studying pareto-frontier solutions to the true front over time. The scalability of the proposed solution is estimated to be 305 CAVs, considering a communication bandwidth of 6 MB/s. Additionally, cooperative AV planning scenario examples are simulated, and the effectiveness of the proposed mechanism is demonstrated by comparing final and initial solutions after solving the MOOP using RAD-VEGA.</div>

Multi-objective optimization of an EDM process for Monel K-500 alloy using response surface methodology-multi-objective dragonfly algorithm

Monel K-500 is a high-performance superalloy composed of nickel and copper, renowned for its exceptional strength, hardness, and resistance to corrosion. To machine this material more precisely and accurately, Electrical Discharge Machining (EDM) is one of the best choices. In EDM, material removal rate (MRR) and electrode wear rate (EWR) are crucial performance parameters that are often conflicting in nature. These parameters depend on several input variables, including peak current (Ip), pulse on time (Ton), duty cycle (Tau), and servo voltage (SV). Optimizing the EDM process is essential for enhancing performance. In this research, a set of experiments were conducted using EDM on Monel K500 alloy to determine the optimal process parameters. The Box–Behnken design was used to prepare the experimental design matrix. Utilizing the experimental data, a second-order mathematical model was developed using Response Surface Methodology (RSM). R2 value is found to be 99.40% and 96.60% for MRR and EWR RSM-based prediction model, respectively. High value of R2 is indicated is indicated good adequacy for prediction. The mathematical model further used in multi-objective dragonfly algorithm (MODA): a new meta-heuristic optimization technique to solve multi-objective optimization problem of EDM. The MODA is a very useful technique to achieve optimal solutions from the multi decision criteria. Utilizing this technique, a set of non-dominated solutions was obtained. Further, the TOPSIS method was used to determine the most desirable optimal solution, which was found to be 0.0135 mm3/min for EWR and 6.968 mm3/min for MRR. These results were obtained when the optimal process parameters were selected as Ip = 6 A, Ton = 200 µs, Tau = 12, and SV = 41.6 V. Operators can machine Monel K500 by selecting the above-mentioned optimal parameters to achieve the best performance.

A Novel Pelican Bird Optimization Algorithm based Optimal Allocation of Combined DGs and EVCSs for Improving Voltage Stability of RDS

Objectives: The main objective of the proposed investigation is to enhance the voltage stability of Radial Distribution System (RDS). It is achieved by proper allocation between combined Electric Vehicle Charging Stations (EVCSs) and Distributed Generators (DGs) in RDS. Here, three objective functions such as Real Power loss, Average Voltage Devotion Index (AVDI) and Voltage Stability Index (VSI) are considered. Methods: The multi-objective optimization problem is implemented using a novel and an effective Pelican Optimization Algorithm (POA) to attain the best compromised solutions. POA is a nature inspired parameter less optimization tool and it is well suited for solution of complex, non-linear voltage stability problem. It determines the most excellent site and size of the EVCSs and DG units. The control parameter of POA considered are population size as 40, the number of variables as 8 and the maximum number of iterations as 100. MATLAB 14.0 platform is utilized for the projected problem. Findings: The bench mark test system of IEEE-33 node system is considered to authenticate the presentation of planned POA methodology. The outcomes such as minimized power loss and AVDI, improved voltage at each bus and VSI are presented. The percentage of loss reduction 39.30% is enhanced, when compared with the base case approach and 5.42 % more improved than the other existing methods like TLBO and HHO approaches. Similarly, the VSI 24.96 % is improved, when compared with the base case method and 1.58 % better than the other obtainable methods. Novelty: The POA is a newly urbanized and well-designed optimization algorithm. It efficiently reaches the global optimal solutions with less time duration. The comparative study with the existing algorithm of TLBO and HHO is considered to prove the performance of Projected POA approach. Keywords: Radial distribution system, Distributed Generators, Electric Vehicles, Charging Stations, Voltage stability, Network loss reduction, Pelican Optimization Algorithm

A novel multi-objective dung beetle optimizer for Multi-UAV cooperative path planning

Path planning for multiple unmanned aerial vehicles (UAVs) is crucial in collaborative operations and is commonly regarded as a complicated, multi-objective optimization problem. However, traditional approaches have difficulty balancing convergence and diversity, as well as effectively handling constraints. In this study, a directional evolutionary non-dominated sorting dung beetle optimizer with adaptive stochastic ranking (DENSDBO-ASR) is developed to address these issues in collaborative multi-UAV path planning. Two objectives are initially formulated: the first one represents the total cost of length and altitude, while the second represents the total cost of threat and time. Additionally, an improved multi-objective dung beetle optimizer is introduced, which integrates a directional evolutionary strategy including directional mutation and crossover, thereby accelerating convergence and enhancing global search capability. Furthermore, an adaptive stochastic ranking mechanism is proposed to successfully handle different constraints by dynamically adjusting the comparison probability. The effectiveness and superiority of DENSDBO-ASR are demonstrated by the constrained problem functions (CF) test, the Wilcoxon rank sum test, and the Friedman test. Finally, three sets of simulated tests are carried out, each including different numbers of UAVs. In the most challenging scenario, DENSDBO-ASR successfully identifies feasible paths with average values of the two objective functions as low as 637.26 and 0. The comparative results demonstrate that DENSDBO-ASR outperforms the other five algorithms in terms of convergence accuracy and population diversity, making it an exceptional optimization approach to path planning challenges.

Learning to Guide Particle Search for Dynamic Multiobjective Optimization.

Dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

Reactive power and voltage control based on reactive power compensation coefficient and sensitivity factor

Abstract Aiming at the problems that the existing reactive power allocation methods do not take into account the specific operating state of each doubly-fed induction generator (DFIG) and the established optimization model has many variables and is complicated, this paper proposes to construct an optimization model based on reactive power compensation coefficient and sensitivity factor, to reduce the number of variables in the mathematical model and simplify the expression of the relationship between each key parameter, so the speed of the reactive power and voltage control are improved. In the process of constructing specific optimization models, the objective of minimizing the active loss takes into account the operating copper consumption of each DFIG. The objective of minimizing the voltage fluctuation of each DFIG is also taken into account, in addition to the operating state constraints of each DFIG, so that the final reactive power allocation is more practical. In solving the multi-objective optimization problem, the improved NSGA-II algorithm is utilized, which can achieve the simultaneous optimization of multiple objectives, and when combined with the simplified model established in this paper, the correctness and speed of obtaining the optimal solution set of Pareto can be further improved. Finally, the effectiveness of the proposed strategy in reducing active losses and voltage fluctuations in wind farms is verified by simulation examples.

Optimal location and sizing of renewable distributed generations and electric vehicle charging stations

Many countries are aiming to replace gasoline-based vehicles with electric vehicles (EVs). The increasing adoption of EVs has led to a surge in the number of charging stations, significantly impacting the electrical grid with issues such as power quality degradation, increased losses, and voltage fluctuations. In response to these challenges, there is a growing interest in integrating distributed generation from unconventional and renewable sources into the grid to power EV Charging Stations (EVCSs). However, this integration poses new complexities, including increased power losses and voltage instability. Consequently, the optimal allocation and sizing of Renewable Distributed Generations (RDGs) and EVCSs have become critical planning considerations. This paper addresses these issues by formulating a multi-objective optimization problem aimed at minimizing power losses and improving the voltage profile of distribution systems. The study introduces several constraints, including the placement of EVCSs and RDGs at separate buses, and employs particle swarm optimization and cuckoo search algorithm to simultaneously determine the optimal locations and sizes of the RDGs and the optimal locations of the EVCSs. The effectiveness of the proposed techniques is demonstrated through simulations on IEEE 33 radial and meshed distribution systems, illustrating their capability to identify optimal configurations for integrating RDGs and EVCSs.

Improving decomposition-based MOEAs for combinatorial optimisation by intensifying corner weights

In the real world, a class of common problems such as supply chain management, project scheduling, portfolio optimisation and facility location design are multi-objective combinatorial optimisation problems (MOCOPs), where there are multiple objectives and the set of feasible solutions is discrete. In MOCOPs, corner solutions are solutions in which at least one objective reaches the optimal value. Corner solutions are important as they are likely to be preferred by the decision maker and are able to help improve algorithm performance. In this paper, we first reveal that in decomposition-based MOEAs, improving the corner weights (as opposed to improving the middle weights) significantly enhances the generation of corner solutions, thereby enhancing the overall performance of algorithms. Based on this, we propose a method to enhance the search for corner solutions in MOCOPs. We act on a class of popular MOEAs, decomposition-based MOEAs, and in their evolutionary mechanism we intensify the weights in the corner areas. To verify the proposed method, we conduct experiments by incorporating the method into three decomposition-based MOEAs, MOEA/D, MOEA/D-DRA-UT and MOEA/D-LdEA (the latter two were designed specifically for enhancing the search of corner solutions). The experimental results demonstrate that the proposed method can improve the spread of solution sets found, without compromising the quality of internal solutions.

Manifold-assisted coevolutionary algorithm for constrained multi-objective optimization

In constrained multi-objective optimization problems (CMOPs), constraints often fragment the Pareto solution space into multiple feasible and infeasible regions. This fragmentation presents a challenge for evolutionary optimization methods as feasible regions can be discrete and isolated by infeasible areas, making exploration difficult and leading to populations getting trapped in local optima. To address these issues, this paper introduces a manifold assisted coevolutionary algorithm for solving CMOPs. Firstly, a guided feasible search strategy is proposed to explore feasible regions, especially those isolated by infeasible barriers. This is achieved by estimating directions to the Constrained Pareto Set (CPS). Secondly, a manifold learning-based exploration strategy is employed to spread the population along the Pareto Set (PS) manifold by estimating the manifold distribution. Moreover, two populations are exploited, where the first population serves as the primary population, considering both constraints and objectives to explore the feasible region and search along the CPS. The second population, on the other hand, does not consider constraints and serves as an auxiliary population to explore the Unconstrained PS. By cooperating, these two populations effectively approach and cover separated CPS segments. The proposed algorithm is evaluated against seven state-of-the-art algorithms on 37 CMOP test functions and 5 CMOPs with fraudulent constraints. The experimental results clearly demonstrate that our algorithm can reliably locate multiple CPSs and is considered state-of-the-art in handling CMOPs.

A grid self-adaptive exploration-based algorithm for multimodal multiobjective optimization

In multimodal multiobjective optimization, the key is to find as many equivalent Pareto optimal solutions as possible through broad exploration in the decision space. The grid search strategy can achieve quick convergence by guiding the evolution with historical information in each grid while enabling broad exploration. However, inaccurate utilization of information in grids may lead to losing numerous potential solutions, especially on imbalanced problems. In order to resolve this issue, a grid self-adaptive exploration-based algorithm (GSEA) is proposed in this paper. In GSEA, the historical information in the grid is accurately utilized through grid-based self-adaptive exploration and niche clearing methods, which retain a large number of solutions with potential and effectively handle multimodal multiobjective optimization problems (MMOPs). Experimental results show that the proposed algorithm outperforms seven other state-of-the-art multimodal multiobjective evolutionary algorithms (MMEAs) on two types of MMOPs, and the approach can effectively deal with the MMOPs with middle-scale decision variables as memory allows.