Single-objective Problem Research Articles

A new heuristic method for solving unbalanced multi-objective assignment problem

Abstract In the era of globalization, institutions face increasing challenges in effectively managing their resources to achieve diverse and differentiated objectives. The unbalanced multi-objective assignment problem reflects these challenges, as the distribution of limited resources requires achieving a balance between objectives such as minimizing time, cost, etc. In this study, an application case in the industrial field of rolling process was investigated, where the objective of the assignment problem is to minimize total assignment. In order to tackle this problem, the multi-objective problem was addressed by converting it into a single-objective problem through the weighted sum method by assigning a weight to each objective. A new heuristic method was then applied to solve the unbalanced single-objective assignment problem where the machines were loaded with more than one job. The Hungarian method was also used to solve the problem in order to assess the proposed method, and the outcomes were then compared. The proposed method proved efficient as it reduced idle time by 28%, increased machine efficiency by 5% and reduced costs by an average of 15%.

Deep contextual bandits-based energy-efficient beamforming for integrated sensing and communication

In this paper, a transmit beamforming design is considered to jointly improve the communication and sensing functionalities in an integrated sensing and communication (ISAC) system, where a dual-functional base station (BS) serves a set of communication users (UEs) while sensing some potential targets (TGs). To this end, a multi-objective beamforming optimization problem is formulated to maximize the weighted linear combination of the communication energy efficiency (EE) and sensing beampattern gains. Using the normalized weighted sum method, the multi-objective problem is relaxed to a single-objective problem. For dealing with the non-convexity nature of the considered problem and the continuity of the beamforming space, a novel deep contextual bandits (DCB) scheme inspired by the soft actor-critic (S-DCB) method is proposed in which the channel state information of UEs is used as the context. Both the reward and policy functions are approximated to solve the problem. Simulation results indicate that the multi-objective function enables an adjustable trade-off between the communication and sensing functionalities. Besides, the effectiveness of the proposed S-DCB algorithm is verified through a comprehensive comparison with the state-of-the-art DCB-DDPG and the upper bound benchmarks.

From single-objective to multi-objective reinforcement learning-based model transformation

AbstractModel-driven optimization allows to directly apply domain-specific modeling languages to define models which are subsequently optimized by applying a predefined set of model transformation rules. Objectives guide the optimization processes which can range from one single objective formulation resulting in one single solution to a set of objectives that necessitates the identification of a Pareto-optimal set of solutions. In recent years, a multitude of reinforcement learning approaches has been proposed that support both optimization cases and competitive results for various problem instances have been reported. However, their application to the field of model-driven optimization has not gained much attention yet, especially when compared to the extensive application of meta-heuristic search approaches such as genetic algorithms. Thus, there is a lack of knowledge about the applicability and performance of reinforcement learning for model-driven optimization. We therefore present in this paper a general framework for applying reinforcement learning to model-driven optimization problems. In particular, we show how a catalog of different reinforcement learning algorithms can be integrated with existing model-driven optimization approaches that use a transformation rule application encoding. We exemplify this integration by presenting a dedicated reinforcement learning extension for MOMoT. We build on this tool support and investigate several case studies for validating the applicability of reinforcement learning for model-driven optimization and compare the performance against a genetic algorithm. The results show clear advantages of using RL for single-objective problems, especially for cases where the transformation steps are highly dependent on each other. For multi-objective problems, the results are more diverse and case-specific, which further motivates the usage of model-driven optimization to utilize different approaches to find the best solutions.

Solving Multi-objective Bi-item Capacitated Transportation Problem with Fermatean Fuzzy Multi-Choice Stochastic Mixed Constraints Involving Normal Distribution

The transportation problem (TP) is an important type of linear programming problem. The aim of TP is to optimize the objective function by allocating product shipments from various sources to multiple destinations. When limitations exist during transportation in the number of products transported from a source to destination due to a variety of factors, such as storage limitations, budgetary constraints, and so on, then TP becomes the capacitated transportation problem (CTP). The business entrepreneurs are keen on transporting multiple items with multiple objectives to generate maximum revenue for an organization, which leads to the development of a multi-objective bi-item capacitated transportation problem (MOBICTP). If a supplier's resources significantly increase or decrease, and the demand needs also significantly increase or decrease, the MOBICTP transforms into a MOBICTP with mixed constraints. Most real-world problems have uncertain parameters due to insufficient data, fluctuating market costs for an item, variation in weather conditions, and so on. Such uncertain parameters are addressed using fuzzy, multi-choice, or stochastic programming. In this article, we examined a novel integrated model for a multi-objective bi-item capacitated transportation problem, which includes a fermatean fuzzy multi-choice stochastic mixed constraint that follows normal distribution. First, the Fermatean fuzzy multi-choice stochastic parameter in the constraints is transformed into a multi-choice stochastic parameter in the constraints by using the (α, β )-cut technique and accuracy function. Then the improved chance-constrained method is developed using Newton divided difference interpolation polynomial. The improved chance-constrained method is used to transform the multi-choice stochastic parameter in the constraints into its equivalent deterministic constraints. Secondly, we propose a novel approach, the improved global weighted sum method, which transforms a multi-objective problem into a single objective problem and utilizes Lingo 18.0 software to find the optimal compromise solution to the equivalent deterministic problem. The main aim of this paper is to help business entrepreneurs improve their profit margins by optimizing the quantity of multiple items while minimizing damage costs, labor costs, transportation time, and transportation costs, and maximizing discounts. To show the model’s validity and significance, a numerical example is solved using the Lingo 18.0 software. In order to emphasize the proposed method, a comparative analysis is conducted with other existing methods. The final component includes a sensitivity analysis and conclusions with future research directions.

Effective deployment strategies for optimizing area coverage in multistatic sonar detection based on Cassini oval approximation and a virtual force algorithm

Multistatic sonar is regarded as a highly promising method for detecting quiet submarines over long distances. This technique exhibits high positioning accuracy, flexible configurations, easy concealment, and robust resistance to interference. However, the sources are more expensive than receivers and performance of multistatic sonar depends strongly on the relative positions of the sources and receivers. In this work, we study the problem of optimal deployment of receivers for one source and multiple receivers type multistatic sonar to achieve maximum area coverage. The area coverage of multistatic sonar is a multi-objective optimization problem (MOOP) balancing maximum coverage against minimal cost. To simplify the MOOP, the area enclosed by a Cassini oval is approximated to two circles and the normalized area difference is analyzed. Then the required number of receivers within a rectangular area of interest (AOI) is calculated based on full coverage theory. So the MOOP is simplified into a single-objective problem focused on achieving maximal coverage with a specific number of receiver nodes. An enhanced virtual force algorithm named Delaunay triangulation hole repair virtual force algorithm (DTHRVFA) is introduced to optimize the deployment positions of receivers as a heterogeneous nodes deployment problem. Simulation results show significant improvement in coverage compared with various methods of heterogeneous nodes deployment. The proposed method effectively addresses area coverage problems associated with the deployment of one source and multiple receivers type multistatic sonar receivers.

Traffic evolution in Software Defined Networks

Software Defined Networking (SDN) offers unprecedented traffic engineering possibilities due to optimal centralized decision making. However, network traffic evolves over time and changes the underlying optimization problem. Frequent application of the model to reflect traffic evolution causes flooding of control messages, traffic re-routing and synchronization problems. This paper addresses the problem of graceful traffic evolution in SDNs (Software Defined Networks) minimizing rule installations and modifications, optimizing the global objectives of minimization of Maximum Link Utilization (MLU) and minimization of the Maximum Switch Table Space Utilization (MSTU). The problem is formulated as multi-objective optimization using Mixed Integer Linear Programming (MILP). Proof of NP-Hardness is provided. Then, we re-formulate the problem as a single-objective problem and propose two greedy algorithms to solve the single-objective problem, namely MIRA-Im and MIRA-Im with Conflict Detection, and experiments are performed to show the effectiveness of the algorithms in comparison to previous state of the art proposals. Simulation results show significant improvements of MIRA-Im with Conflict Detection, especially in terms of number of installed rules (with a gain till 80% with the highest number of flows) and flow table space utilization (with a gain till 55% with the highest number of flows), compared to MIRA-Im and other algorithms available in the literature, while the other metrics are essentially stable.

Risk-informed design: An unavailability allocation approach

Due to the technological complexity of nuclear power plants and the large number of components involved in their design, the objective space for balancing nuclear safety, availability performance, and cost in an optimization model becomes extremely vast. Consequently, this poses challenges in achieving operational optimization at the plant level, complicating the assurance of compliance with regulatory requirements. One solution is to partition the problem and analyze it at a system level to reduce the objective space. In this work, different options are analyzed to optimize cost and unavailability for systems that provide the means for meeting previously proposed unavailability targets. This ensures that licensing basis events (LBE) comply with risk targets and regulatory criteria. Additionally, the role of system unavailability due to maintenance activities and reliability issues related to unplanned component failures (e.g., random failures, common cause failures) in the optimization problem is analyzed. The various proposed optimization methods are implemented in the design of a pressurized water reactor (PWR) system. Evolutionary algorithms are used as optimization methods, with Genetic Algorithms for single-objective problems and Non-dominated Sorting Genetic Algorithm III (NSGA-III) for multi-objective problems. The main finding suggests that traditional models, which aim to minimize costs and unavailability, face challenges in adapting to the systems unavailability target. Therefore, optimization occurs by shifting the focus towards minimizing costs and distance to the unavailability target. This approach ensures that the results closely align with the unavailability target, thereby creating more efficiency in operating and maintenance costs while also ensuring acceptable design and operational regulatory compliance.

Maximizing virtual power plant profit: A two-level optimization model for energy market participation

Managing dispersed generation via virtual power plants (VPPs) is crucial for maximizing profits in electricity markets. This paper presents a model aimed at maximizing VPP profit through participation in the energy market. The proposed model addresses grid and security constraints of units using deterministic programming, formulated as an equilibrium-constrained, two-level mathematical optimization model. The first level focuses on maximizing VPP profit, while the second optimizes social welfare. Applying duality theory transforms this two-level model into a mixed-integer linear programming model, further refined using Karush–Kuhn–Tucker (KKT) optimality conditions. Given the inherent conflict in these objectives, a novel algorithm employing water flow dynamics is proposed for solving the model. To enhance method performance, the Pareto criterion and fuzzy decision-making are incorporated. Model tests are conducted on a standard 24-bus IEEE grid, demonstrating its efficiency. For the single-objective problem without line congestion, the solving time was 12 s. Introducing line congestion increased the profit by 13.4 %, from $40,413.21 to $45,837.32. In the two-objective problem without congestion, the profit ranged between $36,928.72 and $42,813.28, and emissions ranged from 275.21 to 2,916.32 pounds. With congestion, the profit range increased by a maximum of 8.7 %, and emissions were reduced by up to 4.6 %.

Multi-Objective Combinatorial Optimization Algorithm Based on Asynchronous Advantage Actor–Critic and Graph Transformer Networks

Multi-objective combinatorial optimization problems (MOCOPs) are designed to identify solution sets that optimally balance multiple competing objectives. Addressing the challenges inherent in applying deep reinforcement learning (DRL) to solve MOCOPs, such as model non-convergence, lengthy training periods, and insufficient diversity of solutions, this study introduces a novel multi-objective combinatorial optimization algorithm based on DRL. The proposed algorithm employs a uniform weight decomposition method to simplify complex multi-objective scenarios into single-objective problems and uses asynchronous advantage actor–critic (A3C) instead of conventional REINFORCE methods for model training. This approach effectively reduces variance and prevents the entrapment in local optima. Furthermore, the algorithm incorporates an architecture based on graph transformer networks (GTNs), which extends to edge feature representations, thus accurately capturing the topological features of graph structures and the latent inter-node relationships. By integrating a weight vector layer at the encoding stage, the algorithm can flexibly manage issues involving arbitrary weights. Experimental evaluations on the bi-objective traveling salesman problem demonstrate that this algorithm significantly outperforms recent similar efforts in terms of training efficiency and solution diversity.

Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem

Multi-criteria scheduling problems under uncertainty remain a relatively unexplored topic in theoretical computer science despite substantial practical interests. This work studies a bi-objective identical parallel machine scheduling problem under uncertainty, in which the first objective is to minimize the total completion time, and the second is to minimize the makespan. Especially a job’s processing time is assumed to be represented by a polynomial function with respect to scenario u∈U, where U⊂R+ is an interval containing an infinite number of scenarios.In this work, we are looking for a compact and complete description of the set of possibly optimal solutions, along with their objective function values, over the set of scenarios or an approximation with a performance guarantee. First, to better understand the characteristics of the studied problem, we consider two single-objective problems: parallel machine scheduling problem under uncertainty with the total completion time and makespan criterion, respectively. For the problem with the total completion time criterion, we demonstrate that the set of possibly optimal schedules can be found in polynomial time. In contrast, for the problem with the makespan criterion, we provide a (1+ϵ)-approximation algorithm. For the bi-objective problem, we provide a 2-approximation algorithm for any number of parallel machines and a (1+ϵ)-approximation algorithm where a fixed number of parallel machines is considered.

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.

Optimized the locations and sizes of FACTS devices on electrical network involving wind power using a new hybrid stochastic algorithm

This article focuses on utilizing a new hybrid optimization algorithm called the Fitness-Distance Balance-based Archimedes Optimization Algorithm (FDB-AOA) to solve the Optimal Power Flow (OPF) problems within a recently adopted electrical transmission grid, specifically the modified IEEE-30 bus system. This system integrates thermal and wind -based generating units, including various types of Flexible AC Transmission System (FACTS) devices. Several tests are performed where the stochastic wind energy is modeled using probability density functions. The optimization goal takes into account the cost of thermal generation, the direct cost of scheduled wind power, and the penalty cost for underestimating wind power. The locations and sizing of FACTS devices are optimized with aim of reducing several fitness functions. The optimization results achieved by the proposed method in solving single objective functions were more effective in finding the optimal solution compared to several well-known algorithms. The results show the superiority of the proposed method in the majority of case studies, as it achieved a better optimum solution with a total generation cost ( Cgen ) value of 806.9817 $/h, and a real power loss ( Ploss ) value 1.7619 MW, also yields a competitive gross cost ( Cgross ) value of 1104.6652 $/h compared to those obtained by the other algorithms. In contrast, the statistical analysis proven the superiority of this algorithm where the standard deviations (SD) required in solving the single objective problem ( Cgen ) is 0.0996, which are better compared to other techniques. the simulation results demonstrate that the FDB-AOA optimizer is robust than other approaches, like the Success history based-adaptive differential evolution (SHADE) algorithm, MSA (Moth Swarm Algorithm), and ABC (artificial bee colony) integrated with the SF (superiority of feasible solutions) approach, in solving OPF problems involving the integration of both thermal and wind power plants along with FACTS devices.

Balancing Staff Finishing Times vs. Minimizing Total Travel Distance in Home Healthcare Scheduling

Cost reduction and staff retention are important optimization objectives in home healthcare (HHC) systems. Home healthcare operators need to balance their objectives by optimizing resource use, service delivery and profits. Minimizing total travel distances to control costs is a common routing problem objective while minimizing total finishing time differences is a scheduling objective whose purpose is to enhance staff satisfaction. To optimize routing and scheduling, we propose mixed integer linear programming with a bi-objective function, which is a subset of the vehicle routing problem with time windows (VRPTWs). VRPTWs is a known NP-hard problem, and optimal solutions are very hard to obtain in practice. Metaheuristics offer an alternative solution to this type of problem. Our metaheuristic uses the simulated annealing algorithm and weighted sum approach to convert the problems to single-objective problems and is equipped with operators including swapping, moving, path exchange and ruin and recreate. The results show, firstly, that the algorithm can effectively find the Pareto front, and secondly, that minimizing total finishing time differences to balance the number of jobs per caretaker is an efficient way to tackle HHC scheduling. A statistical test shows that the algorithm can obtain the Pareto front with a lower number of weighted sum problems.

Deep reinforcement learning as multiobjective optimization benchmarks: Problem formulation and performance assessment

The successful deployment of Deep learning in several challenging tasks has been translated into complex control problems from different domains through Deep Reinforcement Learning (DRL). Although DRL has been extensively formulated and solved as single-objective problems, nearly all real-world RL problems often feature two or more conflicting objectives, where the goal is to obtain a high-quality and diverse set of optimal policies for different objective preferences. Consequently, the development of Multi-Objective Deep Reinforcement Learning (MODRL) algorithms has gained a lot of traction in the literature. Generally, Evolutionary Algorithms (EAs) have been demonstrated to be scalable alternatives to the classical DRL paradigms when formulated as an optimization problem. Hence it is reasonable to employ Multi-objective Evolutionary Algorithms (MOEAs) to handle MODRL tasks. However, there are several factors constraining the progress of research along this line: first, there is a lack of a general problem formulation of MODRL tasks from an optimization perspective; second, there exist several challenges in performing benchmark assessments of MOEAs for MODRL problems. To overcome these limitations: (i) we present a formulation of MODRL tasks as general multi-objective optimization problems and analyze their complex characteristics from an optimization perspective; (ii) we present an end-to-end framework, termed DRLXBench, to generate MODRL benchmark test problems for seamless running of MOEAs (iii) we propose a test suite comprising of 12 MODRL problems with different characteristics such as many-objectives, degenerated Pareto fronts, concave and convex optimization problems, etc. (iv) Finally, we present and discuss baseline results on the proposed test problems using seven representative MOEAs.

Projection-Pursuit Regression-Based Optimization of Frost Resistance and Mechanical Performance in Alkali-Activated Slag Cement Pavements

In recent years, applying slag micro-powder as a substitute for cement in preparing alkali-activated slag cement stabilized sand (AASCSS) mixtures has become increasingly widespread. In the severe cold regions of Xinjiang, multi-objective optimization of the mechanical and frost resistance properties of AASCSS is particularly crucial. This paper adopts slag micro-powder to replace Portland cement, together with lime and desulfurization gypsum as activators, to explore the effects of activator type and dosage on the mechanical and frost-resistance properties of AASCSS. A prediction model for the mechanical and frost-resistance properties of AASCSS based on projection-pursuit regression (PPR) was proposed and established. Using the developed PPR model, contour plots of the comprehensive performance were calculated, simplifying the multi-objective problem into two single-objective problems focusing on mechanical and frost resistance properties for analysis. This method avoids subjective weighting and hypothesis-based modeling. By analyzing the contour plots of comprehensive performance, the optimal performance indices for mechanical and frost–thaw properties and the corresponding types and dosages of activators can be directly determined. When the required 7-day unconfined compressive strength in road engineering is 5.6 MPa, the optimal value of the freeze–thaw performance index (BDR) is 94.08%. At this point, the corresponding lime content is 2.1%, and the desulfurization gypsum content is 3.3%. The research results provide a reference for applying slag to road-based materials.

Source code obfuscation with genetic algorithms using LLVM code optimizations

Abstract With the advent of the cloud computing model allowing a shared access to massive computing facilities, a surging demand emerges for the protection of the intellectual property tied to the programs executed on these uncontrolled systems. If novel paradigm as confidential computing aims at protecting the data manipulated during the execution, obfuscating techniques (in particular at the source code level) remain a popular solution to conceal the purpose of a program or its logic without altering its functionality, thus preventing reverse-engineering on the program even with the help of computing resources. The many advantages of code obfuscation, together with its low cost, makes it a popular technique. This paper proposes a novel methodology for source code obfuscation that can be used together with other traditional obfuscation techniques, making the code more robust against reverse engineering attacks. Three program complexity metrics are used to define three different single-objective combinatorial optimization versions of the problem, which are solved and analysed. Additionally, three multi-objective problems are defined, those considering each of the selected metrics together with the program execution time, in order to avoid strong obfuscations penalizing the performance. The goal of the defined problems is to find sequences of LLVM optimizations that lead to highly obfuscated versions of the original code. These transformations are applied to the back-end pseudo-assembly code (i.e., LLVM Intermediate Representation), thus avoiding any further optimizations by the compiler. Classical genetic algorithms (GAs) are used to solve the studied problems, namely a basic cellular GA for the single-objective problems and the popular NSGA-II for the multi-objective ones. The promising results show the potential of the proposed technique.

Innovative decision-making for solar photovoltaic system installation in residential energy hubs: A probabilistic dynamic planning approach

This paper introduces an innovative probabilistic dynamic planning model tailored to optimize photovoltaic (PV) system installation within Residential Energy Hubs (REHs). The REH amalgamates diverse components, including PV systems, Combined Heat and Power (CHP) units, and gas boilers, to holistically fulfill residential thermal and electrical energy demands. The model's primary objective is to achieve an optimal equilibrium between minimizing initial investment costs associated with PV systems and managing ongoing energy expenses within the REH framework, encompassing potential PV energy losses over the planning horizon. To augment the flexibility and benefits of PV systems for residential consumers, the model integrates several pioneering features. Particularly notable is the introduction of a heating energy storage system, which complements the REH's thermal requirements and adeptly reacts to fluctuations in gas and electricity prices, thereby maximizing PV system benefits and ensuring homeowners' cost efficiency. Moreover, the model addresses the inherent uncertainty tied to PV generation by employing a two-point estimation method, offering a more realistic depiction of system performance and potential outcomes. To resolve the two-objective problem, an initial conversion into a single-objective problem via a weighted summation method precedes the application of an optimization algorithm inspired by symbiotic organisms. The paper demonstrates the practical application and efficacy of the proposed model through extensive simulations spanning a 10-year planning horizon. The results underscore the model's effectiveness and versatility in guiding residential consumers to make informed and economically viable decisions regarding PV system installation within the broader spectrum of their energy requirements. This research represents a significant stride towards empowering homeowners with invaluable tools for embracing sustainable energy solutions.

Automatic Design of Energy-Efficient Dispatching Rules for Multi-Objective Dynamic Flexible Job Shop Scheduling Based on Dual Feature Weight Sets

Considering the requirements of the actual production scheduling process, the utilization of the genetic programming hyper-heuristic (GPHH) approach to automatically design dispatching rules (DRs) has recently emerged as a popular optimization approach. However, the decision objects and decision environments for routing and sequencing decisions are different in the dynamic flexible job shop scheduling problem (DFJSSP), leading to different required feature information. Traditional algorithms that allow these two types of scheduling decisions to share one common feature set are not conducive to the further optimization of the evolved DRs, but instead introduce redundant and unnecessary search attempts for algorithm optimization. To address this, some related studies have focused on customizing the feature sets for both routing and sequencing decisions through feature selection when solving single-objective problems. While being effective in reducing the search space, the selected feature sets also diminish the diversity of the obtained DRs, ultimately impacting the optimization performance. Consequently, this paper proposes an improved GPHH with dual feature weight sets for the multi-objective energy-efficient DFJSSP, which includes two novel feature weight measures and one novel hybrid population adjustment strategy. Instead of selecting suitable features, the proposed algorithm assigns appropriate weights to the features based on their multi-objective contribution, which could provide directional guidance to the GPHH while ensuring the search space. Experimental results demonstrate that, compared to existing studies, the proposed algorithm can significantly enhance the optimization performance and interpretability of energy-efficient DRs.

Ant colony optimization using two-dimensional pheromone for single-objective transport problems

One of the acclaimed algorithms that is used to solve combinatorial graph problems is ant colony optimization (ACO). In this article, we focus on a novel extended model of the pheromone that is responsible for storing collective knowledge. The presented two-dimensional pheromone is able to accommodate more information that is extracted from feasible solutions that can be used to improve the search of a solution space. The idea is positively evaluated on TSP and VRP problems, achieving better results as compared to the original algorithm. Since it is a universal concept, it can be applied to any single-objective problem that is solvable by ACO.

Communication efficient federated learning with data offloading in fog-based IoT environment

Federated Learning (FL) has become a popular distributed machine learning technique that preserves privacy of data set generated by the Internet of Things (IoT) devices. However, straggler effect, and communication delay are the two major issues that should be properly taken care during model preparation of any FL process. In this study, we propose a novel and efficient scheme, called Fog Cloud Assisted Federated Learning (FCAFL) in IoT platform that address these issues. Specifically, the proposed scheme is shown to reduce the overall communication delay of the global model preparation in the FL process. It is also able to resolve straggler effect by employing clustering of the IoT devices with an efficient scheme of cluster head (CH) selection based on minimum intra-cluster distance and maximum residual energy. In order to reduce communication delay further, we also propose an efficient scheme of fog node selection using Genetic Algorithm (GA) by formulating the data offloading as a single objective problem with latency as an offloading parameter. There are some existing schemes which address straggler effect and communication delay. However, none of their approaches incorporate explicit clustering technique utilizing residual energy and minimum intra-cluster distance of the CHs to select clients, aiming to address the straggler effect. Additionally, their works do not involve any data offloading as a means to reduce communication delay in the FL process. The simulation results demonstrate better performance of the proposed FCAFL as compared to the traditional FL and existing approaches, namely, Hierarchical Federated Edge Learning (HFEL) and FedFog with respect to communication cost. The FCAFL also outperform traditional FL and HFEL with respect to training and testing accuracy of the produced FL model. The validity of the result is additionally proved through a widely recognized statistical technique, the analysis of variance (ANOVA), followed by a least significant difference (LSD) post-hoc analysis.