Multi-objective Simulated Annealing Research Articles

Multi-Objective Optimization in 3D Floorplanning

Three-dimensional integrated circuits can significantly mitigate the challenges posed by shrinking feature sizes and enable heterogeneous integration. This paper focuses on the 3D floorplanning problem. We formulate it as a multi-objective optimization issue and employ multi-objective simulated annealing to simultaneously optimize area, wirelength and number of vias. During the optimization process, neighboring solutions are explored in the design space through inter-layer or intra-layer perturbations, and decision criteria for the exploration process are formulated based on the dominance relationship of solutions. Test results on the GSRC benchmark demonstrate that our approach delivers superior performance in optimizing area and wirelength. Compared to 2D floorplanning, our method reduces the area by approximately 49% and the wirelength by 21%. Compared to other similar 3D floorplanning methods, we raise the success rate in satisfying the fixed-outline constraint to 100% and improve the wirelength by 3%. The multi-objective simulated annealing method proposed in this paper can effectively address the 3D floorplanning problem.

A multi-objective optimized OLSR routing protocol.

The rapid development of mobile communication devices has brought challenges to wireless networks, where data packets are able to organize and maintain local area networks more freely without the constraints of wired devices. Scholars have developed diverse network protocols on how to ensure data transmission while maintaining its self-organizational nature. However, it is difficult for traditional network protocols to meet the needs of increasingly complex networks. In order to solve the problem that the better node set may not be selected when selecting the node set responsible for forwarding in the traditional OLSR protocol, a multi-objective optimized OLSR algorithm is proposed in this paper, which incorporating a new MPR mechanism and an improved NSGA-II algorithm. In the process of route discovery, the intermediate nodes responsible for forwarding packets are determined by the new MPR mechanism, and then the main parameters in the OLSR protocol are provided by the multi-objective optimization algorithm. Matlab was used to build a self-organizing network in this study. In addition, the conventional OLSR protocol, NSGA-II algorithm and multi-objective simulated annealing algorithm are selected to compare with the proposed algorithm. Simulation results show that the proposed algorithm can effectively reduce packet loss and end-to-end delay while obtaining better results in HV and Spacing, two multi-objective optimization result evaluation metrics.

MOLM: Alleviating Congestion through Multi-Objective Simulated Annealing-Based Load Balancing Routing in LEO Satellite Networks

In satellite networks, existing congestion resolution methods do not consider the predictability and stability of paths, leading to frequent path switches and high maintenance costs. In this regard, we propose a novel congestion resolution approach, named MOLM, which introduces a continuous neighbor set during path updates. This set includes nodes capable of establishing sustainable connections with the predecessors and successors of congested nodes. Combined with a multi-objective simulated annealing framework, MOLM iteratively derives an optimal selection from this set to replace congested nodes. Additionally, we employ a Fast Reroute mechanism based on backup paths (FRR-BP) to address node failures. The simulation results indicate that the optimal node endows the new path with optimal path stability and path latency.

Multi-objective simulated annealing algorithm for robotic mixed-model two-sided assembly line balancing with setup times and multiple constraints

Robotic mixed-model two-sided assembly lines (RMTALs) have become increasingly prevalent in manufacturing industries for productivity enhancement. However, only limited attention has been paid to the RMTAL balancing problems that contain both setup times and multiple constraints such as positional constraints, zoning constraints, and synchronism constraints. Given the coexistence of these aspects in real-world scenarios, this study aims to address the RMTAL balancing problem with setup times and the mentioned constraints. To formulate the problem, a mixed integer programming model is proposed to optimize cycle time and total energy consumption. To handle multiple constraints and setup times, a new method based on four-vector encoding is introduced. This method addresses the three constraints during the encoding phase using four intervals and five rules, while setup times are processed during the decoding phase. To solve the problem, a Pareto entropy-based two-mode multi-objective simulated annealing algorithm is developed. The algorithm employs variable neighborhood descent algorithm with switchable objectives to generate the initial Pareto archive. Subsequently, it selects the initial solution with minimal potential in the Pareto archive, alternating between two search modes of exploration and exploitation based on the entropy difference of Pareto solutions. Comparative experiments with four state-of-the-art algorithms on benchmark instances of varying scales demonstrate that the proposed algorithm outperforms the others in over 93% of instances for the hypervolume ratio and inverted generational distance metrics.

Multi-objective SHM sensor path optimisation for damage detection in large composite stiffened panels

This work proposes a novel methodology for the automatic multi-objective optimisation of sensor paths in structural health monitoring (SHM) sensor networks using archived multi-objective simulated annealing. Using all of the sensor paths within a sensor network may not always be beneficial during damage detection. Many sensor paths may experience significant signal noise, attenuation, and wave mode conversion due to the presence of features, such as stiffeners, and hence impair the detection accuracy of the overall system. Many paths will also contribute little to the overall coverage level or damage detection accuracy of the network and can be ignored, reducing complexity. Knowing which paths to include, and which to exclude, can require significant prior expert knowledge, which may not always be available. Furthermore, even when expert knowledge is considered, the optimum path selection might not be achieved. Therefore, this work proposes a novel automatic procedure for optimising the sensor paths of an SHM sensor network to maximise coverage level, maximise damage detection accuracy and minimise the overall signal noise in the network due to geometric features. This procedure was tested on a real-world large composite stiffened panel with many geometric features in the form of frames and stiffeners. Compared to using all of the available sensor pairs, the optimised network exhibits superior performance in terms of detection accuracy and overall noise. It was also found to provide very similar performance, in terms of coverage level and overall signal noise, to a sensor path network designed based on prior expert knowledge but provided up to 35% higher damage detection accuracy. As a result, the novel procedure proposed in this work has the capability to design high-performing SHM sensor path networks for structures with complex geometries but without the need for prior expert knowledge, making SHM more accessible to the engineering community.

Tri-Objective Vehicle Routing Problem to Optimize the Distribution Process of Sustainable Local E-Commerce Platforms

The dramatic growth of online shopping worldwide in the last few years generated negative consequences for local small retailers who do not adopt information technologies. Furthermore, the e-commerce sector is considered a good opportunity to develop sustainable logistic processes. To reach this goal, the proposed paper presents a mathematical model and a metaheuristic algorithm to solve a multi-objective capacitated vehicle routing problem (CVRP) distinguished by economic, green, and ethical objective functions. The proposed algorithm is a multi-objective simulated annealing (MOSA) that is implemented in a software architecture and validated with real-world instances that differ for the product type delivered and the geographic distribution of customers. The main result of each test is a tri-dimensional Pareto front, i.e., a decision-support system for practitioners in selecting the best solution according to their needs. From these fronts, it can be observed that if the economic and environmental performances slightly deteriorate by 1.6% and 4.5%, respectively, the social one improves by 19.4%. Furthermore, the developed MOSA shows that the environmental and social objective functions depend on the product dimensions and the geographic distribution of customers. Regarding the former aspect, this paper reports that, counter-intuitively, the metabolic energy consumption per driver decreases with bigger products because the number of necessary vehicles (and drivers) increases, and, thus, the workload is divided among more employees. Regarding the geographic distribution, this manuscript illustrates that, despite similar traveled distances, highly variable altitudes cause more carbon emissions compared to flat distributions. Finally, this contribution shows that delivering small goods decreases the distance that vehicles travel empty by 59%, with a consequent cost reduction of 16%.

A bi-objective approach for the multi-skilled worker assignment of a hybrid assembly line-seru production system

The flexibility and responsiveness of seru production have caught the attention of manufacturing and electronics industries. However, multi-skilled worker assignment poses a crucial and challenging decision-making problem for seru production systems. The existing literature on this problem for pure seru production systems primarily focuses on improving efficiency indexes, which often leads to an unbalanced workload among workers. To address this issue, this article investigates multi-skilled worker assignment for a hybrid assembly line-seru production system that comprises divisional serus and a short assembly line. To balance workload and optimize production efficiency, a bi-objective integer nonlinear programming model is developed. This model jointly optimizes worker-to-seru, worker-to-line, batch-to-seru, task-to-worker, and the processing sequence of each batch. A meta-heuristic method, combining Non-Dominated Sorting Genetic Algorithm II (NSGA-II) with Multi-Objective Simulated Annealing (MOSA), NSGA-II-MOSA, is designed to solve the model. The results of numerical experiments demonstrate that the proposed model and solving method can greatly reduce workload imbalance while maintaining production efficiency. Moreover, NSGA-II-MOSA provides better Pareto solutions than three well-known multi-objective optimization approaches.

Using common redundancy components for suppliers in a supply chain network design problem considering energy costs and environmental effects

Improving the reliability of factories and suppliers through appropriate allocation of redundancy components is crucial in responding to customer demand. However, if individual factories independently buy and allocate redundancy components, huge investments will be required. To optimize the reliability level and costs of the supply chain network, the present study allocates these components to suppliers based on customer demand. While allocating redundancy components to factories improves the chain's reliability, it increases energy consumption and greenhouse gas emissions. Therefore, a balance between cost, reliability, and pollution needs to be established. The study considers a three-level supply chain, including the supplier (factories), distributor, and retailer, with stochastic and normally distributed demand assumed for each retailer. To address demand fluctuations, the risk pooling effect is implemented. As the problem belongs to the class of NP-hard problems, the study develops three multi-objective meta-heuristic algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGAII), Archived Multi-Objective Simulated Annealing (AMOSA), and Multi-Objective Artificial Bee Colony (MOABC) to solve it. The performance of these algorithms is evaluated using the results of the complete enumeration method. The comparison results based on six multi-objective performance metrics show that the MOABC algorithm has better performance in finding high-quality solutions in less time, while the NSGAII algorithm provides more diverse Pareto optimal solutions.

An improved solution methodology for the urban transit routing problem

An improved solution methodology is proposed in this paper for the urban transit routing problem (UTRP). This methodology includes a procedure for the generation of improved initial solutions as well as improved metaheuristic search approaches, involving the use of hyperheuristics to manage search operators in both trajectory-based and population-based metaheuristics. The UTRP variant considered in this paper is that of deciding upon efficient bus transit routes. The design criteria embedded in our UTRP model are the simultaneous minimisation of the expected average passenger travel time and minimisation of the system operator’s cost (measuring the latter as the sum total of all route lengths in the system). The model takes as input an origin–destination demand matrix for a pre-specified set of bus stops, along with an underlying road network structure, and returns as output a set of bus route trade-off solutions. The decision maker can then select one of these route sets subjectively, based on the desired degree of trade-off between the aforementioned transit system design criteria. This bi-objective minimisation problem is solved approximately in three distinct stages — a solution initialisation stage, an intermediate analysis stage, and an iterative metaheuristic search stage during which high-quality trade-off solutions are sought. A novel procedure is introduced for the solution initialisation stage, aimed at effectively generating high-quality initial feasible solutions. Two metaheuristics are implemented to solve instances of the problem, namely a dominance-based multi-objective simulated annealing algorithm and an improved non-dominated sorting genetic algorithm, each equipped with a hyperheuristic capable of managing the perturbation operators employed. Various novel operators are proposed for these metaheuristics, of which the most noteworthy take into account the demand of passengers.

Two-stage multi-objective optimization for ICU bed allocation under multiple sources of uncertainty

Due to the impact of COVID-19, a significant influx of emergency patients inundated the intensive care unit (ICU), and as a result, the treatment of elective patients was postponed or even cancelled. This paper studies ICU bed allocation for three categories of patients (emergency, elective, and current ICU patients). A two-stage model and an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to obtain ICU bed allocation. In the first stage, bed allocation is examined under uncertainties regarding the number of emergency patients and their length of stay (LOS). In the second stage, in addition to including the emergency patients with uncertainties in the first stage, it also considers uncertainty in the LOS of elective and current ICU patients. The two-stage model aims to minimize the number of required ICU beds and maximize resource utilization while ensuring the admission of the maximum number of patients. To evaluate the effectiveness of the model and algorithm, the improved NSGA-II was compared with two other methods: multi-objective simulated annealing (MOSA) and multi-objective Tabu search (MOTS). Drawing on data from real cases at a hospital in Lyon, France, the NSGA-II, while catering to patient requirements, saves 9.8% and 5.1% of ICU beds compared to MOSA and MOTS. In five different scenarios, comparing these two algorithms, NSGA-II achieved average improvements of 0%, 49%, 11.4%, 9.5%, and 17.1% across the five objectives.

A Multi-Objective Simulated Annealing Local Search Algorithm in Memetic CENSGA: Application to Vaccination Allocation for Influenza

Flu vaccine allocation is of great importance for safeguarding public health and mitigating the impact of influenza outbreaks. In this regard, decision-makers face multifaceted challenges, including limited vaccine supply, targeting vulnerable people, adapting to regional variations, ensuring fairness in distribution, and promoting public trust. The objective of this work is to address the vaccination allocation problem by introducing a novel optimization scheme with the simulated annealing (SA) algorithm. A dual-objective model is developed to both manage infection rates and minimize the unit cost of the vaccination campaign. The proposed approach is designed to promote convergence toward the best Pareto front in multi-objective optimization, wherein SA attempts to embed diversity and uniformity within a memetic version of the controlled elitism nondominated sorting genetic algorithm (CENSGA). To model the underlying vaccination allocation problem, the dynamics of the disease are described using the susceptible–exposed–infectious–recovered (SEIR) epidemiological model to better express hidden flu characteristics. This model specifically analyzes the effects of pulsive vaccination allocation in two phases aiming to minimize the number of infected individuals to an acceptable level in a finite amount of time, which can help in stabilizing the model against sudden flu endemics over the long run. The computational experiments show that the proposed algorithm effectively explores the extensive search space of the vaccination allocation problem. The results of the suggested framework indicate that the obtained Pareto front best represents complete vaccination campaigns. The findings of this research can help in evidence-based decision making that can optimize flu vaccine distribution, contribute to the prevention of illness and reduction in hospitalizations, and potentially save countless lives.

The Optimization of Multi-objective FJSP Based on the Hybrid Algorithm

The flexible job-shop scheduling problem (FJSP) is a critical model in manufacturing systems that assigns operations from different jobs to various machines. However, optimizing multiple targets during the production scheduling process is always necessary. While the non-dominated sorting genetic algorithm (NSGA-II) is an effective method to solve the multi-objective FJSP, it can have the main drawbacks of converging too early and falling into local optimization. To address these issues, this research proposes a hybrid algorithm that combines NSGA-II and multi-objective simulated annealing using a pareto-domination based acceptance criterion (PDMOSA). The PDMOSA has a powerful search performance that can overcome the limitations of NSGA-II. The hybrid algorithm also includes original modification methods such as a deletion criterion, duplicated solution deletion, and new individual adding. Additionally, a plug-in decoding method is introduced. The proposed hybrid algorithm is compared with several improved ways based on NSGA-II in various experiments. The results demonstrate that the performance of the hybrid algorithm is better than the others in multi-objective FJSP.

Metaheuristic algorithms for a sustainable saffron supply chain network considering government policies and product quality under uncertainty

Abstract Iranian saffron products hold a unique place in the global market as the most highly valued agricultural and medicinal commodities. The various uses of saffron make it clear that there is a need for special attention to the supply chain network. Unfortunately, the absence of an integrated supply chain network within the saffron industry has resulted in significant challenges related to supply management and demand fulfillment. Addressing real-world uncertainties is paramount when developing models for optimization problems. Therefore, this research proposes a multi-objective optimization model for designing a saffron supply chain network under uncertainty. The model objectives are to decrease the total cost of the supply chain, increase job opportunities and economic development in regions, and improve the quality of products. The proposed mathematical model is solved using the interactive fuzzy method to deal with multiple functions. Furthermore, possibilistic chance constrained programming is employed to effectively manage uncertain variables such as demand, cost, and social parameters within the model. To demonstrate the applicability and validity of the proposed model and solution method, a real case study was conducted in Khorasan Razavi province, Iran. Additionally, because of the complexity of the proposed model in large-scale networks, non-dominated sorting genetic algorithm-II and multi-objective simulated annealing algorithms are proposed. Different parameters are analyzed to determine their impact on the results so that decision-makers can choose values more accurately. The sensitivity analysis and statistical tests performed on the results support the performance of the proposed model. Overall, the results demonstrate that the exact method and metaheuristic algorithms are capable of solving the problem in different dimensions. The computational results derived from this model offer invaluable managerial insights, empowering decision-makers to align their strategies and preferences more effectively.

A multi-objective optimization algorithm for flow shop group scheduling problem with sequence dependent setup time and worker learning

The optimization of production systems has become increasingly important in manufacturing industries due to the growing competition and market demands. One of the overriding concerns of managers is the efficient exploitation of workers' learning to increase output and decrease downtime. The learning effect symbolizes the improvement of workers' ability and performance through the repetition of similar jobs. On the other hand, it is a critical requirement for decision-makers to have effective management of the transportation phase to achieve an optimal production plan. This paper considers a flow shop sequence-dependent group scheduling problem (FSDGS) with a learning effectto minimize two contradictory objective functions, namely makespan and energy consumption.A mixed-integer linear programming model is proposed to find optimal jobs, group schedules, and appropriate production and transportation speeds to enhance the overall performance of the system. Due to the complexity of the planning process, we propose lower bounds and an efficient resolution method based on multi-objective simulated annealing metaheuristic (MOSA), enhanced by a local search procedure to tackle this problem. The proposed method is evaluated through several experiments based on a real case study, using different learning rates and setup time ratio levels. The obtained results demonstrate the effectiveness of the algorithm in improving the performance of production systems by reducing processing time and energy consumption. These findings have significant implications for the design and optimization of production systems in manufacturing industries.

A Facility Layout Algorithm for Logistics Scenarios Driven by Transport Lines

The layout of facilities in a logistics scenario involves not only the working facilities responsible for processing materials but also the transport lines responsible for transporting materials. The traditional facility layout methods do not take into account the transportation facilities nor calculate the material handling cost by Manhattan distance, thus failing to fulfill the actual requirements of industrial logistics scenarios. In this paper, a facility layout algorithm framework MOSA-FD driven by transport lines is proposed. A multi-objective simulated annealing (MOSA) algorithm is designed for both material handling cost (MHC) and transport facility cost (TFC) objectives. Then, a force-directed (FD) algorithm is applied to correct the unreasonable solutions according to the material transport lines in the logistics workshop, and a better solution is quickly obtained. Finally, by comparing the results with those of other metaheuristic multi-objective algorithms, the acceleration of the force-directed algorithm in this layout problem is demonstrated in experimental instances of different scales, and our method, compared to the MOSA algorithm, can reach optimal ratios of 36% and 80%, respectively, on the multi-objective.

Multi-objective optimisation for sustainable few-to-many pickup and delivery vehicle routing problem

ABSTRACT E-commerce is a continuously growing sector significantly affected by sustainability issues during the last few years. To deal with economic, environmental and social sustainability aspects, e-commerce platforms consolidate orders to pick-up several requests from the same location, defining the so-called Few-to-Many Pick-up and Delivery Vehicle Routing Problem (F-M VRPPD). The proposed contribution addresses the optimisation of this problem by developing a multi-objective simulated annealing algorithm distinguished by four tailored Local Search (LS) operators specifically developed to increase the probability to identify feasible solutions and decrease the computational time. This algorithm is validated with several instances of a case study e-commerce platform based in an European mountain region. Firstly, the original LS operators are compared to benchmark literature ones to solve identical problems, reporting better performance in 84% of these instances. Furthermore, for the most relevant scenarios significant results are presented and discussed concerning the economic, environmental and social performance of the defined solutions according to the characteristics of the instances, as the routes height profile and the drivers’ metabolic energy consumption. The tri-dimensional Pareto frontiers suggest how through a slight worsening in the economic objective function it is possible to improve the social one by up to 18.3% on average.

Multi-objective based demand response strategy optimization considering differential demand on reliability of power system

The reliability of power system will vary with different demand response strategies, and it is significant to make a decision on demand response for satisfying differential reliability demand of power system. First, a peak-valley period partition model with an objective of maximizing silhouette coefficient was established based on the fuzzy clustering and step-wise iteration technology. Second, this paper proposed a multi-objective time of use electricity price optimization model considering the interests of both supply and demand sides, as well as reliability demand, and a multi-objective simulated annealing particle swarm optimization algorithm was developed to obtain solution. Third, the Pareto front curve of the dual-objective function was fitted by using a third-order Hermite interpolation algorithm, and the time of use prices corresponding to the reliability demand was obtained by using the back propagation neural network algorithm. Finally, the proposed model and algorithm were verified by the RBTS system, and the results indicate good rationality and effectiveness of the proposed method.

A hybrid metaheuristic approach for solving a bi-objective capacitated electric vehicle routing problem with time windows and partial recharging

PurposeThe vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.Design/methodology/approachIn this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).FindingsThe results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.Originality/valueIn this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

Scenario-Based Multi-Objective Location-Routing Model for Pre-Disaster Planning: A Philippine Case Study

The demand for humanitarian supply chains grows daily as the incidence of calamities rises. Typhoons cause thousands of casualties each year. As a result, policymakers and governmental authorities must develop effective readiness and response measures as part of pre-disaster plans. This paper proposed a stochastic model for multi-objective location-routing for creating a humanitarian network for pre-disaster response. The model aims to minimize the overall costs of the network’s setup, the time required to travel through it, and the number of vehicles necessary for transferring affected individuals to evacuation centers. The model concentrates on pre-disaster scenarios in uncertainty. The provided model was implemented in an actual scenario in one of the Philippines’ provinces and solved using Multi-Objective Particle Swarm Optimization (MOPSO), which is also contrasted with Multi-Objective Simulated Annealing (MOSA) and the ε-constraint approach. According to empirical findings, the model can be used to identify distribution hubs and evacuation centers and choose the best routes in unexpected and actual disaster scenarios. Given that the ideal number, location, and capacity of DCs and ECs are known in advance, government decision-makers can solve any potential shortages and problems during the disaster.

Performance Analysis of Multi-Objective Simulated Annealing Based on Decomposition

Simulated annealing is a metaheuristic that balances exploration and exploitation to solve global optimization problems. However, to deal with multi- and many-objective optimization problems, this balance needs to be improved due to diverse factors such as the number of objectives. To deal with this issue, this work proposes MOSA/D, a hybrid framework for multi-objective simulated annealing based on decomposition and evolutionary perturbation functions. According to the literature, the decomposition strategy allows diversity in a population while evolutionary perturbations add convergence toward the Pareto front; however, a question should be asked: What is the effect of such components when included as part of a multi-objective simulated annealing design? Hence, this work studies the performance of the MOSA/D framework considering in its implementation two widely used perturbation operators: classical genetic operators and differential evolution. The proposed algorithms are MOSA/D-CGO, based on classical genetic operators, and MOSA/D-DE, based on differential evolution operators. The main contribution of this work is the performance analysis of MOSA/D using both perturbation operators and identifying the one most suitable for the framework. The approaches were tested using DTLZ on two and three objectives and CEC2009 benchmarks on two, three, five, and ten objectives; the performance analysis considered diversity and convergence measured through the hypervolume (HV) and inverted generational distance (IGD) indicators. The results pointed out that there is a promising improvement in performance in favor of MOSA/D-DE.