Simulated Annealing Framework Research Articles

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.

Threshold-Based Responsive Simulated Annealing for Directed Feedback Vertex Set Problem

As a classical NP-hard problem and the topic of the PACE 2022 competition, the directed feedback vertex set problem (DFVSP) aims to find a minimum subset of vertices such that, when vertices in the subset and all their adjacent edges are removed from the directed graph, the remainder graph is acyclic. In this paper, we propose a threshold-based responsive simulated annealing algorithm called TRSA for solving DFVSP. First, we simplify the problem instances with two new reduction rules proposed in this paper and eight reduction rules from the literature. Then, based on a new solution representation, TRSA solves DFVSP with a fast local search procedure featured by a swap-based neighborhood structure and three neighborhood acceleration strategies. Finally, all these strategies are incorporated into a threshold-based responsive simulated annealing framework. Computational experiments on 140 benchmark instances show that TRSA is highly competitive compared to the state-of-the-art methods. Specifically, TRSA can improve the best known results for 53 instances, while matching the best known results for 79 ones. Furthermore, some important features of TRSA are analyzed to identify its success factors.

Faster determination of an initial velocity model for full-waveform inversion based on simulated annealing

Full-waveform inversion (FWI) is a prominent method commonly used to create detailed velocity models of the subsurface. However, because it relies on gradient methods, it suffers from the limitation of getting trapped in local minima. To avoid this problem, FWI needs to start from an initial velocity model that lies in the same region of convexity as the global minimum. Global optimization methods, such as simulated annealing, can be used to find such an initial velocity model. However, the iterative process of simulated annealing entails high computational cost, first because of the large number of iterations needed to explore the variables space, and second because of the large number of simulations needed to adjust the simulation parameters. Although the first issue is a common concern of previous work, the second issue is usually neglected, relying on trial and error. We introduce an approach to tackle the issues and then apply it within a simulated annealing framework we create. Our experiments using the Marmousi data yielded promising results when compared with previous work. We find that our approach almost eliminated the computational effort to fine-tune several simulation parameters. In addition, the number of iterations needed to explore the variables space is reduced by two orders of magnitude. FWI is able to find a detailed velocity model with high quality when using the initial velocity model generated by the method.

A simulated annealing with variable neighborhood descent approach for the heterogeneous fleet vehicle routing problem with multiple forward/reverse cross-docks

With a greater awareness of the challenges regarding environmental, societal, political, and economic factors, where reverse logistics has become a significant part of supply chain networks, this paper presents an integrated forward and reverse logistics network, named the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks (HF-VRPMFRCD). We consider a heterogeneous fleet of vehicles with different loading capacities and transportation costs. We also consider multiple cross-docks with two different operations: forward and reverse processes. The former focuses on delivering the demand from suppliers to customers, while the latter aims at returning unsold products from customers to suppliers. We propose a Simulated Annealing with Variable Neighborhood Descent (SAVND) algorithm for solving HF-VRPMFRCD, where Variable Neighborhood Descent (VND) is a local search heuristic embedded in the framework of Simulated Annealing (SA). SAVND outperforms the state-of-the-art algorithm in solving the Heterogeneous Fleet Vehicle Routing Problem with Multiple Cross-Docks (HF-VRPMCD), where the VND heuristic significantly improves the quality of solutions. For HF-VRPMFRCD benchmark instances, SAVND provides optimal solutions for small-scale instances and better solutions than those of the GUROBI solver for remaining larger instances. Lastly, we present and discuss the benefits of integrating the forward and reverse processes.

A fast and flexible algorithm for microstructure reconstruction combining simulated annealing and deep learning

Microstructural analyses of porous media have considerable research value when studying of macroscopic properties,and the accurate reconstruction of a digital microstructure model is an important component of this research. Computational reconstruction algorithms for microstructures have attracted much attention due to their low cost and excellent performance. However, achieving faster and more efficient reconstruction remains a challenge for computational reconstruction algorithms. The bottleneck lies in the computational reconstruction algorithms themselves, which are either too slow (traditional reconstruction algorithms) or not flexible to the training process (deep learning reconstruction algorithms). To address these limitations, we propose a fast and flexible deep learning algorithm using a neural network based on an improved simulated annealing framework (ISAF-NN). The proposed algorithm adopts structural information of the reference image to guide the network design, and uses the description function to extract feature distribution of the reference image as the objective function to complete the network optimization. Benefit from the network structure is simple and flexible, the proposed algorithm can complete training and reconstruction in a short time. By adjusting the input size, the algorithm can also achieve arbitrary sized reconstruction. The proposed algorithm is experimentally applied to several materials to verify its effectiveness and generalizability.

Simulated annealing framework for generating representative volume elements of materials with complex ligamentous microstructures

At the microscale, various materials from biological tissues to nanoporous metals are formed by networks of ligaments. Here we propose a highly efficient simulated annealing (SA) framework for generating synthetic representative volume elements (RVE) of such materials. It can produce RVE where the microstructural characteristics both on the network level (e.g., node valency and ligament length) and on the level of individual ligaments (e.g., curvature) can be predefined by the user via probability distributions. As an application example of our framework, we generate a large variety of RVEs, analyze their mechanical properties by the finite element method, and establish through this approach links between microstructural descriptors and macromechanical properties of materials with ligamentous microstructures.

Effective metaheuristics for the latency location routing problem

AbstractThe latency location routing problem (LLRP), a combination of the facility location problem and the cumulative capacitated vehicle routing problem, is a recently proposed variant of location routing problems. It corresponds to a customer‐centric problem, in which the aim is to minimize the sum of the arrival times at the customers. This paper proposes three novel metaheuristic algorithms to solve the LLRP. They use a simulated annealing framework, which after each temperature reduction is intensified through a variable neighborhood descent procedure. Each algorithm uses a different search strategy as intensification. Results on 76 benchmark instances indicate that the proposed metaheurstics outperform the state‐of‐the‐art algorithms, finding new best solutions for all the large‐sized instances (over 100 customers), or the currently known optimal ones for most of the small‐ and medium‐sized instances, in comparable computing times. Furthermore, in more than 80% of the instances the average value of the solutions found by the proposed algorithms is better than or equal to that of the current best known solution.

Joint Optimization of Time-Dependent Line Planning and Differential Pricing with Passenger Train Choice in High-Speed Railway Networks

Line planning problems and differential pricing problems are complementary processes in the railway system, but these two problems were generally considered separate processes in most of the existing literature. This paper studies a time-dependent line planning problem and differential pricing problem with passenger train choice in high-speed railway networks under elastic origin-destination-period demand. After clearly and flexibly describing the organization cost of operators, the price cost, and the time cost of passengers in a physical infrastructure-based directed graph, a non-linear joint optimization model is designed with a diversity of optimization goals of maximizing the total revenue of railway operators minus the total travel cost of passengers. An algorithm based on a simulated annealing framework is designed to solve the joint optimization model, and six neighborhood search strategies are designed by combining the features of the studied problem and designed model closely to improve the efficiency of the solution search. The results based on both a toy railway network and a real-world railway network show that the optimized time-dependent line plan and differential price plan are beneficial to increasing the total revenue of railway operators and improving the travel service of railway passengers.

A hybrid bacterial foraging – simulated annealing framework for improving road networks

Effective techniques for reducing traffic congestion include adding new edges to the road network or increasing the capacity of existing edges. To determine the optimal set of improvements that can be made to an existing road network, it is standard practise to solve a Discrete Network Design Problem. Due to the bi-level nature of its formulation, it is one of the most difficult problems to solve to optimality. The Bacterial Foraging Optimization technique has been investigated in a previous work to gauge its effectiveness in determining the n-optimal solution to the Discrete Network Design Problem. This concept is further developed in this paper by hybridizing the Bacterial Foraging Optimization algorithm with Simulated Annealing. In the elimination step, the metropolis criterion from Simulated Annealing ensures a more diverse search of the solution space. We also employ a modified candidate set of improvements that incorporates both edge and capacity additions. The effectiveness of the hybrid bacterial foraging optimization algorithm in determining n-optimal solutions to the Discrete Network Design Problem has been demonstrated by testing it on the 24-node, 76-arc Sioux Falls network.

A Large Neighborhood Search Algorithm with Simulated Annealing and Time Decomposition Strategy for the Aircraft Runway Scheduling Problem

The runway system is more likely to be a bottleneck area for airport operations because it serves as a link between the air routes and airport ground traffic. As a key problem of air traffic flow management, the aircraft runway scheduling problem (ARSP) is of great significance to improve the utilization of runways and reduce aircraft delays. This paper proposes a large neighborhood search algorithm combined with simulated annealing and the receding horizon control strategy (RHC-SALNS) which is used to solve the ARSP. In the framework of simulated annealing, the large neighborhood search process is embedded, including the breaking, reorganization and local search processes. The large neighborhood search process could expand the range of the neighborhood building in the solution space. A receding horizon control strategy is used to divide the original problem into several subproblems to further improve the solving efficiency. The proposed RHC-SALNS algorithm solves the ARSP instances taken from the actual operation data of Wuhan Tianhe Airport. The key parameters of the algorithm were determined by parametric sensitivity analysis. Moreover, the proposed RHC-SALNS is compared with existing algorithms with excellent performance in solving large-scale ARSP, showing that the proposed model and algorithm are correct and efficient. The algorithm achieves better optimization results in solving large-scale problems.

A pivot-based simulated annealing algorithm to determine oblique splits for decision tree induction

We describe a new simulated annealing algorithm to compute near-optimal oblique splits in the context of decision tree induction. The algorithm can be interpreted as a walk on the cells of a hyperplane arrangement defined by the observations in the training set. The cells of this hyperplane arrangement correspond to subsets of oblique splits that divide the feature space in the same manner and the vertices of this arrangement reveal multiple neighboring solutions. We use a pivoting strategy to iterate over the vertices and to explore this neighborhood. Embedding this neighborhood search in a simulated annealing framework allows to escape local minima and increases the probability of finding global optimal solutions. To overcome the problems related to degeneracy, we rely on a lexicographic pivoting scheme. Our experimental results indicate that our approach is well-suited for inducing small and accurate decision trees and capable of outperforming existing univariate and oblique decision tree induction algorithms. Furthermore, oblique decision trees obtained with this method are competitive with other popular prediction models.

Modeling and solving a real world machine scheduling problem with due windows and processing set restrictions

Motivated by a real-world problem situation faced by a large manufacturing company in the last step of their production process, we model and solve an offline, deterministic, non-preemptive, identical, parallel machine scheduling problem with processing set restrictions, availability constraints, release dates, bounded tardiness, blocking constraints and due windows. The objective is to minimize the total tardiness while penalizing the assignment of jobs to larger than necessary machines. We develop a mixed integer linear program and we propose a heuristic solution approach relying on the well known large neighborhood search paradigm which relies on tailored destroy and repair operators, embedded into a simulated annealing framework. The proposed algorithm is tested on artificial instances as well as on real-world data provided by the company and compared to optimal solutions obtained by means of CPLEX. The developed tool is now used for decision support by the company partner.

Simulated annealing for optimization of graphs and sequences

Optimization of discrete structures aims at generating a new structure with the better property given an existing one, which is a fundamental problem in machine learning. Different from the continuous optimization, the realistic applications of discrete optimization (e.g., text generation) are very challenging due to the complex and long-range constraints, including both syntax and semantics, in discrete structures. In this work, we present SAGS, a novel Simulated Annealing framework for Graph and Sequence optimization. The key idea is to integrate powerful neural networks into metaheuristics (e.g., simulated annealing, SA) to restrict the search space in discrete optimization. We start by defining a sophisticated objective function, involving the property of interest and pre-defined constraints (e.g., grammar validity). SAGS searches from the discrete space towards this objective by performing a sequence of local edits, where deep generative neural networks propose the editing content and thus can control the quality of editing. We evaluate SAGS on paraphrase generation and molecule generation for sequence optimization and graph optimization, respectively. Extensive results show that our approach achieves state-of-the-art performance compared with existing paraphrase generation methods in terms of both automatic and human evaluations. Further, SAGS also significantly outperforms all the previous methods in molecule generation.

Conflict resolving – A local search algorithm for solving large scale conflict graphs in freight railway timetabling

We consider the problem of planning the annual timetable for all freight trains in Germany simultaneously. That is, for each train, construct a slot through the network such that no two slots of different trains have a conflict. We denote this task by the Train Path Assignment Problem (TPAP) and present a column generation approach where iteratively, the set of possible slots grows. In each iteration, we look for a maximum subset without any conflicts. Modelling the slots as vertices joint by an edge if they have a conflict, this problem is the Maximum Independent Set problem (MIS). Due to the many slots that are constructed, hence variables that are generated, we deal with large scale MIS instances. Therefore, the MIS is solved heuristically with a local search algorithm called Conflict Resolving (CR) that is tailored to the specially structured instances from the application. CR iteratively perturbs the current solution in order to leave local optima and then repeatedly improves the solution by replacing k−1 solution vertices by k non-solution vertices. These steps are embedded in a simulated annealing framework. In this paper, we present the column generation approach and numerically compare three MIS solution methods, CR, a MIP solver and Iterated Local Search (ILS), a state-of-the-art MIS heuristics. It turns out that CR performs best for the instances from real-world timetabling, and is also comparable to the ILS on MIS benchmark instances. With this approach, we can solve the TPAP for more than 5000 freight trains.

Levelling crane workload in multi-yard rail-road container terminals

In modern rail-road container terminals, container transshipment between trains and trucks is carried out by large gantry cranes that span over rail tracks and road lanes. Prior optimization approaches have mainly focused on the short-term scheduling of these crucial transshipment resources. In this work, we focus on a midterm planning level that assigns inbound trains to yard tracks such that trains can be serviced by yard resources on schedule. This planning task is especially crucial in larger terminal settings which comprise more than a single yard, which is increasingly typical in growing intermodal networks. We describe the planning situation we encountered at a large rail-road terminal in Germany and propose a mixed-integer model formulation that captures the core of the decision problem. Further, we carry out a complexity analysis of problem variants and develop a heuristic solution procedure in a simulated annealing framework based on these structural insights. The approach is tested in a comprehensive computational study which demonstrates the viability of the approach to solve instances of real-world size.

Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

When consumers faced with the choice of competitive chain facilities that offer exclusive services, current rules cannot describe these customers’ behaviors very well. So we propose a partially proportional rule to represent this kind of customer behavior. In addition, the exact demands of customers in many real-world environments are often difficult to determine. This is contradicting to the assumption in most studies of the competitive facility location problem. For the competitive facility location problem with the partially proportional rule, we establish a robust optimization model to handle the uncertainty of customers’ demands. We propose two methods to solve the robust model by studying the properties of the counterpart problem. The first method MIP is presented by solving a mixed-integer optimization model of the counterpart problem directly. The second method SAS is given by embedding a sorting subalgorithm into the simulated annealing framework, in which the sorting subalgorithm can easily solve the subproblem. The effects of the budget and the robust control parameter to the location scheme are analyzed in a quasi-real example. The result shows that changes in the robust control parameter can affect the customer demands that were captured by the new entrants, thereby changing the optimal solution for facility location. In addition, there is a threshold of the robust control parameter for any given budget. Only when the robust control parameter is larger than this threshold, the market share captured by the new entering firm increases with the increases of this parameter. Finally, numerical experiments show the superiority of the algorithm SAS in large-scare competitive facility location problems.

A Power-Driven Stochastic-Deterministic Hierarchical High-Level Synthesis Framework for Module Selection, Scheduling and Binding

We present a power-driven hierarchical framework for module/functional-unit selection, scheduling, and binding in high level synthesis. A significant aspect of algorithm design for large and complex problems is arriving at tradeoffs between quality of solution and timing complexity. Towards this end, we integrate an improved version of the very runtime-efficient list scheduling algorithm called modified list scheduling (MLS) with a power-driven simulated annealing (SA) algorithm for module selection. Our hierarchical framework efficiently explores the problem solution space by an extensive exploration of the power-driven module-selection solution space via SA, and for each module selection solution, uses MLS to obtain a scheduling and (integrated) binding (S&B) solution in which the binding is either a regular one (minimizing number of FUs and thus FU leakage power) or power-driven with mux/demux power considerations. This framework avoids the very runtime intensive exploration of both module selection and S&B within a conventional SA algorithm, but retains the basic prowess of SA by exploring only the important aspect of power-driven module-selection in a stochastic manner. The proposed hierarchical framework provides an average of 9.5% FU leakage power improvement over state of the art (approximate) algorithms that optimize only FU leakage power, and has a smaller runtime by factors of 2.5–3x. Further, compared to a sophisticated flat simulated annealing framework and an optimal 0/1-ILP formulation for total (dynamic and leakage) FU and architecture power optimization under latency constraints, PSA-MLS provides an improvement of 5.3–5.8% with a runtime advantage of 2x, and has an average optimality gap of only 4.7–4.8% with a significant runtime advantage of a factor of more than 1900, respectively.

Improved Tabu Search and Simulated Annealing methods for nonlinear data assimilation

Nonlinear data assimilation can be a very challenging task. Four local search methods are proposed for nonlinear data assimilation in this paper. The methods work as follows: At each iteration, the observation operator is linearized around the current solution, and a gradient approximation of the three dimensional variational (3D-Var) cost function is obtained. Then, samples along potential steepest descent directions of the 3D-Var cost function are generated, and the acceptance/rejection criteria for such samples are similar to those proposed by the Tabu Search and the Simulated Annealing framework. In addition, such samples can be drawn within certain sub-spaces so as to reduce the computational effort of computing search directions. Once a posterior mode is estimated, matrix-free ensemble Kalman filter approaches can be implemented to estimate posterior members. Furthermore, the convergence of the proposed methods is theoretically proven based on the necessary assumptions and conditions. Numerical experiments have been performed by using the Lorenz-96 model. The numerical results show that the cost function values on average can be reduced by several orders of magnitudes by using the proposed methods. Even more, the proposed methods can converge faster to posterior modes when sub-space approximations are employed to reduce the computational efforts among iterations.

A Permutation-Based Heuristic Method for the Blocking Job Shop Scheduling Problem

In the manufacturing of highly customized goods and the operation of automatic logistics systems, efficient schedules constitute an everyday challenge. Therefore, the job shop problem is established as a standard model in scheduling research. While classical variants are well studied, the involvement of practically relevant conditions, such as the absence of intermediate buffers and customer-oriented optimization criteria, shows a lack of theoretical understanding. This work provides a study in this research direction by examining the applicability of a scheduling-tailored heuristic search method to the blocking job shop problem with total tardiness minimization. Permutation-based encodings are used to represent a schedule. Appearing redundancy and feasibility issues are discussed. Two well-known neighborhood structures for sequencing problems are applied and an advanced repairing technique to construct feasible blocking job shop schedules is proposed. The computational results obtained by embedding the components in a simulated annealing framework highlight advantages of the heuristic solution approach against existing general-purpose methods.

HotSpot Thermal Floorplan Solver Using Conjugate Gradient to Speed Up

We proposed to use the conjugate gradient method to effectively solve the thermal resistance model in HotSpot thermal floorplan tool. The iterative conjugate gradient solver is suitable for traditional sparse matrix linear systems. We also defined the relative sparse matrix in the iterative thermal floorplan of Simulated Annealing framework algorithm, and the iterative method of relative sparse matrix could be applied to other iterative framework algorithms. The experimental results show that the running time of our incremental iterative conjugate gradient solver is speeded up approximately 11x compared with the LU decomposition method for case ami49, and the experiment ratio curve shows that our iterative conjugate gradient solver accelerated more with increasing number of modules.