Conventional Simulated Annealing Research Articles

Ferroelectric compute-in-memory annealer for combinatorial optimization problems

Computationally hard combinatorial optimization problems (COPs) are ubiquitous in many applications. Various digital annealers, dynamical Ising machines, and quantum/photonic systems have been developed for solving COPs, but they still suffer from the memory access issue, scalability, restricted applicability to certain types of COPs, and VLSI-incompatibility, respectively. Here we report a ferroelectric field effect transistor (FeFET) based compute-in-memory (CiM) annealer for solving larger-scale COPs efficiently. Our CiM annealer converts COPs into quadratic unconstrained binary optimization (QUBO) formulations, and uniquely accelerates in-situ the core vector-matrix-vector (VMV) multiplication operations of QUBO formulations in a single step. Specifically, the three-terminal FeFET structure allows for lossless compression of the stored QUBO matrix, achieving a remarkably 75% chip size saving when solving Max-Cut problems. A multi-epoch simulated annealing (MESA) algorithm is proposed for efficient annealing, achieving up to 27% better solution and ~ 2X speedup than conventional simulated annealing. Experimental validation is performed using the first integrated FeFET chip on 28nm HKMG CMOS technology, indicating great promise of FeFET CiM array in solving general COPs.

Fast-Converging Simulated Annealing for Ising Models Based on Integral Stochastic Computing.

Probabilistic bits (p-bits) have recently been presented as a spin (basic computing element) for the simulated annealing (SA) of Ising models. In this brief, we introduce fast-converging SA based on p-bits designed using integral stochastic computing. The stochastic implementation approximates a p-bit function, which can search for a solution to a combinatorial optimization problem at lower energy than conventional p-bits. Searching around the global minimum energy can increase the probability of finding a solution. The proposed stochastic computing-based SA method is compared with conventional SA and quantum annealing (QA) with a D-Wave Two quantum annealer on the traveling salesman, maximum cut (MAX-CUT), and graph isomorphism (GI) problems. The proposed method achieves a convergence speed a few orders of magnitude faster while dealing with an order of magnitude larger number of spins than the other methods.

A Network-on-Chip-Based Annealing Processing Architecture for Large-Scale Fully Connected Ising Model

Combinatorial optimization problems are prevalent in many different fields. Most of these problems are NP-hard and challenging for computers with conventional Von-Neumann architecture. Ising machines with a number of spins have the potential to solve these problems by emulating the natural annealing process of solid matter. Recent research has explored some hardware implementation methods of Ising machines to accelerate the convergence process of such problems at room temperature. However, most of them are suffering from low scalability and low parallel processing capability due to the huge hardware cost and high complexity. In this paper, a novel network-on-chip-based annealing processing architecture (NoCAPA) for a large-scale Ising processor is described to address these issues with a NoC computing paradigm, a distributed storage scheme, and a fully pipelined structure design. Several techniques are developed to further increase convergence speed and reduce hardware resource consumption, including a dynamic multithread parallel update algorithm, a router with merge and deflection abilities, and a unique multiply-accumulate operation. The prototype is implemented in FPGA with the maximum operation frequency of 200MHz, achieving up to 120.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> faster than conventional simulated annealing method when solving the max-cut problem while supporting high scalability.

3D hybrid stochastic reconstruction of catalyst layers in proton exchange membrane fuel cells from 2D images

Proton exchange membrane fuel cells show promise in a variety of applications, aiding global efforts to achieve net-zero emissions. Its catalyst layer is a source of significant efficiency loss due to resistance to transport and reaction mechanisms in its porous structure. A computational reconstruction model of the porous microstructure is required to study the applicable pore-scale phenomena in the catalyst layer. A hybrid stochastic reconstruction technique is presented which reconstructs a catalyst layer from 2D scanning electron microscope experimental images, combining a sphere-packing approach with sphere-based simulated annealing and simultaneously optimizing the microstructure using the two-point correlation and the lineal path distribution. This technique (Method 2) is compared to a conventional sphere-based simulated annealing method (Method 1) and to a fabrication-based reconstruction (Method 0). Pore size distributions, surface area, porosity, mean pore diameter and mean chord lengths are used to validate the model and evaluate the accuracy of each reconstruction method. Both Method 1 and 2 result in porosity values within approximately 0.0001% of the reference porosity. Method 2 achieves higher accuracy than Methods 1 and 0 in the mean chord lengths and surface area, and both Methods 1 and 2 improve in the mean pore size over Method 0.

Memory-Efficient FPGA Implementation of Stochastic Simulated Annealing

Simulated annealing (SA) is a well-known algorithm for solving combinatorial optimization problems. However, the computation time of SA increases rapidly, as the size of the problem grows. Recently, a stochastic simulated annealing (SSA) algorithm that converges faster than conventional SA has been reported. In this paper, we present a hardware-aware SSA (HA-SSA) algorithm for memory-efficient FPGA implementations. HA-SSA can reduce the memory usage of storing intermediate results while maintaining the computing speed of SSA. For evaluation purposes, the proposed algorithm is compared with the conventional SSA and SA approaches on maximum cut combinatorial optimization problems. HA-SSA achieves a convergence speed that is up to 114-times faster than that of the conventional SA algorithm depending on the maximum cut problem selected from the G-set which is a dataset of the maximum cut problems. HA-SSA is implemented on a field-programmable gate array (FPGA) (Xilinx Kintex-7), and it achieves up to 6-times the memory efficiency of conventional SSA while maintaining high solution quality for optimization problems.

Multi-spin-flip engineering in an Ising machine

A merge process is proposed to engineer a multi-spin flip in an Ising machine. The merge process deforms the Hamiltonian (energy function) of the Ising model. We prove a theorem for the merge process and show that a single-spin flip in the deformed Hamiltonian is equivalent to a multi-spin flip in the original Hamiltonian. A merge process induces a transition within the subspace of feasible solutions. We propose a hybrid simulated annealing (SA) algorithm with the merge process. The hybrid algorithm outperforms the conventional SA algorithm, genetic algorithm, and tabu search in the binary quadratic knapsack problems (QKP) and the quadratic assignment problems (QAP). Finally, the hybrid merge process is used in a real Ising machine. The performance is improved in QKP and QAP instances. The merge process is generally applicable to existing Ising machine hardware because the deformed Hamiltonian keeps the format of the Ising model.

Near-surface velocity inversion from Rayleigh wave dispersion curves based on a differential evolution simulated annealing algorithm

The utilization of urban underground space in a smart city requires an accurate understanding of the underground structure. As an effective technique, Rayleigh wave exploration can accurately obtain information on the subsurface. In particular, Rayleigh wave dispersion curves can be used to determine the near-surface shear-wave velocity structure. This is a typical multiparameter, high-dimensional nonlinear inverse problem because the velocities and thickness of each layer must be inverted simultaneously. Nonlinear methods such as simulated annealing (SA) are commonly used to solve this inverse problem. However, SA controls the iterative process though temperature rather than the error, and the search direction is random; hence, SA always falls into a local optimum when the temperature setting is inaccurate. Specifically, for the inversion of Rayleigh wave dispersion curves, the inversion accuracy will decrease with an increasing number of layers due to the greater number of inversion parameters and large dimension. To solve the above problems, we convert the multiparameter, high-dimensional inverse problem into multiple low-dimensional optimizations to improve the algorithm accuracy by incorporating the principle of block coordinate descent (BCD) into SA. Then, we convert the temperature control conditions in the original SA method into error control conditions. At the same time, we introduce the differential evolution (DE) method to ensure that the iterative error steadily decreases by correcting the iterative error direction in each iteration. Finally, the inversion stability is improved, and the proposed inversion method, the block coordinate descent differential evolution simulated annealing (BCDESA) algorithm, is implemented. The performance of BCDESA is validated by using both synthetic data and field data from western China. The results show that the BCDESA algorithm has stronger global optimization capabilities than SA, and the inversion results have higher stability and accuracy. In addition, synthetic data analysis also shows that BCDESA can avoid the problems of the conventional SA method, which assumes the S-wave velocity structure in advance. The robustness and adaptability of the algorithm are improved, and more accurate shear-wave velocity and thickness information can be extracted from Rayleigh wave dispersion curves. • We convert the high-dimensional inverse problem into multiple low-dimensional optimizations to improve accuracy by using BCD. • We ​use the error as control conditions different from that in SA to avoid the inversion falling into local optima. • We introduce DE to ensure that the iterative error steadily decreases by correcting the iterative error direction.

A systematic approach in remanufacturing for high efficiency and low cost: The selective parallel disassembly sequence planning

With the growth of environmental awareness, remanufacturing and sustainable manufacturing have become hot issues. Disassembly is the first step and critical activity in remanufacturing. Traditional disassembly sequence planning (DSP) focusses on sequential disassembly. However, it is inefficient for complicated products because only one manipulator is employed to execute disassembly operations. Thus, this work focusses on parallel DSP (PDSP) and proposes a selective parallel disassembly sequence planning (SPDSP) methodology, which performs disassembly compared to sequential DSP and PDSP. In this paper, a mathematical model is used to describe the constraint and precedence relationships, and a parallel sequence model is designed for parallel disassembly. A novel hybrid genetic algorithm (NHGA) based-multi-objective model of SPDSP is proposed for optimisation. In this model, two indicators are integrated: disassembly time (including basic disassembly time, tool exchange time and direction change time) and disassembly costs. A transmission box is used as an instance, and a comparison with conventional genetic algorithm (GA), simulated annealing (SA) and tabu search (TS) is made to validate the practicality of the proposed methodology.

Circumventing spin-glass traps by microcanonical spontaneous symmetry breaking.

The planted p-spin interaction model is a paradigm of random-graph systems possessing both a ferromagnetic phase and a disordered phase with the latter splitting into many spin-glass states at low temperatures. Conventional simulated annealing dynamics is easily blocked by these low-energy spin-glass states. Here we demonstrate that actually this planted system is exponentially dominated by a microcanonical polarized phase at intermediate energy densities. There is a discontinuous microcanonical spontaneous symmetry breaking transition from the paramagnetic phase to the microcanonical polarized phase. This transition can serve as a mechanism to avoid all the spin-glass traps, and it is accelerated by the restart strategy of microcanonical random walk. We also propose an unsupervised learning problem on microcanonically sampled configurations for inferring the planted ground state.

Group layout design of manufacturing cells incorporating assembly and energy aspects

Cell Formation (CF) and Group Layout (GL) are two important problems in designing a cellular manufacturing system. This article addresses an integrated CF and GL model as a mixed-integer program, considering energy consumption, assembly aspects and process routing. As a novel feature, machines are assumed to be capable of processing operations with different energy consumption rates and processing times. This model aims to determine concurrently machine cells, the layout of facilities (machines, workstations and cells), process routes and processing speed of operations so that the materials handling cost and the electric energy consumption are minimized. To demonstrate the applicability of the model, managerial insights are provided by a case study. Owing to the computational complexity of the problem, a hybrid solution approach combining a Genetic Algorithm (GA) and Simulated Annealing (SA) is proposed. The computational results demonstrate the superiority of the hybrid approach over CPLEX and conventional GAs and SA.

Traffic signal optimization on a square lattice with quantum annealing

The spread of intelligent transportation systems in urban cities has caused heavy computational loads, requiring a novel architecture for managing large-scale traffic. In this study, we develop a method for globally controlling traffic signals arranged on a square lattice by means of a quantum annealing machine, namely the D-Wave quantum annealer. We first formulate a signal optimization problem that minimizes the imbalance of traffic flows in two orthogonal directions. Then we reformulate this problem as an Ising Hamiltonian, which is compatible with quantum annealers. The new control method is compared with a conventional local control method for a large 50-by-50 city, and the results exhibit the superiority of our global control method in suppressing traffic imbalance over wide parameter ranges. Furthermore, the solutions to the global control method obtained with the quantum annealing machine are better than those obtained with conventional simulated annealing. In addition, we prove analytically that the local and the global control methods converge at the limit where cars have equal probabilities for turning and going straight. These results are verified with numerical experiments.

Sequence-based protein structure optimization using enhanced simulated annealing algorithm on a coarse-grained model.

The understanding of protein structure is vital to determine biological function. We presented an enhanced simulated annealing (ESA) algorithm to investigate protein three-dimensional (3D) structure on a coarse-grained model. Inside the algorithm, we adjusted exploration equations to achieve good search intensity. To that end, our algorithm used (i) a multivariable disturbance operator for diversification of solution, (ii) a sign function to improve randomness of solution, and (iii) taking remainder operation performed on floating-point number to tackle out-of-range solution. By monitoring energy value throughout the simulation, the energy-optimal state can be found. The ESA algorithm was tested on artificial and real protein sequences with different lengths. The results show that our algorithm outperforms conventional simulated annealing algorithm and can compete with the reported algorithms before. Especially, our algorithm can obtain folding conformations with specific structural features. Further analysis shows that simulating trajectory of seeking the lowest energy can exhibit thermodynamic behavior of protein folding. Graphical Abstract.

Multiple User Cooperative Mobility in Mobile Ad Hoc Networks: An Interaction Position Game

Mobile ad hoc networks (MANETs) have been widely used by individuals for residential or commercial usage in small-scale areas depending on fifth-generation (5G) and device-to-device (D2D) advancements. MANET demands extremely high system throughput, low latency, and best quality of service (QoS) maintenance. The current user mobility approaches only analyze the single movable user and use intuitive methods but cannot fundamentally solve multiple user cooperative mobility in practical applications. In this paper, we first jointly consider multiple user mobility and different geographical places and distances among all users. Then, we propose an interaction position game (IPG) to achieve high throughput and decrease computational cost. In this game, cooperative behaviors among movable users are proposed instead of assumed selfishness, as in traditional game models. In addition, we also present the simulated annealing (SA) algorithm to solve this NP-hard problem as a performance comparison. Finally, we evaluate the performance of this proposed game in various position cases. The results show that this game method improves the maximum throughput ratio evidently by 57.35% and 27.27% compared with the conventional intuitive method and SA algorithm, respectively. Compared with the exhaustive algorithm, this game reduces the computation cost by 82.79%.

ARBSA: Adaptive Range-Based Simulated Annealing for FPGA Placement

Placement has always been the most time-consuming part of the field programmable gate array (FPGA) compilation flow. Conventional simulated annealing has been unable to keep pace with ever increasing sizes of designs and FPGA chip resources. Without utilizing information of the circuit topology, it relies on large amounts of random swap operations, which are time-costly. This paper proposes an adaptive range-based algorithm to improve the behavior of swap operations and limit the swap distances by introducing the concept of range-limiting strategy for nets. It avoids unnecessary design space exploration, and thus can converge to near-optimal solutions much more quickly. The experimental results are based on the Titan benchmarks, which contain 4K to 30K blocks, including logic array blocks, inputs and outputs, digital signal processors, and random access memories. This approach achieves $2.82\boldsymbol \times $ speed up, 4.8% reduction on wire length, 4.1% improvement on critical path compared with the SA from VTR with wire length-driven optimization, and $1.78\boldsymbol \times $ speed up, 10% reduction on wire length, 2% reduction on critical path with path timing-driven optimization. It also manifests better scalability on larger benchmarks.

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&amp;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&amp;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.

Crystalizing Effect of Simulated Annealing on Boltzmann Machine

This paper proposes a method to estimate the posterior distribution of a Boltzmann machine. Due to high feature extraction ability, a Boltzmann machine is often used for both of supervised and unsupervised learning. It is expected to be suitable for multimodal data because of its bi-directional connection property. However, it needs a sampling method to estimate the posterior distribution, which becomes a problem during an inference period because of the computation time and instability. Therefore, it is usually converted to feedforward neural networks, which means to lose its bi-directional property. To deal with these problems, this paper proposes a method to estimate the posterior distribution of a Boltzmann machine fast and stably without converting it to feedforward neural networks. The key idea of the proposed method is to estimate the posterior distribution using a simulated annealing on non-uniform temperature distribution. The advantage of the proposed method against Gibbs sampling and conventional simulated annealing is shown through experiments with artificial dataset and MNIST. Furthermore, this paper also gives the mathematical analysis of Boltzmann machine’s behaviour with regard to temperature distribution.

A hybrid simulated annealing for scheduling in dual-resource cellular manufacturing system considering worker movement

ABSTRACTThis paper presents a novel linear mathematical model for integrated cell formation and task scheduling in the cellular manufacturing system (CMS). It is suitable for the dual-resource constrained setting, such as garment process, component assembly, and electronics manufacturing. The model can handle the manufacturing project composing of some tasks with precedence constraints. It provides a method to assign the multi-skilled workers to appropriate machines. The workers are allowed to move among the machines such that the processing time of tasks might be reduced. A hybrid simulated annealing (HSA) is proposed to minimize the makespan of manufacturing project in the CMS. The approach combines the priority rule based heuristic algorithm (PRBHA) and revised forward recursion algorithm (RFRA) with conventional simulated annealing (SA). The result of extensive numerical experiments shows that the proposed HSA outperforms the conventional SA accurately and efficiently.

Optimal-Stopping Spectrum Sensing in Energy Harvesting Cognitive Radio Systems

In this paper, a cognitive radio system in which the secondary user (SU) is powered by energy harvested exclusively from environment is considered. The SU operates in a timeslotted mode and uses a timeslot in turn for energy harvesting, spectrum sensing and data transmission. In order to optimize the SU’s expected achievable throughput, strategy for energy harvesting and spectrum sensing should be carefully designed to tackle the tradeoff among the three. Such a problem leads to a parametrized optimal stopping problem, i.e., a mash-up of static and dynamic optimization problems in which save-ratio for energy harvesting is fixed (as a static variable parameter) while spectrum sensing runs in a channel-by-channel manner based on sensing results (as an optimal stopping problem). We propose an efficient algorithm to derive the optimal save-ratio and spectrum sensing rule, which is significantly faster than conventional simulated annealing algorithm. To further reduce the computational complexity, we also propose a suboptimal solution with an alternative optimization problem, where save-ratio and number of channels to be sensed are both static variables to be optimized. The alternative problem is formulated as a mixed-integer non-linear programming (MINLP) problem and closed-form solution is derived with in-depth analysis. We show that the proposed suboptimal solution is close in performance to the optimal one and outperforms a baseline strategy, which decouples optimization for energy harvesting and spectrum sensing by combining two existing techniques.

Improved local search approaches to solve the post enrolment course timetabling problem

In this work, we are addressing the post enrollment course timetabling (PE-CTT) problem. We combine different local search algorithms into an iterative two stage procedure. In the first stage, Tabu Search with Sampling and Perturbation (TSSP) is used to generate feasible solutions. In the second stage, we propose an improved variant of Simulated Annealing (SA), which we call Simulated Annealing with Reheating (SAR), to improve the solution quality of feasible solutions. SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. SAR eliminates the need for extensive tuning as is often required in conventional SA. The proposed methodologies are tested on the three most studied datasets from the scientific literature. Our algorithms perform well and our results are competitive, if not better, compared to the benchmarks set by the state of the art methods. New best known results are provided for many instances.

Implementation and Evaluation of FPGA-based Annealing Processor for Ising Model by use of Resource Sharing

The non-von Neumann computer architecture has been widely studied to prepare us for the post-Moore era. The authors implemented this kind of architecture, which finds the lower energy state of the Ising model using circuit operations inspired by simulated annealing in SRAM-based integrated circuits. Our previous prototype was suited for the Ising model because of its simple and typical structure such as its three-dimensional lattice topology, but it could not be used in real world applications. A reconfigurable prototyping environment is needed to develop the architecture and to make it suitable for applications. Here, we describe an FPGA-based prototyping environment to develop the annealing processor's architecture for the Ising model. We implemented the new architecture using a prototyping environment. The new architecture performs approximated simulated annealing for the Ising model, and it supports a highly complex topology. It consists of units having fully-connected multiple spins. Multiple units are placed in a two-dimensional lattice topology, and neighboring units are connected to perform interactions between spins. The number of logic elements was reduced by sharing the operator among multiple spins within the unit. Furthermore, a pseudo-random number generator, which produces random pulse sequences for annealing, is also shared among all the units. As a result, the number of logic elements was reduced to less than 1/10, and the solution accuracy became comparable to that of a conventional computer's simulated annealing.