Simulated Annealing-based Algorithm Research Articles

Simulated annealing with auxiliary knowledge for process planning optimization in reconfigurable manufacturing

In this paper, three simulated annealing based algorithms that exploit auxiliary knowledge in different ways are devised and employed to handle a manufacturing process planning problem for reconfigurable manufacturing. These algorithms are configured based on a generic combination of the simulated annealing technique with; (a) heuristic knowledge, and (b) metaknowledge. Capabilities of the implemented algorithms are tested and their performances compared against a basic simulated annealing algorithm. Computational and optimization performances of the implemented algorithms are investigated and analyzed for two problem sizes. Each problem size consists of five different forms of a manufacturing process planning problem. The five forms are differentiated by five alternative objective functions. Experimental results show that the implemented simulated annealing algorithms are able to converge to good solutions in reasonable time. A computational analysis indicates that significant improvements towards a better optimal solution can be gained by implementing simulated annealing based algorithms that are supported by auxiliary knowledge.

An Effective Simulated Annealing-Based Mathematical Optimization Algorithm for Minimizing the Lennard-Jones Potential

The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of N atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form Minimize subject to Where ,is the coordinates ofatom. This paper is to minimize the L-J potential on ,where n = 3N. however it is a challenging and diffcult problem for many optimization methods when N is larger. This paper presents an effective mathematical optimization algorithm for minimizing the LJ Potential and a series of elegant optimal solutions of atoms up to 310 were got.

A simulated annealing-based algorithm for iterative class discovery using fuzzy logic for informative gene selection

Within a gene expression matrix, there are usually several particular macroscopic phenotypes of samples related to some diseases or drug effects, such as diseased samples, normal samples or drug treated samples. The goal of sample-based clustering is to find the phenotype structures or subsamples. We present a novel method for automatically discovering clusters of samples which are coherent from a genetic point of view. Each possible cluster is characterized by a fuzzy pattern which maintains a fuzzy discretization of relevant gene expression values. Possible clusters are randomly constructed and iteratively refined by following a probabilistic search and an optimization schema. Evaluation of the proposed algorithm on publicly available microarray datasets shows high accuracy in spite of noise and the presence of other clusters. The results obtained support the appropriateness of using fuzzy logic to represent and filter gene expression values following an iterative approach. The proposed method complements our previous GENECBR system and both are freely available under GNU General Public License from http://www.genecbr.org/fpclustering.htm and http://www.genecbr.org/, respectively.

Model and heuristic for berth allocation in tidal bulk ports with stock level constraints

We consider the problem of allocating berth positions for vessels in tidal bulk port terminals. A berth is defined as a specific location alongside a quay where a ship loader is available for loading or unloading vessels, accommodating only one vessel at a time. In tidal ports, draft conditions depend on high tide conditions, since available depth at low tide is not adequate for the movement of ships. Some port terminals are associated with important transnational enterprises which maintain strong control over the stock level of their goods. Since the stock level sometimes depends on a continuous process of consumption or production of minerals, the decision to load or unload vessels must consider the amount of the bulk cargo stored in the port yards. Therefore, a basic criterion for decision making is to give priority to the vessels related to the most critical mineral stock level. A second basic criterion is to decide what sequence of vessels reduces the overall demurrage within a given planning horizon. This paper presents an integer linear programming model based on the transportation problem to represent the Berth Allocation Problem in Tidal Bulk ports with Stock level conditions (BAPTBS). Problem instances are solved by a commercial solver and by a Simulated Annealing-based algorithm (SA). The SA employs a problem-specific heuristic, becoming a valid alternative for finding out good solutions for difficult instances.

Constrained mean-risk portfolio optimisation: an application of multiobjective simulated annealing

We solve different constrained mean-risk portfolio optimisation models using a recently developed simulated annealing-based multiobjective optimisation algorithm. We consider practical and widely used constraints in portfolio modelling, i.e., the cardinality constraint which imposes a limit on the number of assets in the portfolio and the quantity constraints which restrict the proportion of each asset in the portfolio to lie between lower and upper bounds. Various risk measures are employed – the classical variance and three risk measures that form the so called downside-risk family, i.e., expected shortfall, value-at-risk and semivariance. The experimental results demonstrate that the algorithm generates a number of efficient portfolios capturing a great range of the trade-offs between mean and risk independently of the risk function used. Comparison with benchmark (when possible) efficient frontiers provides strong evidence that the algorithm effectively solves the discrete constrained mean-risk problems. Furthermore, a computational comparison with a population-based evolutionary algorithm, namely SPEA2, shows that the simulated annealing-based multiobjective optimisation technique achieves almost as good performance in a timely manner.

Makespan minimization for scheduling unrelated parallel machines with setup times

This study considers the problem of scheduling jobs on unrelated parallel machines with machine-dependent and job sequence-dependent setup times. In this study, a restricted simulated annealing (RSA) algorithm which incorporates a restricted search strategy is presented to minimize the makespan. The proposed RSA algorithm can effective reduce the search effort required to find the best neighborhood solution by eliminating ineffective job moves. The effectiveness and efficiency of the proposed RSA algorithm is compared with the basic simulated annealing and existing meta-heuristics on a benchmark problem dataset used in earlier studies. Computational results indicate that the proposed RSA algorithm compares well with the state-of-the-art meta-heuristic for small-sized problems, and significantly outperforms basic simulated annealing algorithm and existing algorithms for large-sized problems.

Structural Shape Optimization Using an Adaptive Simulated Annealing

In structural design optimization, numerical techniques are increasingly used. In typical structural optimization problems there may be many locally minimum configurations. For that reason, the application of a global method, which may escape from the locally minimum points, remain essential. In this paper, a new hybrid simulated annealing algorithm for global optimization with constraints is proposed. We have developed a new algorithm called Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the Basic Simulated Annealing algorithm ( BSA) that gives the region containing the global solution of an objective function. In addition, the stochastic method Simultaneous Perturbation Stochastic Approximation (SPSA), for solving unconstrained optimization problems, is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The proposed method is applicable for any problem where the topology of the structure is not fixed, it is simple and capable of handling problems subject to any number of nonlinear constraints. Extensive tests on the ASA as a global optimization method are presented, its performance as a viable optimization method is demonstrated by applying it first to a series of benchmark functions with 2 - 30 dimensions and then it is used in structural design to demonstrate its applicability and efficiency. It is found that the best results are obtained by ASA compared to those provided by the commercial software ANSYS.

Link weight optimization for routing in communication networks

In the shortest path routing algorithm for communication networks, the end-to-end path of each session is found such that the sum of weights of links on the path is minimized. Hence, to find a `good' path for each session, it is important to assign the appropriate weight to each link in the network. In this paper, we study this problem considering the utilization of each link. Since this problem is known to be NP-hard[1], we use a heuristic approach. Our algorithm is based on the simulated annealing algorithm. However, with taking into account the properties of our problem, we modify the basic simulated annealing algorithm, which results in a faster and more robust convergence.

A Global Stochastic Optimization Method for Large Scale Problems

In this paper, a new hybrid simulated annealing algorithm for constrained global optimization is proposed. We have developed a stochastic algorithm called ASAPSPSA that uses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to the basic simulated annealing algorithm (SA) that gives the region containing the global solution of an objective function. In addition, Simultaneous Perturbation Stochastic Approximation (SPSA) method, for solving unconstrained optimization problems, is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The combination of both techniques ASA and PSPSA provides a powerful hybrid optimization method. The proposed method has a good balance between exploration and exploitation with very fast computation speed, its performance as a viable large scale optimization method is demonstrated by testing it on a number of benchmark functions with 2 - 500 dimensions. In addition, applicability of the algorithm on structural design was tested and successful results were obtained

Joint estimation of source number and DOA using simulated annealing algorithm

The array signal processing problem has to do with two main issues: 1) the determination of source number; and 2) estimation of the directions-of-arrival (DOA) of these sources. In the classical methods, the determination of source number and the estimation of DOA parameters are executed independently rather than jointly. To jointly estimate source number and DOA, this paper proposes a simulated annealing-based algorithm. The key points of this paper are: i) the prior choices for some unknown parameters are calibrated to compute more efficiently; ii) a penalty term for the parameter number is added to the corresponding objective function Additionally to avoid overfitting; and iii) in order to move to the regions of interest quickly, some cumulants of properly chosen sensor outputs from the uniform linear array (ULA) is computed and their moduluses of Fourier transform (MFT) are mapped trickly to the uniform distribution. Finally simulation results are presented to validate the performance of the proposed method.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n 2 / 3 . The local search procedure employs the stopping criterion ( m / δ ) D / γ , where m is an estimation of the average number of neighbouring conformations, γ relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1 − δ is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems.

The grocery superstore vehicle scheduling problem

Scheduling the deliveries from a regional distribution centre (RDC) to large stores of a major retailer of fast moving consumer goods includes every possible vehicle routeing complexity. Usual constraints, like the size of the vehicle and the length of the driving day, apply. More importantly, loading feasibility is a major factor, with frozen goods being at the front, produce and perishable products in the middle, and groceries at the tail of the rear end loading vehicle. Moreover, these three product types have different time windows, determined store by store. Items like medium movers and alcoholic drinks may only be stocked at particular hub depots, from where they must be collected and then delivered to the retail outlets. Collections of salvage are made from the stores and goods from suppliers are backhauled to an RDC, which may not be the vehicle base. Then there may be trunking between RDCs. In this case study, deliveries and collections by vehicles at an RDC are presently scheduled by updating daily a basic plan prepared every 6 months, using the skills of an experienced distribution professional. A simulated annealing-based algorithm has been developed to speed up the process by circumventing the need for the skeletal schedule. In the application tested, the solution produced by the algorithm requires the same number of vehicles as actually used, although the total delivery time is slightly longer. Further improvements, particularly in the quality of the initial solution, may be possible by exploiting the problem structure in recognizable ways.

Dynamic Optimization of Batch Emulsion Polymerization Using MSIMPSA, a Simulated-Annealing-Based Algorithm

The aim of this paper is to present a global approach to dynamic optimization of batch emulsion polymerization reactors using a stochastic optimizer. The objective is to minimize the final batch time with constraints on the final conversion and molecular weight, using the reactor temperature as the manipulated variable. First, results from the standard SQP-based approach are presented to illustrate how this problem is prone to be stuck in local minima. Then, in this study, the applicability of MSIMPSA, a simulated annealing-based algorithm, is evaluated. The results obtained are only marginally superior to those reported in the literature. However, the main outcomes of this study are: (i) MSIMPSA can be applied in an easy and straightforward manner to such optimal control problems. (ii) Though MSIMPSA is a stochastic algorithm, the best obtained solution is so good that it cannot be improved further by local optimization methods.

A Heterogeneous Built-In Self-Repair Approach Using System-Level Synthesis Flexibility

Summary and Conclusions -A novel methodology is proposed for designing fault-tolerant real-time multi-processor systems-on-a-chip to achieve optimal productivity. The methodology employs the heterogeneous built-in-self-repair (BISR) based on graceful degradation and yield enhancement techniques as an embedded optimization engine. The technique exploits the flexibility provided in task-level scheduling and algorithm selection steps. A hardware fault model is developed for modern super-scalar processors and multi-processors which enables an efficient treatment of the synthesis and compilation goals. For the first time, heterogeneous BISR is used at the task level. The key idea is to adapt scheduling and algorithm selection to the available nonfaulty resources. If there is a fault in memory, the algorithms that use less memory are selected and the scheduler exploits the other abundant resource, viz, the processors, more vigorously to compensate for the loss of part of memory. Similarly, a fault in a processor is backed up by memory. The synthesis approach minimizes the degradation in performance for single or multiple faults using simulated annealing-based algorithm selection, scheduling, and assignment algorithms. On the large set of examples this adaptive algorithm selection and scheduling technique has achieved important improvement of throughput compared to conventional nonadaptive schemes. The experimental results also indicate that important improvement in productivity can be achieved by using the extra throughput gained from the technique.

Approximation of Boolean Functions by Local Search

Usually, local search methods are considered to be slow. In our paper, we present a simulated annealing-based local search algorithm for the approximation of Boolean functions with a proven time complexity that behaves relatively fast on randomly generated functions. The functions are represented by disjunctive normal forms (DNFs). Given a set of m uniformly distributed positive and negative examples of length n generated by a target function F(x1,…,xn), where the DNF consists of conjunctions with at most e literals only, the algorithm computes with high probability a hypothesis H of length m · e such that the error is zero on all examples. Our algorithm can be implemented easily and we obtained a relatively high percentage of correct classifications on test examples that were not presented in the learning phase. For example, for randomly generated F with n e 64 variables and a training set of m e 16384 examples, the error on the same number of test examples was about 19% on positive and 29% on negative examples, respectively. The proven complexity bound provides the basis for further studies on the average case complexity.

SOLVING VEHICLE ROUTING PROBLEM WITH BACKHAULS

ABSTRACT This paper modifies the definition of the traditional vehicle routing problems with backhaul (VRPB) and presents a simulated annealing-based heuristic algorithm. Computational results demonstrate that the proposed algorithm not only has the capability of handling situations encountered in practice, but also consumes less transportation costs the traditional algorithms.

Module placement with boundary constraints using B*-trees

The module placement problem is to determine the co-ordinates of logic modules in a chip such that no two modules overlap and some cost (e.g. silicon area, interconnection length, etc.) is optimised. To shorten connections between inputs and outputs and/or make related modules adjacent, it is desired to place some modules along the specific boundaries of a chip. To deal with such boundary constraints, we explore the feasibility conditions of a B*-tree with boundary constraints and develop a simulated annealing-based algorithm using B*-trees. Unlike most previous work, the proposed algorithm guarantees a feasible B*-tree with boundary constraints for each perturbation. Experimental results show that the algorithm can obtain a smaller silicon area than the most recent work based on sequence pairs.

The convergence of stochastic algorithms solving flow shop scheduling

In the paper, we apply logarithmic cooling schedules of simulated annealing-based algorithms to flow shop scheduling. In our problem setting, the objective to minimize the overall completion time which is called the makespan. We prove a lower bound for the number of steps that are sufficient to approach an optimum solution with a certain probability. The result is related to the maximum escape depth Γ from local minima of the underlying energy landscape. In our approach, we need n O(Γ) + log O(1) (1/δ) steps to be in an optimum solution with probability 1−δ, where n denotes the total number of tasks. The auxiliary computations are of polynomial complexity. Since the model cannot be approximated arbitrarily closely in the general case (unless P= NP ), the approach can be used to obtain approximation algorithms that work well in the average case.

Unit load and material-handling considerations in facility layout design

The effectiveness of a layout design cannot be completely measured if the operational characteristics of the manufacturing system are ignored. There is, therefore, a need to develop integrated manufacturing system design models. In this paper, the integration of unit load and material-handling considerations in a facility layout design is presented. This integration is based on a stochastic model that captures the operational characteristics of the manufacturing system and a nonlinear mixed-integer program that incorporates a department formation and facility layout. The non-linear mixed-integer program is solved using a simulated annealing-based algorithm. Analytical results for different manufacturing system scenarios are presented and compared with results obtained using alternative QAP-type formulations. Based on our experiments and the characteristics of the different formulations, key observations are presented and discussed.

Search heuristics for operation sequencing in process planning

The operation-sequencing problem in process planning is considered to produce a part with the objective of minimizing the sum of machine, setup and tool change costs. In general, the problem has combinatorial characteristics and complex precedence relations, which makes the problem difficult to solve. Six local search heuristics have been developed based on simulated annealing and tabu search to obtain good solutions for practical-sized problems within a reasonable amount of computation time. Application of the algorithms is illustrated using an example part. Also, computational experiments were done on randomly generated problems and the results show that the tabu search-based algorithms are better than the simulated annealing-based algorithms on overall average. In particular, one of the tabu search algorithms suggested here gave optimal solutions for most small-sized test problems within very short computation times.