Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem (CB-CTT), which has been tackled by many researchers and for which there are many available benchmarks.The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Second, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks.A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison.     

Design, engineering, and experimental analysis of a simulated annealing approach to the post-enrolment course timetabling problem

The post-enrolment course timetabling (PE-CTT) is one of the most studied timetabling problems, for which many instances and results are available. In this work we design a metaheuristic approach based on simulated annealing to solve the PE-CTT. We consider all the different variants of the problem that have been proposed in the literature and we perform a comprehensive experimental analysis on all the available public instances. The outcome is that our solver, properly engineered and tuned, performs very well on all cases, providing the new best known results on many instances and state-of-the-art values for the others.     

Combining simulated annealing with Lagrangian relaxation and weighted Dantzig–Wolfe decomposition for integrated design decisions in wireless sensor networks

A Wireless Sensor Network (WSN) is the outcome of the collaborative effort of multi-functional, low-power, low-cost, tiny electronic devices called sensors. Their ability to work autonomously provides a distributed environment capable to monitor even remote or inaccessible areas, which explains the wide application range of WSNs. There are four main issues in the design of a WSN: determining sensor locations (deployment), scheduling sensors, finding sink locations, and obtaining sensor-to-sink data routes. Sensors have very limited energy resources and their efficient management becomes critical for elongating network lifetime. As a result, most of the works on optimal WSN design are concerned with efficient energy usage. Unfortunately, only a few of them use an integrated approach and try to address these four issues simultaneously. In this work we also follow this line of research and develop first a monolithic mixed-integer linear programming model that maximizes network lifetime by optimally determining sensor and sink locations, sensor-to-sink data flows, active and stand-by periods of the sensors subject to data flow conservation, energy consumption and budget usage constraints. Then we propose a nested solution method consisting of two procedures: simulated annealing that performs search for the best sink locations in the outer level and Lagrangian relaxation based heuristic employed with weighted Dantzig–Wolfe decomposition for the multiplier update in the inner level, which determines sensor locations, activity schedules of the sensors and data flows routes. We demonstrate the efficiency and accuracy of the new approach on randomly generated instances by extensive numerical experiments.     

A heuristic algorithm based on Lagrangian relaxation for the closest string problem

The closest string problem that arises in both computational biology and coding theory is to find a string minimizing the maximum Hamming distance from a given set of strings. This study proposes an efficient heuristic algorithm for this NP-hard problem. The key idea is to apply the Lagrangian relaxation technique to the problem formulated as a mixed-integer programming problem. This enables us to decompose the problem into trivial subproblems corresponding to each position of the strings. Furthermore, a feasible solution can be easily obtained from a solution of the relaxation. Based on this, a heuristic algorithm is constructed by combining a Lagrangian multiplier adjustment procedure and a tabu search. Computational experiments will show that the proposed algorithm can find good approximate solutions very fast.     

A simulated annealing algorithm for dynamic layout problem

Increased level of volatility in today's manufacturing world demanded new approaches for modelling and solving many of its well-known problems like the facility layout problem. Over a decade ago Rosenblatt published a key paper on modelling and solving dynamic version of the facility layout problems. Since then, various other researchers proposed new and improved models and algorithms to solve the problem. Balakrishnan and Cheng have recently published a comprehensive review of the literature about this subject. The problem was defined as a complex combinatorial optimisation problem. The efficiency of SA in solving combinatorial optimisation problems is very well known. However, it has recently not been applied to DLP based on the review of the available literature. In this research paper a SA-based procedure for DLP is developed and results for test problems are reported.

Scope and purpose

One of the characteristic of today's manufacturing environments is volatility. Under a volatile environment (or dynamic manufacturing environment) demand is not stable. To operate efficiently under such environments facilities must be adaptive to changing demand conditions. This requires solution of the dynamic layout problem (DLP). DLP is a complex combinatorial optimisation problem for which optimal solutions can be found for small size problems. This research paper makes use of a SA algorithm to solve the DLP. Simulated annealing (SA) is a well-established stochastic neighbourhood search technique. It has a potential to solve complex combinatorial optimisation problems. The paper presents in detail how to apply SA to solve DLP and an extensive computational study. The computational study shows that SA is quite effective in solving dynamic layout problems.     

Solving dynamic double row layout problem via combining simulated annealing and mathematical programming

Double row layout problem (DRLP) is to allocate facilities on two rows separated by a straight aisle. Aiming at the dynamic environment of product processing in practice, we propose a dynamic double-row layout problem (DDRLP) where material flows change over time in different processing periods. A mixed-integer programming model is established for this problem. A methodology combining an improved simulated annealing (ISA) with mathematical programming (MP) is proposed to resolve it. Firstly, a mixed coding scheme is designed to represent both of sequence of facilities and their exact locations. Secondly, an improved simulated annealing algorithm is suggested to produce a solution to DDRLP. Finally, MP is used to improve this solution by determining the optimal exact location for each facility. Experiments show that this methodology is able to obtain the optimal solutions for small size problems and outperforms an exact approach (CPLEX) for problems of realistic size.     

Fast simulated annealing hybridized with quenching for solving job shop scheduling problem

Various heuristic based methods are available in literature for optimally solving job shop scheduling problems (JSSP). In this research work a novel approach is proposed which hybridizes fast simulated annealing (FSA) with quenching. The proposed algorithm uses FSA for global search and quenching for localized search in neighborhood of current solution, while tabu list is used to restrict search from revisiting previously explored solutions. FSA is started with a relatively higher temperature and as search progresses temperature is gradually reduced to a value close to zero. The overall best solution (BS) is maintained throughout execution of the algorithm. If no improvement is observed in BS for certain number of iterations then quenching cycle is invoked. During quenching cycle current temperature is reduced to nearly freezing point and iterations are increased by many folds, as a result of this change search becomes nearly greedy. The strength of the proposed algorithm is that even in quenching mode escape from local optima is possible due to use of Cauchy probability distribution and non-zero temperature. At the completion of quenching cycle previous values of search parameters are restored and FSA takes over, which moves search into another region of solution space. Effectiveness of proposed algorithm is established by solving 88 well known benchmark problems taken form published work. The proposed algorithm was able to solve 45 problems optimally to their respective best known values in reasonable time. The proposed algorithm has been compared with 18 other published works. The experimental results show that the proposed algorithm is efficient in finding solution to JSSP.     

A Lagrangian relaxation technique for the general assembly line balancing problem

This paper addresses the problem of balancing assembly or fabrication lines. In order to achieve a given production rate or to optimize the use of workstations, one has to tackle the problem of balancing the production lines. It is well known that this problem belongs to the class of NP-hard problems. In this paper the polyhedron of the feasible solutions of the assembly line balancing problem is first studied. Then a Lagrangian relaxation algorithm that incorporates the set of cycle constraints in the objective function is proposed. These constraints are the complicating restrictions in the model. The relaxed problem has the interesting property that its linear programming relaxation always has integer optimal solutions. The subgradient algorithm is then used to maximize the Lagrangian dual. A heuristic is also used to find primal feasible solutions for the original line balancing integer program. These two bounds are then used to reduce the size of the branch-and-bound tree.     

A simulated annealing heuristic for the open location-routing problem

This paper introduces the open location-routing problem (OLRP) that is a variant of the capacitated location-routing problem (CLRP). OLRP is motivated from the rise in contracting with third-party logistic (TPL) companies and is different from CLRP in that vehicles do not return to the distribution center after servicing all customers. The goal of OLRP is to minimize the total cost, consisting of facility operation costs, vehicle fixed costs, and traveling costs. We propose a simulated annealing (SA)-based heuristic for solving OLRP, which is tested on OLRP instances that have been adopted from three sets of well-known CLRP benchmark instances with up to 318 customers and 4 potential depots. The computational results indicate that the proposed heuristic efficiently solves OLRP.     

A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem

The rectangle knapsack packing problem is to pack a number of rectangles into a larger stock sheet such that the total value of packed rectangles is maximized. The paper first presents a fitness strategy, which is used to determine which rectangle is to be first packed into a given position. Based on this fitness strategy, a constructive heuristic algorithm is developed to generate a solution, i.e. a given sequence of rectangles for packing. Then, a greedy strategy is used to search a better solution. At last, a simulated annealing algorithm is introduced to jump out of the local optimal trap of the greedy strategy, to find a further improved solution. Computational results on 221 rectangular packing instances show that the presented algorithm outperforms some previous algorithms on average.     

A simulated annealing algorithm for multi-manned assembly line balancing problem

Assembly line balancing problems with multi-manned workstations usually occur in plants producing high volume products (e.g. automotive industry) in which the size of the product is reasonably large to utilize the multi-manned assembly line configuration. In these kinds of assembly lines, usually there are multi-manned workstations where a group of workers simultaneously performs different operations on the same individual product. However, owing to the high computational complexity, it is quite difficult to achieve an optimal solution to the balancing problem of multi-manned assembly lines with traditional optimization approaches. In this study, a simulated annealing heuristic is proposed for solving assembly line balancing problems with multi-manned workstations. The line efficiency, line length and the smoothness index are considered as the performance criteria. The proposed algorithm is illustrated with a numerical example problem, and its performance is tested on a set of test problems taken from literature. The performance of the proposed algorithm is compared to the existing approaches. Results show that the proposed algorithm performs well.     

A distributed implementation of simulated annealing for the travelling salesman problem

This paper describes and analyses a novel distributed implementation of the simulated annealing algorithm to find a good solution to the travelling salesman problem. The implementation runs on a linear chain of processors driven by a host processor, which plays only a supervisory role, so that the bulk of processing takes place on the chain and the efficiency of the algorithm remains high as the number of processors is increased.     

求解动态停泊计划问题的拉格朗日松弛算法

研究钢铁企业原料码头动态停泊计划问题,其动态特征主要体现在原料船动态到达并有两个或两个以上连续泊位且在停泊计划开始执行时每一泊位上仅有部分泊位长度可利用。针对这个问题,建立了一个数学模型并设计了改进拉格朗日算法在很短的时间内求得了近优解。在改进算法中使用了所提出的四个性质来分别加速求解子问题、乘子更新和获得可行解的过程。通过包含50个实际规模问题的算法性能实验表明改进的拉格朗日松弛算法相比未改进算法减少了80%的运行时间。     

利用模糊次梯度算法求解拉格朗日松弛对偶问题

针对利用次梯度算法处理拉格朗日松弛对偶问题时，计算过程容易出现振荡，求解效率较低的问题，首先提出了一种基于模糊理论的次梯度算法，利用隶属度函数给出迭代过程中所有次梯度的合适权重，并将它们线性加权得到新的迭代方向；其次证明了算法的收敛性；最后通过仿真实验验证了该方法的有效性．     

A simulated annealing approach to the traveling tournament problem

Automating the scheduling of sport leagues has received considerable attention in recent years, as these applications involve significant revenues and generate challenging combinatorial optimization problems. This paper considers the traveling tournament problem (TTP) which abstracts the salient features of major league baseball (MLB) in the United States. It proposes a simulated annealing algorithm (TTSA) for the TTP that explores both feasible and infeasible schedules, uses a large neighborhood with complex moves, and includes advanced techniques such as strategic oscillation and reheats to balance the exploration of the feasible and infeasible regions and to escape local minima at very low temperatures. TTSA matches the best-known solutions on the small instances of the TTP and produces significant improvements over previous approaches on the larger instances. Moreover, TTSA is shown to be robust, because its worst solution quality over 50 runs is always smaller or equal to the best-known solutions. A Preliminary version of this paper was presented at the CP'AI'OR'03 Workshop.     

A simulated annealing heuristic for the dynamic layout problem with budget constraint

Facility layout problem has been extensively studied in the literature because the total material handling cost can be a significant portion in the operational costs for a company and in the manufacturing cost of a product. Today’s severe global competition, rapid changes in technology and shortening life cycle of products force companies to evaluate and modify their facility layout in a periodic fashion. This type of layout problems is categorized as the dynamic facility layout problem (DFLP). As a realistic dimension of the problem, one has to consider also the limited budget to cover the cost of changing the layout. In this study, we propose a simulated annealing heuristic for the DFLP with budget constraint, and show the effectiveness of this heuristic on a set of numerical experiments.     

A theoretical framework for simulated annealing

Simulated Annealing has been a very successful general algorithm for the solution of large, complex combinatorial optimization problems. Since its introduction, several applications in different fields of engineering, such as integrated circuit placement, optimal encoding, resource allocation, logic synthesis, have been developed. In parallel, theoretical studies have been focusing on the reasons for the excellent behavior of the algorithm. This paper reviews most of the important results on the theory of Simulated Annealing, placing them in a unified framework. New results are reported as well.This research was sponsored by SRC and DARPA monitored by SNWSC under contract numbers N00039-87-C-012 and N00039-88-C-0292.     

Bi-criteria simulated annealing for the curriculum-based course timetabling problem with robustness approximation

Journal of Scheduling - In the process of developing a university’s weekly course timetable, changes in the data, such as the available time periods of professors or rooms, render the...     

A Lagrangian relaxation approach for a large scale new variant of capacitated clustering problem

This paper studies a new variant of capacitated clustering problem (VCCP). In the VCCP, p facilities which procure a raw material from a set of suppliers are to be located among n potential sites (n > p) such that the total cost of assigning suppliers to the facilities and opening such facilities is minimized. Each supplier has a limited supply volume and each facility has a minimum supply requirement that must be satisfied by assigning enough suppliers to the facility. Each supplier can be assigned to at most one facility. When a supplier is assigned to a facility, the former will supply its all available volume to the latter. In order to solve the VCCP, a Lagrangian relaxation approach (LR) with two phases of dual optimization, the subgradient deflection in the first phase and the standard subgradient method in the second phase, is proposed. In the approach, the assignment constraints are relaxed. The resulting Lagrangian relaxed problem can be decomposed into a set of independent knapsack problems, which can be solved to optimality efficiently. At each Lagrangian iteration, a feasible solution is constructed from that of the Lagrangian relaxed problem by applying a greedy algorithm. Finally, the best feasible solution found so far is improved by a simple tabu search algorithm. Numerical tests on random instances show that the proposed LR can produce a tight lower bound and a high quality feasible solution for all instances with up to 4000 suppliers, 200 potential sites, and 100 plants to locate.     

Ant algorithms and simulated annealing for multicriteria dynamic programming

The paper presents a comparison of ant algorithms and simulated annealing as well as their applications in multicriteria discrete dynamic programming. The considered dynamic process consists of finite states and decision variables. In order to describe the effectiveness of multicriteria algorithms, four measures of the quality of the nondominated set approximations are used.