Global optimization for track finding

In this paper, we address the flowpath design issue of Automated Guided Vehicle Systems (AGVSs). In particular, we concentrate on the design of unidirectional flowpaths (i.e. vehicles are restricted to travel only in one direction along a given segment of the flowpath). We have developed intelligent heuristics — simulated annealing and tabu search algorithms for the design of unidirectional AGVSs. Different versions of simulated annealing and tabu search algorithms are implemented. Our extensive computational results indicate that both simulated annealing and tabu search yield solutions of adequate quality for all practical purposes. A tabu search implementation with the use of a frequency-based memory structure dominates all tested heuristics in terms of solution quality (i.e. percent deviation from optimality), with an impressive average performance over 45 test problems of less than 0.85% deviation from optimality.

Hopfield neural networks (HNN) and simulated annealing (SA) are two recent approaches to solving many combinatorial optimization problems. But, the disadvantages of HNN are that it can often converge at local minimum and the quality of solutions depends on the initial state because of sensitivity of parameterization. On the other hand, SA is designed to cope with the problem of convergence to a local minimum. SA, however, requires unacceptably large computing time. So, a new algorithm called mean field annealing (MFA) which can be interpreted as a generalization of HNN, is applied to optimization problems efficiently. In this paper, we propose a new approach based on MFA to solving of the minimization problem. Also we show that our approach can be applied to multi-layer as well as two-layer routing, and optimal solutions can be obtained by properly adjusting the parameter in the given energy function.

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.

Optimization is an important subject in solving scientific and engineering problems. One conventional searching technique for finding the global minimum is to use gradient descent, which finds the direction for the next iteration from the gradient of the objective function. For complicated problems, the gradient descent technique often gets stuck at a local minimum where the objective function has surrounding barriers. In addition, the complexity of most combinatorial optimization problems increases dramatically with the problem size and makes it very difficult to obtain the globally optimal solution in a reasonably computational time. Complicated optimization problems could also be solved by using branch-and-bound searching method [1], or by relaxing some constraints and solving the simplified problems [2]. Several attractive methods have been reported to help the solutions of the optimization problems to escape from local minima [3 4, 5, 6, 7, 8, 9, 10]. Simulated annealing is one of the popular approaches which is widely applicable to the combinatorial optimization problems [3, 4]. Simulated annealing is a generalization of iterative improvement methods in that it accepts, with a non-zero but gradually decreasing probability, deterioration in the cost function of an optimization problem. A solution from simulated annealing is close to the global minimum within a polynomial upper bound for the computational time and is independent of the initial condition. Mean field annealing is a deterministic approximation to simulated annealing [7]. It analytically approximates the relevant Boltzmann distribution and can execute at 50 times faster than simulated annealing for some problems. The quality of the solutions produced by mean field annealing is highly dependent on the choice of the initial temperature, the cooling speed and the final temperature. So far, simulated annealing has been successfully reported in layout generation of VLSI circuits [11, 12], test pattern generation [13], integrated-circuit delay reduction [14], image segmentation [15] and noise filtering in image processing [16].

Research Highlights: (1) Optimizing mid-rotation thinning increased modeled land expectation values by as much as 5.1–10.1% over a representative reference prescription on plots planted at 2.7 and 3.7 m square spacings. (2) Eight heuristics, five of which were newly applied to selecting individual trees for thinning, produced thinning prescriptions of near identical quality. (3) Based on heuristic sampling properties, we introduced a variant of the hero heuristic with a 5.3–20% greater computational efficiency. Background and Objectives: Thinning, which is arguably the most subjective human intervention in the life of a stand, is commonly executed with limited decision support in tree selection. This study evaluated heuristics’ ability to support tree selection in a factorial experiment that considered the thinning method, tree density, thinning age, and rotation length. Materials and Methods: The Organon growth model was used for the financial optimization of even age Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) harvest rotations consisting of a single thinning followed by clearcutting on a high-productivity site. We evaluated two versions of the hero heuristic, four Monte Carlo heuristics (simulated annealing, record-to-record travel, threshold accepting, and great deluge), a genetic algorithm, and tabu search for their efficiency in maximizing land expectation value. Results: With 50–75 years rotations and a 4% discount rate, heuristic tree selection always increased land expectation values over other thinning methods. The two hero heuristics were the most computationally efficient methods. The four Monte Carlo heuristics required 2.8–3.4 times more computation than hero. The genetic algorithm and the tabu search required 4.2–8.4 and 21–52 times, respectively, more computation than hero. Conclusions: The accuracy of the resulting thinning prescriptions was limited by the quality of stand measurement, and the accuracy of the growth and yield models was linked to the heuristics rather than to the choice of heuristic. However, heuristic performance may be sensitive to the chosen models.

In this paper, we study the resource management problem in Direct Sequence-Wideband Code Division Multiple Access (DS-WCDMA) systems. The control variables, transmission power, and transmission rate for resource management are considered. Three meta-heuristic techniques, Genetic Algorithms (GA), Simulated Annealing (SA), and Tabu Search (TS), are utilized to solve this optimization problem. Also, a nonlinear programming technique, Generalized Reduced Gradient (GRG) method, is adopted to compare with the three meta-heuristic techniques. Two approaches, the single objective approach and the multiobjective approach, are used in the simulation. The results obtained by GA, SA, TS, and GRG are compared in a single objective approach. In a multiobjective approach, Multiobjective Genetic Algorithm (MOGA) is employed to compare with the other two well-known multiobjective evolutionary algorithms (MOEAs), Pareto Archived Evolution Strategy (PAES) and Micro-Genetic Algorithms (MICRO-GA). Two scenarios, scenario (a): 25 users and scenario (b): 50 users, are considered for both approaches. The simulation results of a single objective approach show that GA outperforms SA, TS, and GRG in the two scenarios. Also, the simulation results of a multiobjective approach show that MOGA outperforms PAES and MICRO-GA, and obtains nondominated trade-off solutions with better convergence and diversity between trade minimization of total power and maximization of total rate in two scenarios.

This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual “natural” permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the permutation-based methods have a higher likelihood of generating an optimal solution, but are less robust in that some poor solutions are obtained. Of the neighborhood search methods, tabu search clearly dominates the others. Multistart descent performs remarkably well relative to simulated annealing and threshold accepting.

This paper presents an optimal design method by means of mean field annealing (MFA). The mean field theory (MFT) is introduced, and a certain MFA application extension based on Peierls inequality is explained in detail, the critical temperature that is important for classes of problem while applying MFA is discussed. With MFA, the optimal size design of electromagnetic device is carried out. The results are compared with two existing algorithms, the modified simulated annealing (MSA) and one-variable stochastic simulated annealing based MFA (S-MFA), in both operating cost and final quantities. To modify the final results to reach the global optimum, Hooke-Jeeves pattern search method is adopted. Favorable results show the effectiveness of the proposed scheme.

Bayesian regularised genetic neural network (BRGNN) has been used for modelling the inhibition activity of 141 biphenylalanine derivatives as integrin antagonists. Three local pattern search (PS) methods, simulated annealing and threshold acceptance were combined with BRGNN in the form of a hybrid genetic algorithm (HGA). The results obtained revealed that PS is a suitable method for improving the ability of BRGNN to break out from the local minima. The proposed HGA technique is able to retrieve important variables from complex systems and nonlinear search spaces for optimisation. Two models with 8-3-1 artificial neural network (ANN) architectures were developed for describing α 4 β 7 and α 4 β 1 modulatory activities of integrin antagonists. Monte Carlo cross-validation was performed to validate the models and Q 2 values of 0.75 and 0.74 were obtained for α 4 β 7 and α 4 β 1 inhibitory activities, respectively. The scrambling technique was used for sensitivity analysis of descriptors appearing in ANN models. Frequencies of repetition and sensitivity analysis of molecular descriptors revealed that 3D-Morse descriptors are influential factors for describing α 4 β 7 inhibitory activity, while in the case of α 4 β 1 inhibitory activity, the Randic shape index, the lowest eigenvalue of the Burden matrix and the number of rotatable bonds are important parameters.

Scheduling problems in real systems often require sequence-dependent setup times. The topic of sequence-dependent setup times has not been addressed adequately, and improved competitiveness is thus not achieved. This study proposes a hybrid approach that takes advantage of simulated annealing (SA) and tabu search (TS) to solve single-machine tardiness problems with sequence-dependent setup times. To verify the proposed approach, experiments were conducted on benchmark problem sets that included both the weighted and un-weighted tardiness problems. The results show that the performance of the hybrid approach is superior to that of the SA, genetic algorithm, TS and ant colony optimization approaches, and is comparable with the Tabu-VNS approach. And the proposed approach found new upper bound values for many benchmark problems with an acceptable computational time.

We describe a global optimization method called mean field annealing (MFA) and its application to two basic problems in seismic data processing: Seismic deconvolution and surface related multiple attenuation. MFA replaces the stochastic nature of the simulated annealing method with a set of deterministic update rules that act on the average value of the variables rather than on the variables themselves, based on the mean field approximation. As the temperature is lowered, the MFA rules update the variables in terms of their values at a previous temperature. By minimizing averages, it is possible to converge to an equilibrium state considerably faster than a standard simulated annealing method. The update rules are dependent on the form of the cost function and are obtained easily when the cost function resembles the energy function of a Hopfield network. The mapping of a problem onto a Hopfield network is not a precondition for using MFA, but it makes analytic calculations simpler. The seismic deconvolution problem can be mapped onto a Hopfield network by parameterizing the source and the reflectivity in terms of binary neurons. In this context, the solution of the problem is obtained when the neurons of the network reach their stable states. By minimizing the cost function of the network with MFA and using an appropriate cooling schedule, it is possible to escape local minima. A similar idea can also be applied to design an operator that attenuates surface related multiple reflections from plane‐wave transformed seismograms assuming a 1-D earth. The cost function for the multiple elimination problem is based on the criterion of minimum energy of the multiple suppressed data.

This paper presents an unsupervised segmentation approach applying the mean field annealing (MFA) heuristic with the modified cost function. The idea is to cast a clustering problem as a minimization problem where the criteria for the optimum segmentation is chosen as the minimization of the Euclidean distance between samples to cluster centers. To resolve the optimal problem using a Hopfield or simulated annealing neural network, the penalty terms are combined into a weighted sum using several coefficients determined by user. Using the MFA network to medical image segmentation, the need for finding weighting factors in the energy function can be eliminated and the rate of convergence is much faster than that of simulated annealing. The experimental results show that good and valid solutions can be obtained using the MFA neural network.

Multi-constrained quality-of-service routing (QoSR) is to find a feasible path that satisfies multiple constraints simultaneously, as an NPC problem, which is also a big challenge for wireless mesh networks. In this paper, we propose a novel Routing Scheme based on Mean Field Annealing (MFA_RS) to solve this problem. MFA_RS first uses a function of the wireless link’s delay and capacity as the cost function, both of which are QoS parameters, and then seeks to find a feasible path by mean field annealing. Because MFA_RS uses a set of deterministic equations to replace the stochastic process in Simulated Annealing (SA), and uses saddle point approximation in the calculation of the stationary probability distribution at equilibrium, thus the convergence time is much less than the algorithm based on SA. Simulation results demonstrate that MFA_RS is an effective algorithm and is very fit for wireless mesh networks where the topology may be changing constantly.

Early attempts of optimised structural designs go back to the 1600s, when Leonardo da Vinci and Galileo conducted tests of models and full-scale structures [1]. A 1994`s review of structural optimization can be found in the study by Cohn and Dinovitzer [2], who pointed out that there was a gap between theoretical studies and the practical application in practice. They also noted the short number of studies that concentrated on concrete structures. A review of structural concrete optimization can be found in the 1998`s study by Sarma and Adeli [3]. The methods of structural optimization may be classified into two broad groups: exact methods and heuristic methods. The exact methods are the traditional approach. They are based on the calculation of optimal solutions following iterative techniques of linear programming [4,5]. The second main group comprises the heuristic methods, whose recent development is linked to the evolution of artificial intelligence procedures. This group includes a broad number of search algorithms [6-9], such as genetic algorithms, simulated annealing, threshold accepting, tabu search, ant colonies, etc. These methods have been successful in areas different to structural engineering [10]. They consist of simple algorithms, but require a great computational effort, since they include a large number of iterations in which the objective function is evaluated and the structural restrictions are checked. Among the first studies of heuristic optimization applied to structures, the contributions of Jenkins [11] and of Rajeev and Krishnamoorthy [12] in the early 1990s are to be mentioned. Both authors applied genetic algorithms to the optimization of the weight of steel structures. As regards RC structures, early applications in 1997 include the work of Coello et al [13], who applied genetic algorithms to the economic optimization of RC beams. Recently, there has been a number of RC applications [14-16], which optimize RC beams and building frames by genetic algorithms. Also recently, our research group has applied simulated annealing and threshold acceptance to the optimization of walls, frame bridges and building frames [17-20]. However, despite advances on structural concrete optimization, present design-office practice of concrete structures is much conditioned by the experience of structural engineers. Most procedures are based on the adoption of cross-section dimensions and material grades based on sanctioned common practice. Once the structure is defined, it follows the analysis of stress resultants and the computation of passive and active O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

This chapter presents a comparison of population-based (e.g. Genetic Algorithms (GA), Firefly Algorithm (FA), and Ant Colony Optimization (ACO))and single point search meta-heuristic methods (e.g. Simulated Annealing (SA), Threshold Accepting (TA), and Tabu Search (TS)) applied to an optimal tuning of a universal digital proportional-integral-derivative (PID) controller. The PID controllers control feed rate and maintain glucose concentration at the desired set point for an E. coli MC4110 fed-batch cultivation process. The model of the cultivation process is represented by dynamic non-linear mass balance equations for biomass and substrate. In the control the design measurement, process noise, and time delay of the glucose measurement system were taken into account. To achieve good closed-loop system the constants (Kp, Ti, Td, b, c and N) were tuned in the PID controller algorithm so the controller can provide control action designed for the specific process requirements resulting in an optimal set of PID controller settings. For a time the controllers set and maintained the control variable at the desired set point during the E. coli MC4110 fed-batch cultivation process. Average, best, and worst objective function values and PID controller's parameters were used as criteria to compare the performance of the considered meta-heuristic algorithms. This indicates that the population-based meta-heuristics performs better than the single point search methods. GA and ACO show better performance than FA. It also indicates that TS results are comparable to those of FA. The results show that SA and TA algorithms failed to solve the PID controller tuning problem.