A comparative study of annealing methods for batch scheduling problems
TL;DR: In this paper, the performance of four different annealing strategies, Simulated Annealing (SA), Threshold Acceptance (TA), and Multicanonical Jump Walk Annealing, with and without window factor scheduling have been compared for small and large size problems.
Abstract: Batch Scheduling is an important problem, relevant to a large sector of the processing industries. Methods like Simulated Annealing have been traditionally used in dealing with scheduling problems that are combinatorially complex. In this paper the performance of four different annealing strategies, Simulated Annealing (SA), Threshold Acceptance (TA) and Multicanonical Jump Walk Annealing (MJWA) with and without window factor scheduling have been compared for small and large size problems. Criteria such as robustness of the method and mean deviation from the optimal solution reveal that the MJWA with window factor scheduling is far superior to SA, TA or MJWA without window factor scheduling.
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TL;DR: In this article, the authors studied the consequences of contamination of raw skim milk with Pseudomonas fluorescens CNRZ 798 on the stability of the corresponding UHT milk during storage.
Abstract: Among the incriminating factors in the destabilisation of ultra-high-temperature (UHT) milk during storage, the heat-resistant proteases of Pseudomonas are considered to play a role. The objective of this work was to study the consequences of contamination of raw skim milk with Pseudomonas fluorescens CNRZ 798 on the stability of the corresponding UHT milk during storage. After 92 days, milk destabilisation was determined by the presence of a gelled sediment and low value to phosphate test (2.4 mL for control against 0 mL of phosphate solution for milk contaminated before UHT treatment) and the presence of aggregates. For the UHT control milk and UHT milk manufactured from raw skim milk contaminated with P. fluorescens, an increase in the size of the casein micelles (205 and 332 nm, respectively), a decrease in the zeta potential (−16.6 and −14.0 mV, respectively) and decrease in the level of hydration (2.00 and 1.55 g of water per gramme of dried pellet, respectively) were detected. The increase in pH 4.6-soluble nitrogen and trichloroacetic acid-soluble nitrogen content for UHT milk previously contaminated were ten- and fivefold higher than those for control milk, respectively. The trichloroacetic acid-soluble nitrogen fraction of the milk contaminated before treatment contained 118, 22, 4 and 9 peptides from β-, αs1-, αs2- and κ-caseins in comparison to only 22, 19, 6 and 4 peptides for the control milk. This study showed that destabilisation of UHT milk was due to proteolysis of casein micelles.
39 citations
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TL;DR: The method introduced in this paper, the Standing Wave Annealing Technique (SWAT), will extend the applicability of the standing wave equations to solve efficiently any single or multiobjective optimization problem for binary SMB systems with linear adsorption isotherms.
Abstract: In this paper a nonlinear mathematical programming model is formulated and is solved by an innovative stochastic optimization algorithm, Simulated Annealing. The model is designed for simultaneous optimization of all variables that determine the design and construction as well as the operating costs of an SMB system. At the core of this model are the standing wave equations, which are algebraic relationships that offer a significant modeling advantage in optimizing SMB systems. Specifically, by solving these equations the desired purity and yield for nonideal systems is guaranteed. They also provide computational efficiency and tractability by eliminating numerical solutions of ordinary or partial differential equations. The method introduced in this paper, the Standing Wave Annealing Technique (SWAT), will extend the applicability of the standing wave equations to solve efficiently any single or multiobjective optimization problem for binary SMB systems with linear adsorption isotherms. Two examples from...
19 citations
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TL;DR: A constraint-based model and system for batch-process scheduling and it is found that the approach can schedule complex plants and solve large-size problems by finding feasible solutions satisfying all imposed constraints, which include some hard ones such as those of finite wait time.
Abstract: Batch processing plants are attractive due to their suitability for the manufacturing of small-volume, high-value added products. Scheduling batch plants by using computer-aided systems is important for improving the plant productivity, since it harmonizes the entire plant operation efficiently to achieve production goals. However, the current scheduling approaches for batch plants are inadequate. This research develops a constraint-based model and system for batch-process scheduling and investigates their performance. The proposed constraint model analyses and brings together many scheduling constraints, adds new constraints and categorizes them according to their functionality. A computer scheduling system, Batch Processing Scheduler, is developed in C++ to apply the model. A number of examples have been devised to study the performance of our constraint-based approach. It is found that the approach can schedule complex plants and solve large-size problems by finding feasible solutions satisfying all imposed constraints, which include some hard ones such as those of finite wait time. It is also identified that the first feasible solution can be found very quickly, but much more time, even exponentially more, is required to find the optimal solution particularly for complex and large-size problems. Feasibility and limitations of the proposed methodology are demonstrated by the results.
16 citations
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TL;DR: In this paper, a support vector regression-based process model was developed for approximating the non-linear relationship between the fermentation operating variables and the α-amylase yield.
Abstract: The Streptomyces lonarensis strain NCL 716 hydrolyses starch to produce a mixture of maltotriose (G3) and maltotetraose (G4) along with maltose (G2). The objective of the present work was to determine an optimum cost effective media composition for the production of α-amylase from this strain. The most influential factor was found to be starch while the least influential factor found was peptone by Plackett–Burman method. Peptone amount was kept constant throughout the fermentation. Peptone, which is one of the expensive media components was used at a concentration of 1 g/L, which made the optimum media composition cost effective. A support vector regression-based process model was developed for approximating the non-linear relationship between the fermentation operating variables and the α-amylase yield. Multicanonical Jump Walk Annealing, a stochastic optimization technique is used to obtain optimal operating variables to maximize amylase yield. The maximum amylase activity thus obtained was in good agreement with the experimental values at the optimized levels. The optimum media composition obtained by this method was: yeast extract: 4.53 g/L, starch: 20.246 g/L, K2HPO4: 0.0827%, MgSO4: 0.15%, peptone: 1 g/L. A maximum enzyme activity of 297 U/mL, which was achieved using the above approaches compares well with the activity of reported amylases producing maltooligosaccharides.
8 citations
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TL;DR: This research proposes a scheduling model in batch plants, considering complex real-world constraints that were seldom addressed together, and finds that the CP approach has a better performance in solving batch plant scheduling problems with complex constraints although it needs longer time.
Abstract: The application of parallel machines and storage facilities provides flexibility but raises challenges for batch plants. This research proposes a scheduling model in batch plants, considering complex real-world constraints that were seldom addressed together. Two optimisation approaches, genetic algorithm GA and constraint programming CP, are applied to solve the complex batch plant scheduling problem. A case study and scalability tests are conducted to investigate different performance of GA and CP in the problem to prepare for further research application. It is found that the CP approach has a better performance in solving batch plant scheduling problems with complex constraints although it needs longer time. The 'restart' search strategy is better than two other search strategies for the CP approach.
2 citations
References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
38,868 citations
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TL;DR: A numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100 and a high-precision computation of the interfacial free energy per unit area is reported.
Abstract: Relying on the recent proposed multicanonical algorithm, we present a numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100\ifmmode\times\else\texttimes\fi{}100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to ${\mathit{L}}^{2.65}$. On our largest lattice we gain more than 2 orders of magnitude as compared to a standard heat-bath algorithm. As a first physical application we report a high-precision computation of the interfacial free energy per unit area.
1,349 citations
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IBM1
TL;DR: In this article, a new general purpose algorithm for the solution of combinatorial optimization problems is presented, which is even simpler structured than the wellknown simulated annealing approach, and demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error-correcting codes.
Abstract: A new general purpose algorithm for the solution of combinatorial optimization problems is presented. The new threshold accepting method is even simpler structured than the wellknown simulated annealing approach. The power of the new algorithm is demonstrated by computational results concerning the traveling salesman problem and the problem of the construction of error-correcting codes. Moreover, deterministic (!) versions of the new heuristic turn out to perform nearly equally well, consuming only a fraction of the computing time of the stochastic versions. As an example, the deterministic threshold accepting method yields very-near-to-optimum tours for the famous 442-cities traveling salesman problem of Grotschel within 1 to 2 s of CPU time.
1,081 citations
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TL;DR: In this article, a general framework for handling a wide range of scheduling problems arising in multiproduct/multipurpose batch chemical plants is presented, where the use of utilities by the various tasks may vary over the task processing time, and may be constant or proportional to the batchsize.
Abstract: A general framework for handling a wide range of scheduling problems arising in multiproduct/multipurpose batch chemical plants is presented. Batch processes involving a variety of complexities are represented using a state-task network. The novel feature of this representation is that both the individual batch operations (“tasks”) and the feedstocks, intermediate and final products (“states”) are included explicitly as network nodes. Processes involving sharing of raw materials and intermediates, batch splitting and mixing and recycles of material, can be represented unambiguously as such networks. The short-term scheduling problem is formulated as a mixed integer linear program (MILP) based on a discrete time representation. Flexible equipment allocation, variable batchsizes and mixed intermediate storage policies involving both dedicated and multipurpose storage vessels are taken into account. Limited availability of raw materials, both at the start and during the time horizon of interest, is accommodated. Product deliveries may take place at any time during the horizon, and the amounts involved may be either fixed or variable. The use of utilities by the various tasks may vary over the task processing time, and may be constant or proportional to the batchsize. The availability and/or cost of utilities may vary over the time horizon of interest. The objective function is the maximization of a profit function involving the value of the products, and the cost of raw materials, utilities and material storage. The formulation may result in MILPs involving large numbers of binary variables. Issues pertaining to the efficient solution of these problems are discussed in Part II of this paper.
923 citations
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TL;DR: In this paper, the authors presented a mathematical formulation for short-term scheduling of batch plants based on a continuous time representation and results in a mixed integer linear programming (MILP) problem.
Abstract: During the last decade, the problem of production scheduling has been realized to be one of the most important problems in industrial plant operations especially when multipurpose/multiproduct batch processes are involved. This paper presents a novel mathematical formulation for the short-term scheduling of batch plants. The proposed formulation is based on a continuous time representation and results in a mixed integer linear programming (MILP) problem. The novel elements of the proposed formulation are (i) the decoupling of the task events from the unit events, (ii) the time sequencing constraints, and (iii) its linearity. In contrast to the previously presented continuous-time scheduling formulations, the proposed approach leads to smaller and simpler mathematical models which exhibit fewer binary and continuous variables, have smaller integrality gaps, require fewer constraints, need fewer linear programming relaxations, and can be solved in significantly less CPU time. Several examples are presented ...
443 citations
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