Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems. (C) 2004 Elsevier Ltd. All rights reserved.

Evolutionary Algorithm for the Determination of Optimal Mode of Bioreactor Operation

Stirred tank bioreactors, employed in the production of a variety of biologically active chemicals, are often operated in batch, fed-batch, and continuous modes of operation. The optimal design of bioreactor is dependent on the kinetics of the biological process, as well as the performance criteria (yield, productivity, etc.) under consideration. In this paper, a general framework is proposed for addressing the two key issues related to the optimal design of a bioreactor, namely, (i) choice of the best operating mode and (ii) the corresponding flow rate trajectories. The optimal bioreactor design problem is formulated with initial conditions and inlet and outlet flow rate trajectories as decision variables to maximize more than one performance criteria (yield, productivity, etc.) as objective functions. A computational methodology based on genetic algorithm approach is developed to solve this challenging multiobjective optimization problem with multiple decision variables. The applicability of the algorithm is illustrated by solving two challenging problems from the bioreactor optimization literature.

Studies in biogas technology. Part I. Performance of a conventional biogas plant

This paper gives an account of a conventional 5.66 m3/day (200 cubic ft/day) biogas plant which has been instrumented, operated and monitored for 2 1/2 years. The observations regarding input to the plant, sludge and biogas outputs, and conditions inside the digester, have been described. Three salient features stand out. First, the observed average daily gas yield is much less than the rated capacity of the plant. Secondly, the plants show ease of operation and a very slow response to reductions and cessations of dung supply. Thirdly, the unexpectedly marked uniformity of density and temperature inside the digester indicates the almost complete absence of the stratification which is widely believed to take place; hence, biogas plants may be treated as isothermal, ‘ uniform ’ density, most probably imperfectly mixed, fed-batch reactors operating at the mean ambient temperature and the density of water.

Room-temperature synthesis of gold nanoparticles - Size-control by slow addition

We report a simple and rapid process for the room-temperature synthesis of gold nanoparticles using tannic acid, a green reagent, as both the reducing and stabilising agent. We systematically investigated the effect of pH on the size distribution of nanoparticles synthesized. Based on induction time and zeta- potential measurements, we show that particle size distribution is controlled by a fine balance between the rates of reduction (determined by the initial pH of reactants) and coalescence (determined by the pH of the reaction mixture) in the initial period of growth. This insight led to the optimal batch process for size-controlled synthesis of 2-10 nm gold nanoparticles - slow addition (within 10 minutes) of chloroauric acid into tannic acid.

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.

Temperature characteristics of the billet and the dies in a small batch forging production

The work reported herein is part of an on-going programme to develop a computer code which, given the geometrical, process and material parameters of the forging operation, is able to predict the die and the billet cooling/heating characteristics in forging production. The code has been experimentally validated earlier for a single forging cycle and is now validated for a small batch production. To facilitate a step-by-step development of the code, the billet deformation has so far been limited to its surface layers, a situation akin to coining. The code has been used here to study the effects of die preheat-temperature, machine speed and rate of deformation the cooling/heating of the billet and the dies over a small batch of 150 forgings. The study shows: that there is a pre-heat temperature at which the billet temperature changes little from one forging to the next; that beyond a particular number of forgings, the machine speed ceases to have any pronounced influence on the temperature characteristics of the billet; and that increasing the rate of deformation reduces the heat loss from the billet and gives the billet a stable temperature profile with respect to the number of forgings. The code, which is simple to use, is being extended to bulk-deformation problems. Given a practical range of possible machine, billet and process specifics, the code should be able to arrive at a combination of these parameters which will give the best thermal characteristics of the die-billet system. The code is also envisaged as being useful in the design of isothermal dies and processes.

Experimental investigation of die wear in small-batch hammer-forging under unlubricated conditions

Wear of dies is a serious problem in the forging industry. The materials used for the dies are generally expensive steel alloys and the dies require costly heat treatment and surface finishing operations. Degeneration of the die profile implies rejection of forged components and necessitates resinking or replacement of the die. Measures which reduce wear of the die can therefore aid in the reduction of production costs. The work reported here is the first phase of a study of the causes of die wear in forging production where the batch size is small and the machine employed is a light hammer. This is a problem characteristic of the medium and small scale area of the forging industry where the cost of dies is a significant proportion of the total capital investment. For the same energy input and under unlubricated conditions, die wear has been found to be sensitive to forging temperature; in cold forging the yield strength of the die material is the prime factor governing the degeneration of the die profile, whilst in hot forging the wear resistance of the die material is the main factor which determines the rate of die wear. At an intermediate temperature, such as that characteristic of warm forging, the die wear is found to be less than that in both cold and hot forging. This preliminary study therefore points to the fact that the forging temperature must be taken into account in the selection of die material. Further, the forging industry must take serious note of the warm forging process, as it not only provides good surface finish, as claimed by many authors, but also has an inherent tendency to minimize die wear.

Two temperature viscous accretion flows around rotating black holes: Description of under-fed systems to ultra-luminous X-ray sources

We discuss two temperature accretion disk flows around rotating black holes. As we know that to explain observed hard X-rays the choice of Keplerian angular momentum profile is not unique, we consider the sub-Keplerian regime of the disk. Without any strict knowledge of the magnetic field structure, we assume the cooling mechanism is dominated by bremsstrahlung process. We show that in a range of Shakura-Sunyaev viscosity parameter 0.2 greater than or similar to alpha greater than or similar to 0.0005, flow behavior varies widely, particularly by means of the size of disk, efficiency of cooling and corresponding temperatures of ions and electrons. We also show that the disk around a rotating black hole is hotter compared to that around a Schwarzschild black hole, rendering a larger difference between ion and electron temperatures in the former case. With all the theoretical solutions in hand, finally we reproduce the observed luminosities (L) of two extreme cases-the under-fed AGNs and quasars (e.g. Sgr A') with L greater than or similar to 10(33) erg/s to ultra-luminous X-ray sources with L similar to 10(41) erg/s, at different combinations of mass accretion rate, ratio of specific heats, Shakura-Sunyaev viscosity parameter and Kerr parameter, and conclude that Sgr A' may be an intermediate spinning black hole.

Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time.

Effect of process variables on die-billet temperature history in a slow speed hot coining type process

A computer code is developed as a part of an ongoing project on computer aided process modelling of forging operation, to simulate heat transfer in a die-billet system. The code developed on a stage-by-stage technique is based on an Alternating Direction Implicit scheme. The experimentally validated code is used to study the effect of process specifics such as preheat die temperature, machine ascent time, rate of deformation, and dwell time on the thermal characteristics in a batch coining operation where deformation is restricted to surface level only.

Performance comparison of batch and continuous flow surface aeration systems

The oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. The aeration process can be analyzed in two ways such as batch and continuous systems. The process behaviors of batch and continuous flow systems are different from each other. The experimental and numerical results obtained through the batch systems cannot be relied on and applied for the designing of the continuous aeration tank. Based on the experimentation on batch and continuous type systems, the present work compares the performance of both the batch and continuous surface aeration systems in terms of their oxygen transfer capacity and power consumption. A simulation equation developed through experimentation has shown that continuous flow surface aeration systems are taking more energy than the batch systems. It has been found that batch systems are economical and better for the field application but not feasible where large quantity of wastewater is produced.

Minimizing total completion time on a batch processing machine with job families

We consider the problem of minimizing the total completion time on a single batch processing machine. The set of jobs to be scheduled can be partitioned into a number of families, where all jobs in the same family have the same processing time. The machine can process at most B jobs simultaneously as a batch, and the processing time of a batch is equal to the processing time of the longest job in the batch. We analyze that properties of an optimal schedule and develop a dynamic programming algorithm of polynomial time complexity when the number of job families is fixed. The research is motivated by the problem of scheduling burn-in ovens in the semiconductor industry

Minimizing total completion time on batch processing machines

We study the problem of minimizing total completion time on single and parallel batch processing machines. A batch processing machine is one which can process up to B jobs simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. This problem is motivated by burn-in operations in the final testing stage of semiconductor manufacturing and is expected to occur in other production environments. We provide an exact solution procedure for the single-machine problem and heuristic algorithms for both single and parallel machine problems. While the exact algorithms have limited applicability due to high computational requirements, extensive experiments show that the heuristics are capable of consistently obtaining near-optimal solutions in very reasonable CPU times.

Heuristic algorithms for scheduling of a batch processor in automobile gear manufacturing

In this paper we address a scheduling problem for minimising total weighted tardiness. The motivation for the paper comes from the automobile gear manufacturing process. We consider the bottleneck operation of heat treatment stage of gear manufacturing. Real life scenarios like unequal release times, incompatible job families, non-identical job sizes and allowance for job splitting have been considered. A mathematical model taking into account dynamic starting conditions has been developed. Due to the NP-hard nature of the problem, a few heuristic algorithms have been proposed. The performance of the proposed heuristic algorithms is evaluated: (a) in comparison with optimal solution for small size problem instances, and (b) in comparison with `estimated optimal solution' for large size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently obtaining near-optimal solutions (that is, statistically estimated one) in very reasonable computational time.

Strategies for efficient start-up of continuous biooxidation process for refractory gold ores

Strategies for efficient start-up of a continuous process for biooxidation of refractory gold ore and concentrate obtained from Hutti, Gold Mines Limited (HGML), India are discussed in this work. The biooxidation of the concentrate at high pulp density (10%) with wild strain of Thiobacillus ferrooxidans isolated from HGML mines is characterized by significant lag phase (20 days) and incomplete oxidation (35%) even after prolonged operation (60 days). Two strategies, biooxidation with concentrate adapted cells and a step leaching strategy, in which the pulp density is progressively increased from 2% to 10% were considered and the latter resulted in efficient biooxidation of concentrate. Conversion of such a process from batch to continuous operation is shown to result in complete biooxidation of the concentrate and gold extraction efficiency in excess of 90%. (C) 2002 Elsevier Science Ltd. All rights reserved.