Multi-Objective Optimization

The following sections are included:

• Preface to the Second Edition
• Preface to the First Edition
• Contents

The following sections are included:

• Process Optimization
• Multi-Objective Optimization: Basics
• Multi-Objective Optimization: Methods
• Alkylation Process Optimization for Two Objectives
  • Alkylation Process and its Model
  • Multi-Objective Optimization Results and Discussion
• Scope and Organization of the Book
• References
• Exercises

Multi-objective optimization (MOO) has received considerable attention from researchers in chemical engineering. Bhaskar et al. (2000a) have reviewed reported applications of MOO in chemical engineering until 2000. In this chapter, nearly hundred MOO applications in chemical engineering reported in journals from 2000 until mid 2007 are reviewed briefly. These are categorized into five groups: (1) process design and operation, (2) biotechnology and food industry, (3) petroleum refining and petrochemicals, (4) pharmaceuticals and other products/processes, and (5) polymerization. Applications reported in this book are not included in this review.

In this chapter, we provide a general overview of evolutionary multiobjective optimization, with particular emphasis on algorithms in current use. Several applications of these algorithms in chemical engineering are also discussed and analyzed. We also provide some additional information about public-domain resources available for those interested in pursuing research in this area. In the final part of the chapter, some potential areas for future research are briefly described.

Two popular evolutionary techniques used for solving multi-objective optimization problems, namely, genetic algorithm and simulated annealing, are discussed. These techniques are inherently more robust than conventional optimization techniques. Incorporating a macro-macro mutation operator, namely, the jumping gene operator, inspired from biology, reduces the computational time required for convergence, significantly. It also helps to obtain the global optimal Pareto set where several Paretos exist. In this article, detailed descriptions of genetic algorithm and simulated annealing with the various jumping gene adaptations are presented and then three benchmark problems are solved using them.

For most practical optimization problems involving computationally expensive analysis, a brute force approach relying on actual analysis is not computationally viable. Surrogates and approximations are regularly used in lieu of computationally expensive analysis during the course of optimization. Existing surrogate assisted optimization approaches often use the same approximation model (surrogate) for all objectives and constraints in all regions of the search space. The choice of a type of surrogate model over another is non-trivial and such an a priori choice limits flexibility in representation. In this chapter, we introduce a multi-objective evolutionary algorithm embedded with multiple adaptive spatially distributed surrogates of multiple types. A nondominated sorting genetic algorithm is used as the underlying optimizer. Instead of a single global surrogate, local surrogates of multiple types are constructed around each offspring solution and a multi-objective search is conducted using the best surrogate for the objective and the constraint function. The set of nondominated solutions obtained from each of such local searches are merged to form the potential offspring pool. Top N offspring solutions identified via nondominated sorting and crowding are evaluated using actual analysis resulting in the offspring population. Such an approach offers the flexibility of representation that is often required in practical problems and at the same time capitalizes on the benefits offered by various types of surrogates in different regions of the search space. The performance of the proposed algorithm i.e. surrogate assisted multi-objective optimization algorithm (SAMO) is compared with the baseline Nondominated Sorting Genetic Algorithm II (NSGA-II) to highlight the benefits. The results obtained by SAMO is consistently better (at par with a few) than NSGA-II for the problems presented in this chapter based on an hypervolume metric. One can observe significant benefits in terms of the rate of convergence for SAMO over NSGA-II.

Problems in chemical engineering, like most real-world optimization problems, typically, have several conflicting performance criteria or objectives and they often are computationally demanding, which sets special requirements on the optimization methods used. In this chapter, we point out some shortcomings of some widely used basic methods of multi-objective optimization. As an alternative, we suggest using interactive approaches where the role of a decision maker or a designer is emphasized. Interactive multi-objective optimization has been shown to suit well for chemical process design problems because it takes the preferences of the decision maker into account in an iterative manner that enables a focused search for the best Pareto optimal solution, that is, the best compromise between the conflicting objectives. For this reason, only those solutions that are of interest to the decision maker need to be generated making this kind of an approach computationally efficient. Besides, the decision maker does not have to compare many solutions at a time which makes interactive approaches more usable from the cognitive point of view. Furthermore, during the interactive solution process the decision maker can learn about the interrelationships among the objectives. In addition to describing the general philosophy of interactive approaches, we discuss the possibilities of interactive multi-objective optimization in chemical process design and give some examples of interactive methods to illustrate the ideas. Finally, we demonstrate the usefulness of interactive approaches in chemical process design by summarizing some reported studies related to, for example, paper making and sugar industries. Let us emphasize that the approaches described are appropriate for problems with more than two objective functions.

This chapter presents a description of two multi-objective optimization (MOO) methods, Net Flow Method (NFM) and Rough Set Method (RSM), with a particular focus on engineering applications. Each of the methods provides its own algorithm for ranking the Pareto domain. NFM, which is a hybrid of the ELECTRE and PROMETHEE optimization schemes, employs the preferences of decision-makers in the form of three threshold values for each criterion and one set of relative weights that are used to classify the entire Pareto domain. RSM uses a set of decision rules that are based on the preferences of decision-makers that are established through the ranking of a small, diverse sample set extracted from the Pareto domain. These rules are then applied to the entire Pareto domain to determine the preferred zone of operation. Both methods require the intervention of experts to provide their knowledge and their preferences regarding the operation of the process.

The two methods are used to optimize the production of gluconic acid for multiple objectives. In this fermentation process, it is desired mainly to maximize the productivity and the final concentration of gluconic acid. Other objective functions, the final substrate concentration and the initial inoculum biomass concentration, can also be added to make a three- and four-objective optimization problem. It is shown that NFM and some variants of RSM performed similarly and possess good robustness.

Liquefied natural gas (LNG) is a clean burning fossil fuel, which offers an energy density comparable to petrol and diesel fuels. LNG production has grown five-fold in the last 25 years. Although there are a few dominant processes for land-based liquefaction plants, there is much interest in the production of LNG off-shore, particularly “Floating LNG” or FLNG. One option for FLNG is gas phase refrigeration cycles, which are very flexible and inherently safer than condensing refrigeration processes. A shaftwork targeting method has recently been developed for multi-stage gas-phase refrigeration systems (Shah and Hoadley, 2007). In this chapter, a study has been carried out to optimize these systems for multiple objectives, by varying the operating parameters such as the minimum temperature driving force (ΔT_min) and pressure ratio. An interesting aspect of this study is the use of a superstructure model for the process simulation in order to allow for different numbers of refrigeration stages (from 2 to 7 stages). The two objective functions considered in the present optimization study are the capital cost and the energy requirement. A Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to generate the Pareto-optimal front, and an extended range of process parameters including the number of refrigeration stages is tested. The multi-objective optimization results are presented and discussed for two cases: cooling of a nitrogen stream using a nitrogen gas refrigerant, and the dual nitrogen/natural gas refrigerant process for LNG.

Feed optimization in the fluidized catalytic cracking (FCC) process is a prominent chemical engineering problem, where the objective is to maximize the production of high-quality gasoline stocks at a low energy consumption level. However, the various feeds, based on the density and volumetric flow rate of its constituent stream, are conflicting in nature and subjected to many practical constraints. As such, this chapter presents the application of a multi-objective evolutionary algorithm (MOEA) which will simultaneously optimize the various flow streams in a FCC feed surge drum of a local refinery. An interactive Graphical User Interface (GUI) based MOEA toolbox developed by the authors is used as the platform for optimization. The various trade-off surfaces between the different objectives evolved by the MOEA provide further insights to this problem and allow more optimal choices during the decision making process. Lastly, a performance comparison based on several key performance indexes shows that the overall economic gain offered by MOEA optimization against the conventional approach like linear programming is significantly higher.

For optimal design of chemical processes, selectivity, productivity or simple profit is often used as the sole objective for optimization. Several studies in the past decade have investigated multi-objective optimization (MOO) of chemical processes with selectivity, yield, productivity and/or energy as the objectives; economic criterion such as profit was not an objective in many of these studies. Further, environmental objectives are gaining importance due to the increasing emphasis on environmental protection and sustainability. In this chapter, the optimal design of several processes for multiple economic and environmental objectives is studied. Simultaneous optimization of the selected objectives was carried out using the jumping gene version of the elitist Non-dominated Sorting Genetic Algorithm (NSGA-II-aJG).

For process optimization with respect to several economic criteria such as net present worth, payback period and operating cost, the classical Williams and Otto (WO) process and an industrial low-density polyethylene (LDPE) plant are considered. Results show that either single optimal solution or Pareto-optimal solutions are possible for process design problems depending on the objectives and model equations. Subsequently, industrial ecosystems are studied for optimization with respect to both economic and environmental objectives. Economic objective is important as companies are inherently profit-driven, and there is often a tradeoff between profit and environmental impact. Pareto-optimal fronts were successfully obtained for the 6-plant industrial ecosystem optimized for multiple objectives by NSGA-II-aJG. The study and results reported in this chapter show the need and potential for optimization of processes for multiple economic and environmental objectives.

The handling of certain quantities of hazardous materials (toxic, flammable and/or explosive) can potentially create major accidents endangering the public and worker’s health, as well as the environment. Emergency response planning consists in assessing protective actions (evacuation, building protection of various degrees) for each and every area section around a hazardous facility. This chapter presents a methodology for the optimization of the response to an emergency situation around chemical plants processing hazardous substances (e.g. oil refineries, pesticide plants) by taking into account multiple criteria. A Multi-Objective Evolutionary Algorithm for the determination of the efficient set of solutions is presented.

cDNA microarray experiments produce expression ratios of thousands of genes across tens of experimental attributes. In this work, development of a robust clustering algorithm and a graph-theoretic model for reverse engineering the gene networks and their implementation using NSGA-II are reported. Clustering results on synthetic datasets as well as on a real life dataset are very encouraging. The clusters for synthetic as well as real life datasets obtained from the robust clustering are used for reverse engineering the gene regulatory networks using the graph-theoretic model inspired by ‘small world phenomena’. A set of Pareto-optimal models have been proposed. The models generated for the real life dataset concur with the available biological information. Newer functionalities and interactions are also proposed that concur with the observed cDNA microarray data.

Genetic algorithms, which have been successfully employed in various areas of chemical engineering in recent years, enable us to probe deeper into the influences of alternate metabolic pathways on multi-product synthesis. In this chapter, optimization of enzyme activities in Escherichia coli for multiple objectives is proposed and explored using a non-dominated sorting genetic algorithm for multi-objective optimization (MOO) and a detailed, non-linear dynamic model for central carbon metabolism in Escherichia coli. A wide range of optimal enzyme activities regulating the amino acid synthesis is successfully obtained for selected, integrated pathway scenarios. Identical results are obtained for gene knockouts via exhaustive search and interactive branch and bound driven by genetic algorithm. The predicted potential improvements of the optimized metabolic pathway recipe using the MOO strategy are highlighted and discussed in detail.

Evolutionary Multi-Objective Optimization (MOO) is typically employed when a decision maker wants to analyse the trade-offs involved between multiple conflicting objectives. It has the advantage of yielding a set of Pareto-optimal or equally-good solutions in a single run. However, this approach is often criticized for being extremely time consuming for chemical engineering applications. To a large extent, the solution time for evolutionary MOO depends on the computational complexity of objective functions (and constraints); the higher the computational complexity, the greater would be the time required to get to the final Pareto-optimal solution set. This is because evolutionary algorithms need to perform a large number of objective function evaluations. A significant amount of time could however be saved by replacing the computationally expensive objective functions with their cheaper approximations, known as surrogates or response surface models in an optimization framework known as surrogate-assisted MOO. This chapter compares two existing surrogate-assisted MOO strategies using two test problems from Chapter 5. Then, the computationally intensive optimization of a complex flowsheet simulation of a coal to ammonia process involving Carbon Capture and Sequestration (CCS) is solved with the modified Multiple Adaptive Spatially Distributed Surrogates (MASDS) algorithm. The results obtained by this algorithm are compared with those obtained from the Business-As-Usual (BAU) approach which evaluates objective functions directly without any surrogate-assistance. Results show significant savings, measured in terms of the hypervolume spanned by the Pareto-front obtained from the two approaches, for a fixed computation budget. The surrogate-assisted strategy thus allows for better integration of computationally complex units into large-scale plant simulations. It also yields an array of surrogates, which can be used for any future prediction of the objective function values.

Heat exchanger networks (HENs) are employed in process industries to decrease external utilities required. Retrofitting HENs in numerous plants designed in the past and operating currently can achieve significant energy savings for a small investment. For solving HEN retrofitting problems, stochastic global optimization (SGO) methods such as genetic algorithm and differential evolution are gaining popularity. This chapter is on an important issue in HEN retrofitting using SGO methods. HEN retrofitting often has inequality constraints on approach temperatures, which can be handled in SGO methods by using the penalty function method or feasibility approach. In this chapter, these two common methods are analyzed for HEN retrofitting by integrated differential evolution for single-objective optimization and elitist nondominated sorting genetic algorithm for multi-objective optimization, to establish their relative advantages. Results on two case studies for single and bi-objective optimization show that the penalty function method with a reasonable value for the penalty parameter gives better optimal solutions than the feasibility approach for HEN retrofitting problems tested.

This chapter presents three MS Excel programs, namely, EMOO (Excel based Multi-Objective Optimization), NDS (Non-Dominated Sorting) and PM (Performance Metrics) useful for Multi-Objective Optimization (MOO) studies. The EMOO program is for finding non-dominated solutions of a given MOO problem. It has both binary-coded and realcoded NSGA-II (Elitist Non-Dominated Sorting Genetic Algorithm), and two termination criteria based on chi-squared test and steady state detection. The known/true Pareto-optimal front for the application problems is not available unlike that for benchmark problems. Hence, a procedure for obtaining known/true Pareto-optimal front is described in this chapter. The NDS program is for non-dominated sorting and crowding distance calculations of the non-dominated solutions obtained from several optimization runs using same or different MOO programs. The PM program can be used to calculate the values of performance metrics between the non-dominated solutions obtained using a MOO program and the true/known Pareto optimal front. It is useful for comparing the performance of MOO programs to find the non-dominated solutions. Finally, use of EMOO, NDS and PM programs is demonstrated on MOO of amine absorption process for natural gas sweetening.

The following sections is included:

• Index