Multiobjective Optimization of Bioethanol Production via Hydrolysis Using Hopfield-Enhanced Differential Evolution

Multiobjective Optimization of Bioethanol Production via Hydrolysis Using Hopfield-Enhanced Differential Evolution

T. Ganesan (Universiti Teknologi Petronas, Malaysia), I. Elamvazuthi (Universiti Teknologi Petronas, Malaysia), K. Z. K. Shaari (Universiti Teknologi Petronas, Malaysia) and P. Vasant (Universiti Teknologi Petronas, Malaysia)
DOI: 10.4018/978-1-4666-6252-0.ch017
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Abstract

Many industrial problems in process optimization are Multi-Objective (MO), where each of the objectives represents different facets of the issue. Thus, having in hand multiple solutions prior to selecting the best solution is a seminal advantage. In this chapter, the weighted sum scalarization approach is used in conjunction with three meta-heuristic algorithms: Differential Evolution (DE), Hopfield-Enhanced Differential Evolution (HEDE), and Gravitational Search Algorithm (GSA). These methods are then employed to trace the approximate Pareto frontier to the bioethanol production problem. The Hypervolume Indicator (HVI) is applied to gauge the capabilities of each algorithm in approximating the Pareto frontier. Some comparative studies are then carried out with the algorithms developed in this chapter. Analysis on the performance as well as the quality of the solutions obtained by these algorithms is shown here.
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Introduction

In recent times, emerging technologies in engineering optimization frequently present themselves in multi-objective (MO) settings (Eschenauer et al., 1990; Statnikov and Matusov 1995). Strategies in MO optimization can be simply classified into two groups. First being methods that use the concept of Pareto-optimality to trace out the non-dominated solutions at the Pareto curve, for instance in; Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele, 1998) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) by Deb et al., (2002). The second group of methods is known as the scalarization/weighted approaches. During the application of these methods, the objective functions are aggregated into a single weighted function which is then resolved for a finite series of scalar (weight) values. Some established scalarization techniques include the Weighted Sum method (Fishburn, 1967; Triantaphyllou, 2000), Goal Programming (Luyben and Floudas, 1994) and Normal-Boundary Intersection method (NBI) (Das and Dennis, 1998). Using these techniques, the scalars are used to consign relative trade-offs to the objectives during the aggregation procedure. Hence, alternative near-optimal solutions are generated for various values of the scalars. See Eschenauer et al., (1990), Sandgren, (1994) and Statnikov and Matusov (1995) for detail investigations and explanations on MO techniques in engineering optimization.

In MO optimization problems, determining a highly efficient set of solutions can be a very daunting process. Some headway regarding this issue (revolving around concepts such as diversity and convergence) has been proposed in the last years. These ideas were then used as indicators to evaluate the solution set produced by the optimization algorithm (Grosan, 2003). Such assessments were then used to benchmark the algorithm’s performance. These concepts unfortunately could not absolutely state and rank the superiority of solution sets produced by an algorithm against other such sets by other algorithms. The only known concept that can be used generally for the overall ranking of solution sets is the idea of ‘Pareto-dominance’. The Hypervolume Indicator (HVI) (Zitzler et al., 2008) is a set measure reflecting the volume enclosed by a Pareto front approximation and a reference set (Knowles and Corne, 2003; Igel et al., 2007; Emmerich et al., 2005). The HVI thus guarantees strict monotonicity regarding Pareto dominance (Fleischer, 2003; Zitzler et al., 2003). This makes the ranking of solution sets and hence algorithms possible for any given MO problem.

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