Multiobjective Optimization of a Biofuel Supply Chain Using Random Matrix Generators

Introduction

Real-world industrial optimization often revolves around systems which have various complexities and uncertainties. Therefore heavy computational rigor becomes required when faced with these problems. This is when metaheuristic techniques become indispensable (Ganesan et al., 2016; Ganesan et al., 2018a; Yang, 2013). A few examples of such complexities are: multiobjective (MO), non-convex, highly nonlinear, interlinked variables and multivariate. All these issues existing in a single problem have the capability to overwhelm the computational technique (conventional metaheuristics) - resulting in weak optimization capability. Thus, conventional metaheuristics are often improved via hybridization or other algorithmic enhancements (Ganesan et al., 2015; Ganesan et al., 2018b; Hong et al., 2016; Dong et al., 2016). As for optimization problems which are MO, the following frameworks have been introduced in the past:

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  Strength Pareto Evolutionary Algorithm (SPEA-2) (Zhao et al., 2016)

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  Weighted sum approach (Naidu et al., 2014)

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  Normal-Boundary Intersection (NBI) (Ahmadi et al., 2015; Ganesan et al., 2013)

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  Non-Dominated Sorting Genetic Algorithm (NSGA-II) (Mousavi et al., 2016)

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  Epsilon-constraint method (Bouziaren and Brahim Aghezzaf, 2018)

Scalarization and NBI approaches involve the aggregation of multiple target objectives. This effectively transforms the MO problem into a single objective one - reducing its complexity to a high degree and thus making it easier to solve. Although other techniques like non-dominated sorting, SPEA and epsilon-constraint approaches are equally effective for solving triple-objective MO problems, the weighted sum approach (scalarization technique) was used in this work since it was easier to work with. This is in the sense that scalarization approaches are readily compatible when used with a variety of metaheuristics as compared to other methods (e.g. nondominated sorting methods). Once the objective function is aggregated, the problem could be solved using a variety metaheuristic as a single objective problem. This makes the weighted sum approach a very attractive option since a plethora of metaheuristic techniques could be implemented alongside it. On the other hand, the epsilon-constraint method could become tedious when dealing with problems having more than two objectives since the problem has to be solved multiple times with varying epsilon constraints - making it a computationally expensive approach.

In recent works, Cuckoo Search (CS) has been seen to be highly effective in solving MO supply chain problems as compared to other heuristics (e.g. bee colony optimization, genetic algorithm, particle swarm optimization and artificial fish swarm) (Elkazzaz et al., 2018; Liang and Sun, 2019, Srivastav and Agrawal, 2015). Therefore CS approach was utilized in conjunction with the weighted sum approach to tackle the biofuel supply chain problem in this work.