PurposeThe mucilage of the Linum usitatissimum L. seed (Linseed) is one of the natural mucilages that presents a great potential to provide a food hydrocolloid with potential applications in both food and pharmaceutical industries. To increase the yield and quality of linseed oil during its production process, it is necessary to previously extract its polysaccharides. Because of this, flax mucilage production can be made viable as a byproduct of oil extraction process, which is already a product of high commercial value consolidated in the market. Thus, the purpose of this work is to optimize the mucilage extraction process of L. usitatissimum L. using the normal-boundary intersection (NBI) multiobjective optimization method.Design/methodology/approachCurrently, the variables of the process of polysaccharide extraction from different sources are optimized using the response surface methodology. However, when the optimal points of the responses are conflicting it is necessary to study the best conditions to achieve a balance between these conflicting objectives (trade-offs) and to explore the available options it is necessary to formulate an optimization problem with multiple objectives. The multiobjective optimization method used in this work was the NBI developed to find uniformly distributed and continuous Pareto optimal solutions for a nonlinear multiobjective problem.FindingsThe optimum extraction point to obtain the maximum fiber concentration in the extracted material was pH 3.81, temperature of 46°C, time of 13.46 h. The maximum extraction yield of flaxseed was pH 6.45, temperature of 65°C, time of 14.41 h. This result confirms the trade-off relationship between the objectives. NBI approach was able to find uniformly distributed Pareto optimal solutions, which allows to analyze the behavior of the trade-off relationship. Thus, the decision-maker can set extraction conditions to achieve desired characteristics in mucilage.Originality/valueThe novelty of this paper is to confirm the existence of a trade-off relationship between the productivity parameter (yield) and the quality parameter (fiber concentration in the extracted material) during the flaxseed mucilage extraction process. The NBI approach was able to find uniformly distributed Pareto optimal solutions, which allows us to analyze the behavior of the trade-off relationship. This allows the decision-making to the extraction conditions according to the desired characteristics of the final product, thus being able to direct the extraction for the best applicability of the mucilage.
A Weighted Biobjective Transformation Technique for Locating Multiple Optimal Solutions of Nonlinear Equation Systems