Multiobjective optimization of the flaxseed mucilage extraction process using normal-boundary intersection approach

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.

Download Full-text

A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization

Axioms ◽

10.3390/axioms8010032 ◽

2019 ◽

Vol 8 (1) ◽

pp. 32 ◽

Cited By ~ 1

Author(s):

Benjamín Barán ◽

Marcos Villagra

Keyword(s):

Combinatorial Optimization ◽

Multiobjective Optimization ◽

Theorem Proving ◽

Optimization Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Quantum Annealing ◽

Multiobjective Optimization Problems ◽

First Time

In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.

Download Full-text

Smoothing of the pareto optimal solutions set in linear multiobjective optimization problems

Annual Review in Automatic Programming ◽

10.1016/0066-4138(85)90032-1 ◽

1985 ◽

Vol 12 ◽

pp. 230-235 ◽

Cited By ~ 1

Author(s):

Jakub Gutenbaum

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Multiobjective Optimization Problems

Download Full-text

Towards a small diverse pareto-optimal solutions set generator for multiobjective optimization problems

Proceedings of the Genetic and Evolutionary Computation Conference Companion on - GECCO '18 ◽

10.1145/3205651.3205691 ◽

2018 ◽

Author(s):

Courtney Powell ◽

Katsunori Miura ◽

Masaharu Munetomo

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Multiobjective Optimization Problems

Download Full-text

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

RAIRO - Operations Research ◽

10.1051/ro/2017058 ◽

2019 ◽

Vol 53 (3) ◽

pp. 867-886

Author(s):

Mehrdad Ghaznavi ◽

Narges Hoseinpoor ◽

Fatemeh Soleimani

Keyword(s):

Multiobjective Optimization ◽

Newton Method ◽

Optimization Problems ◽

Order Relation ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Objective Functions ◽

Multiobjective Optimization Problems ◽

Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

Download Full-text

A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method

European Journal of Operational Research ◽

10.1016/0377-2217(89)90353-6 ◽

1989 ◽

Vol 39 (1) ◽

pp. 61-70 ◽

Cited By ~ 14

Author(s):

Hitoshi Yano ◽

Masatoshi Sakawa

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Unified Approach ◽

Multiobjective Optimization Problems ◽

Hyperplane Method

Download Full-text

Multi-objective enhanced PSO algorithm for optimizing power losses and voltage deviation in power systems

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-02-2015-0030 ◽

2016 ◽

Vol 35 (1) ◽

pp. 350-372 ◽

Cited By ~ 8

Author(s):

Gonggui Chen ◽

Lilan Liu ◽

Yanyan Guo ◽

Shanwai Huang

Keyword(s):

Power Systems ◽

Differential Evolution Algorithm ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Power Losses ◽

Content Type ◽

Multi Objective ◽

Dependent Variables ◽

Voltage Deviation

Purpose – For one thing, despite the fact that it is popular to research the minimization of the power losses in power systems, the optimization of single objective seems insufficient to fully improve the performance of power systems. Multi-objective VAR Dispatch (MVARD) generally minimizes two objectives simultaneously: power losses and voltage deviation. The purpose of this paper is to propose Multi-Objective Enhanced PSO (MOEPSO) algorithm that achieves a good performance when applied to solve MVARD problem. Thus, the new algorithm is worthwhile to be known by the public. Design/methodology/approach – Motivated by differential evolution algorithm, cross-over operator is introduced to increase particle diversity and reinforce global searching capacity in conventional PSO. In addition to that, a constraint-handling approach considering Constrain-prior Pareto-Dominance (CPD) is presented to handle the inequality constraints on dependent variables. Constrain-prior Nondominated Sorting (CNS) and crowding distance methods are considered to maintain well-distributed Pareto optimal solutions. The method combining CPD approach, CNS technique, and cross-over operator is called the MOEPSO method. Findings – The IEEE 30 node and IEEE 57 node on power systems have been used to examine and test the presented method. The simulation results show the MOEPSO method can achieve lower power losses, smaller voltage deviation, and better-distributed Pareto optimal solutions comparing with the Multi-Objective PSO approach. Originality/value – The most original parts include: the presented MOEPSO algorithm, the CPD approach that is used to handle constraints on dependent variables, and the CNS method which is considered to maintain a well-distributed Pareto optimal solutions. The performance of the proposed algorithm successfully reflects the value of this paper.

Download Full-text

MODIFICATION OF FIREWORKS METHOD FOR MULTIOBJECTIVE OPTIMIZATION BASED ON NON-DOMINATED SORTING

Civil Aviation High TECHNOLOGIES ◽

10.26467/2079-0619-2019-22-3-67-78 ◽

2019 ◽

Vol 22 (3) ◽

pp. 67-78

Author(s):

A. V. Panteleev ◽

A. U. Krychkov

Keyword(s):

Multiobjective Optimization ◽

Optimization Problems ◽

Complex Structure ◽

Optimal Solution ◽

Future Research ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Equal Importance ◽

Approximate Result

The article suggests a modification for numerical fireworks method of the single-objective optimization for solving the problem of multiobjective optimization. The method is metaheuristic. It does not guarantee finding the exact solution, but can give a good approximate result. Multiobjective optimization problem is considered with numerical criteria of equal importance. A possible solution to the problem is a vector of real numbers. Each component of the vector of a possible solution belongs to a certain segment. The optimal solution of the problem is considered a Pareto optimal solution. Because the set of Pareto optimal solutions can be infinite; we consider a method for finding an approximation consisting of a finite number of Pareto optimal solutions. The modification is based on the procedure of non-dominated sorting. It is the main procedure for solutions search. Non-dominated sorting is the ranking of decisions based on the values of the numerical vector obtained using the criteria. Solutions are divided into disjoint subsets. The first subset is the Pareto optimal solutions, the second subset is the Pareto optimal solutions if the first subset is not taken into account, and the last subset is the Pareto optimal solutions if the rest subsets are not taken into account. After such a partition, the decision is made to create new solutions. The method was tested on well-known bi-objective optimization problems: ZDT2, LZ01. Structure of the location of Pareto optimal solutions differs for the problems. LZ01 have complex structure of Pareto optimal solutions. In conclusion, the question of future research and the issue of modifying the method for problems with general constraints are discussed.

Download Full-text

Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

Evolutionary Computation ◽

10.1162/106365602760234108 ◽

2002 ◽

Vol 10 (3) ◽

pp. 263-282 ◽

Cited By ~ 872

Author(s):

Marco Laumanns ◽

Lothar Thiele ◽

Kalyanmoy Deb ◽

Eckart Zitzler

Keyword(s):

Evolutionary Algorithms ◽

Multiobjective Optimization ◽

Optimization Problems ◽

Fundamental Problem ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Pareto Optimal Set ◽

Multiobjective Optimization Problems ◽

Baseline Algorithm

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

Download Full-text