Mutual benefits of two multicriteria analysis methodologies: A case study for batch plant design

This paper presents a MultiObjective Genetic Algorithm (MOGA) optimization framework for batch plant design. For this purpose, two approaches are implemented and compared with respect to three criteria, i.e., investment cost, equipment number and a flexibility indicator based on work in process (the so-called WIP) computed by use of a discrete-event simulation model. The first approach involves a genetic algorithm in order to generate acceptable solutions, from which the best ones are chosen by using a Pareto Sort algorithm. The second approach combines the previous Genetic Algorithm with a multicriteria analysis methodology, i.e., the Electre method in order to find the best solutions. The performances of the two procedures are studied for a large-size problem and a comparison between the procedures is then made

A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

Multi-criteria analysis applied to multi-objective optimal pump scheduling in water systems

This work presents a multi-criteria-based approach to automatically select specific non-dominated solutions from a Pareto front previously obtained using multi-objective optimization to find optimal solutions for pump control in a water supply system. Optimal operation of pumps in these utilities is paramount to enable water companies to achieve energy efficiency in their systems. The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) is used to rank the Pareto solutions found by the Non-Dominated Sorting Genetic Algorithm (NSGA-II) employed to solve the multi-objective problem. Various scenarios are evaluated under leakage uncertainty conditions, resulting in fuzzy solutions for the Pareto front. This paper shows the suitability of the approach for quasi real-world problems. In our case-study, the obtained solutions for scenarios including leakage represent the best trade-off among the optimal solutions, under some considered criteria, namely, operational cost, operational lack of service, pressure uniformity and network resilience. Potential future developments could include the use of clustering alternatives to evaluate the goodness of each solution under the considered evaluation criteria

Linking objective and subjective modeling in engineering design through arc-elastic dominance

Engineering design in mechanics is a complex activity taking into account both objective modeling processes derived from physical analysis and designers’ subjective reasoning. This paper introduces arc-elastic dominance as a suitable concept for ranking design solutions according to a combination of objective and subjective models. Objective models lead to the aggregation of information derived from physics, economics or eco-environmental analysis into a performance indicator. Subjective models result in a confidence indicator for the solutions’ feasibility. Arc-elastic dominant design solutions achieve an optimal compromise between gain in performance and degradation in confidence. Due to the definition of arc-elasticity, this compromise value is expressive and easy for designers to interpret despite the difference in the nature of the objective and subjective models. From the investigation of arc-elasticity mathematical properties, a filtering algorithm of Pareto-efficient solutions is proposed and illustrated through a design knowledge modeling framework. This framework notably takes into account Harrington’s desirability functions and Derringer’s aggregation method. It is carried out through the re-design of a geothermal air conditioning system