Aras Ahmadi

Some efficient approaches for multi-objective constrained optimization of computationally expensive black-box model problems

Abstract Multi-objective constrained optimization problems which arise in many engineering fields often involve computationally expensive black-box model simulators of industrial processes which have to be solved with limited computational time budget, and hence limited number of simulator calls. This paper proposes two heuristic approaches aiming to build proxy problem models, solvable by computationally efficient optimization methods, in order to quickly provide a sufficiently accurate approximation of the Pareto front. The first approach builds a multi-objective mixed-integer linear programming (MO-MILP) surrogate model of the optimization problem relying on piece-wise linear approximations of objectives and constraints obtained through brute-force sensitivity computation. The second approach builds a multi-objective nonlinear programming (MO-NLP) surrogate model using curve fitting of objectives and constraints. In both approaches the desired number of approximated solutions of the Pareto front are generated by applying the ɛ-constraint method to the multi-objective surrogate problems. The proposed approaches are tested for the cost vs. life cycle assessment (LCA)-based environmental optimization of drinking water production plants. The results obtained with both approaches show that a good quality approximation of Pareto front can be obtained with a significantly smaller computational time than with a state-of-the-art metaheuristic algorithm.

Linear programming-based directed local search for expensive multi-objective optimization problems: Application to drinking water production plants

Local search (LS) is an essential module of most hybrid meta-heuristic evolutionary algorithms which are a major approach aimed to solve efficiently multi-objective optimization (MOO) problems. Furthermore, LS is specifically useful in many real-world applications where there is a need only to improve a current state of a system locally with limited computational budget and/or relying on computationally expensive process simulators. In these contexts, this paper proposes a new neighborhood-based iterative LS method, relying on first derivatives approximation and linear programming (LP), aiming to steer the search along any desired direction in the objectives space. The paper also leverages the directed local search (DS) method to constrained MOO problems. These methods are applied to the bi-objective (cost versus life cycle assessment-based environmental impact) optimization of drinking water production plants. The results obtained show that the proposed method constitutes a promising local search method which clearly outperforms the directed search approach.

Cost versus life cycle assessment-based environmental impact optimization of drinking water production plants.

Empowering decision makers with cost-effective solutions for reducing industrial processes environmental burden, at both design and operation stages, is nowadays a major worldwide concern. The paper addresses this issue for the sector of drinking water production plants (DWPPs), seeking for optimal solutions trading-off operation cost and life cycle assessment (LCA)-based environmental impact while satisfying outlet water quality criteria. This leads to a challenging bi-objective constrained optimization problem, which relies on a computationally expensive intricate process-modelling simulator of the DWPP and has to be solved with limited computational budget. Since mathematical programming methods are unusable in this case, the paper examines the performances in tackling these challenges of six off-the-shelf state-of-the-art global meta-heuristic optimization algorithms, suitable for such simulation-based optimization, namely Strength Pareto Evolutionary Algorithm (SPEA2), Non-dominated Sorting Genetic Algorithm (NSGA-II), Indicator-based Evolutionary Algorithm (IBEA), Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), Differential Evolution (DE), and Particle Swarm Optimization (PSO). The results of optimization reveal that good reduction in both operating cost and environmental impact of the DWPP can be obtained. Furthermore, NSGA-II outperforms the other competing algorithms while MOEA/D and DE perform unexpectedly poorly.

An archive-based multi-objective evolutionary algorithm with adaptive search space partitioning to deal with expensive optimization problems: Application to process eco-design

Abstract In eco-design, the integration of environmental aspects into the earliest stage of design is considered with the aim of reducing adverse environmental impacts throughout a products life cycle. An eco-design problem is therefore multi-objective, where several objectives (environmental, economic, and technological) are to be simultaneously optimized. The optimization of industrial processes usually requires solving expensive multi-objective optimization problems (MOPs). Aiming to solve efficiently MOPs, with a limited computational budget, this paper proposes a new framework called AMOEA-MAP. The framework relies on the structure of the NSGAII algorithm and possesses two novel operators: a memory-based adaptive partitioning strategy, which provides an adaptive reticulation of the search space for a quick identification of optimal zones with less computational effort; and a bi-population evolutionary algorithm, tailored for expensive optimization problems. To ascertain its generality, the framework is first tested on several tough benchmarks. Its performance is subsequently validated on a real-world eco-design problem.

Operational integration of time dependent toxicity impact category in dynamic LCA

Life Cycle Assessment (LCA) is the most widely used method for the environmental evaluation of an anthropogenic system and its capabilities no longer need to be proved. However, several limitations have been pointed out by LCA scholars, including the lack of a temporal dimension. The objective of this study is to develop a dynamic approach for calculating the time dependent impacts of human toxicity and ecotoxicity within LCA. A new framework is proposed, which includes dynamic inventory and dynamic impact assessment. This study focuses on the dynamic fate model for substances in the environment, combined with the USEtox® model for toxicity assessment. The method takes into account the noisy and random nature of substance emissions in function of time, as in the real world, and uses a robust solver for the dynamic fate model resolution. No characterization factors are calculated. Instead, a current toxicity is calculated as a function of time i.e. the damage produced per unit of time, together with a time dependent cumulated toxicity, i.e. the total damage produced from time zero to a given time horizon. The latter can be compared with the results obtained by the conventional USEtox® method: their results converge for a very large time horizon (theoretically at infinity). Organic substances are found to disappear relatively rapidly from the environmental compartments (in the time period in which the emissions occur) while inorganic substances (i.e. metals) tend to persist far beyond the emission period.

Sensitivity analysis of temporal parameters in a dynamic LCA framework

Including the temporal dimension in the Life Cycle Assessment (LCA) method is a very recent research subject. A complete framework including dynamic Life Cycle Inventory (LCI) and dynamic Life Cycle Impact Assessment (LCIA) was proposed with the possibility to calculate temporal deployment of climate change and ecotoxicity/toxicity indicators. However, the influence of different temporal parameters involved in the new dynamic method was not still evaluated. In the new framework, LCI and LCIA results are obtained as discrete values in function of time (vectors and matrices). The objective of this study is to evaluate the influence of the temporal profile of the dynamic LCI and calculation time span (or time horizon in conventional LCA) on the final LCA results. Additionally, the influence of the time step used for the impact dynamic model resolution was analysed. The range of variation of the different time steps was from 0.5day to 1year. The graphical representation of the dynamic LCA results shown important features such as the period in time and the intensity of the worst or relevant impact values. The use of a fixed time horizon as in conventional LCA does not allow the proper consideration of essential information especially for time periods encompassing the life time of the studied system. Regarding the different time step sizes used for the dynamic LCI definition, they did not have important influence on the dynamic climate change results. At the contrary, the dynamic ecotoxicity and human toxicity impacts were strongly affected by this parameter. Similarly, the time step for impact dynamic model resolution had no influence on climate change calculation (step size up to 1year was supported), while the toxicity model resolution requires adaptive time step definition with maximum size of 0.5day.