Single and multi-objective dynamic optimization study of an industrial scale fed batch reactor

Municipal solid waste incineration (MSWI) process is a complex industrial process with strong nonlinearity. It is a challenge to build a model for the MSWI process and carry out the corresponding optimization works. To solve this problem, the multiobjective optimization studies are conducted for both modeling and concerned indexes of the MSWI process, including the nitrogen oxides (NOx) emissions and the combustion efficiency (CE). First, a data-driven-based multiple-input multiple-output model is established for the NOx emissions and the CE of the MSWI process based on Takagi–Sugeno–Kang fuzzy neural network. Second, an adaptive large-scale multiobjective competitive swarm optimization (ALMOCSO) algorithm is designed for solving the multiobjective optimization problems (MOPs) of the MSWI process. A comprehensive evaluation system is proposed to complete the optimization foundation, and an adaptive scheme and multistrategy learning are proposed to improve the optimization effect of the ALMOCSO algorithm in solving complex MOPs. Then, a Pareto optimal set obtained from massive historical data is utilized as optimization reference to realize the dynamic multiobjective optimization for the NOx emissions and the CE of the MSWI process. Finally, the feasibility and effectiveness of the proposed methodology for optimizing the MSWI process are confirmed by the experiments using the data collected from a real MSWI plant. The results indicate that the modeling accuracy is satisfactory, and the CE is improved over 10% and the reduction of the NOx emissions is achieved 15.58%.

Multi-objective optimization problems (MOP) are frequently encountered in practice. In some cases, different computationally expensive analyses may be independently used for computing different objectives of the MOP. Additionally, the analyses may be executed to obtain estimates with different fidelity, typically higher fidelity requiring a longer run-time. For instance, in automotive design, the aerodynamic drag is computed using computational fluid dynamic (CFD) analysis and its crashworthiness/strength is assessed using finite element analysis (FEA). Both the objectives can be independently computed and the underlying fidelity of each analysis can also be controlled using different mesh sizes/thresholds on the residual errors. While there exist a number of generic MOP benchmark problems in the literature, there is scarce work on constructing MOPs with multi-fidelity (MF) analyses to support the development of multi-fidelity, multi-objective optimization algorithms. The existing MF benchmarks are limited to unconstrained, single-objective optimization problems only. Towards addressing this gap, in this paper, we introduce a test suite for multi-objective, multi-fidelity optimization (MOMF). The problems are derived by combining existing unconstrained, multi-objective design optimization problems with resolution/stochastic/instability errors that are common manifestations of MF simulations. The method allows for the construction of any number of low-fidelity functions with desired level of correlations for a given high-fidelity objective function. We hope that the test suite would motivate novel algorithmic developments to support optimization involving computationally expensive and independently evaluable objectives.

This paper deals with the multi-objective optimization of tire reinforcement structures such as the tread belt and the carcass path. The multi-objective functions are defined in terms of the discrete-type design variables and approximated by artificial neutral network, and the sensitivity analyses of these functions are replaced with the iterative genetic evolution. The multi-objective optimization algorithm introduced in this paper is not only highly CPU-time-efficient but it can also be applicable to other multi-objective optimization problems in which the objective function, the design variables and the constraints are not continuous but discrete. Through the illustrative numerical experiments, the fiber-reinforced tire belt structure is optimally tailored. The proposed multi-objective optimization algorithm is not limited to the tire reinforcement structure, but it can be applicable to the generalized multi-objective structural optimization problems in various engineering applications.

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Construction site layout is multi-objective optimization (MOO) problem. However, the previous researchers treated site layout as a single objective optimization problem, which is far away from the reality. In this study, site layout was treated as MOO problem. The two objective functions are minimizing the likelihood of accidents happened and total handling cost of interaction flows between the facilities. The modified Pareto-based ant colony optimization (ACO) algorithm was proposed to solve site layout problem. Moreover, fuzzy rule-based system was used to quantify the interaction flows. Finally, a case of office building was used to evaluate the modified Pareto-based ACO algorithm for solving MOO site layout problem. The results showed the feasibility and effectiveness of the modified Pareto-based ACO algorithm to solve MOO site layout problem.

Aiming at the problems such as low computational efficiency and long process in dynamic topology optimization, combined with bi-directional evolutional structure optimization, the dynamic optimization problem is transformed into the static optimization problem in multiple load cases. Newmark method is used to analyze the structure dynamics load. The topology optimization model based on equivalent static load is established. On the basis of the equivalent static load, multi-objective dynamics evolutionary structure optimization is studied. And the mathematical model of the dynamic stiffness and natural frequency about the multi-objective optimization is established. The mathematical formula of the sensitivity is deduced. Then a complete optimization iterative process is given. The numerical example illustrates that it is feasible to solve the multi-objective dynamic topology optimization with equivalent static loads. Modal tracking technique is introduced to the multi-objective dynamic topology optimization. The numerical example shows that modal tracking technology can track the required modal in the optimization process.

The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints.

Ensemble prediction-based dynamic robust multi-objective optimization methods

In the real word, optimization problems in multi-objective optimization (MOP) and dynamic optimization can be seen everywhere. During the last decade, among various swarm intelligence algorithms for multi-objective optimization problems, glowworm swarm optimization (GSO) and bacterial foraging algorithm (BFO) have attracted increasing attention from scholars. Although many scholars have proposed improvement strategies for GSO and BFO to keep a good balance between convergence and diversity, there are still many problems to be solved carefully. In this paper, a new coupling algorithm based on GSO and BFO (MGSOBFO) is proposed for solving dynamic multi-objective optimization problems (dMOP). MGSOBFO is proposed to achieve a good balance between exploration and exploitation by dividing into two parts. Part I is in charge of exploitation by GSO and Part II is in charge of exploration by BFO. At the same time, the simulation binary crossover (SBX) and polynomial mutation are introduced into the MGSOBFO to enhance the convergence and diversity ability of the algorithm. In order to show the excellent performance of the algorithm, we experimentally compare MGSOBFO with three algorithms on the benchmark function. The results suggests that such a coupling algorithm has good performance and outperforms other algorithms which deal with dMOP.

Decision makers tend to define their optimization problems as multi-objective optimization problems. Generating the whole nondominated set is often unrealistic due to its size but also because most of these points are irrelevant to the decision maker. Another approach consists in obtaining preference information and integrating it a priori, in order to reduce the size of the nondominated set and have a gain in computation time. In this work we focus on a partial preference relation based on requirement and tolerance thresholds that translate the Pareto dominance cone. After introducing this preference relation, we present adaptations to use it in existing discrete multi-objective optimization algorithms. Numerical experiments on multi-objective combinatorial optimization problems show the applicabiliy of our approach.

It is shown that finding the equivalence set for solving multiobjective discrete optimization problems is advantageous over finding the set of Pareto optimal decisions. An example of a set of key parameters characterizing the economic efficiency of a commercial firm is proposed, and a mathematical model of its activities is constructed. In contrast to the classical problem of finding the maximum profit for any business, this study deals with a multiobjective optimization problem. A method for solving inverse multiobjective problems in a multidimensional pseudometric space is proposed for finding the best project of firm’s activities. The solution of a particular problem of this type is presented.

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

In many recent works, the potential of Exploratory Landscape Analysis (ELA) features to numerically characterize single-objective continuous optimization problems has been demonstrated. These numerical features provide the input for all kinds of machine learning tasks in the domain of continuous optimization problems, ranging, for example, from High-level Property Prediction to Automated Algorithm Selection and Automated Algorithm Configuration. Without ELA features, analyzing and understanding the characteristics of single-objective continuous optimization problems is-to the best of our knowledge-very limited. Yet, despite their usefulness, as demonstrated in several past works, ELA features suffer from several drawbacks. These include, in particular, (1) a strong correlation between multiple features, as well as (2) its very limited applicability to multiobjective continuous optimization problems. As a remedy, recent works proposed deep learning-based approaches as alternatives to ELA. In these works, among others, point-cloud transformers were used to characterize an optimization problem's fitness landscape. However, these approaches require a large amount of labeled training data. Within this work, we propose a hybrid approach, Deep-ELA, which combines (the benefits of) deep learning and ELA features. We pre-trained four transformers on millions of randomly generated optimization problems to learn deep representations of the landscapes of continuous single- and multiobjective optimization problems. Our proposed framework can either be used out of the box for analyzing single- and multiobjective continuous optimization problems, or subsequently fine-tuned to various tasks focusing on algorithm behavior and problem understanding.

The goal of the multi-objective optimization algorithm is to quickly and accurately find a set of trade-off solutions. This paper develops a clustering-based competitive multi-objective particle swarm optimizer using the enhanced grid for solving multi-objective optimization problems, named EGC-CMOPSO. The enhanced grid mechanism involved in EGC-CMOPSO is designed to locate superior Pareto optimal solutions. Subsequently, a hierarchical-based clustering is established on the grid for improving the accuracy rate of the grid selection. Due to the adaptive division of clustering centers, EGC-CMOPSO is applicable for solving MOPs with various Pareto front (PF) shapes. Particularly, the inferior solutions are discarded and the leading particles are identified by the comprehensive ranking of particles in each cluster. Finally, the selected leading particles compete against each other, and the winner guides the update of the current particle. The proposed EGC-CMOPSO and the eight latest multi-objective optimization algorithms are performed on 21 test problems. The experimental results validate that the proposed EGC-CMOPSO is capable of handling multi-objective optimization problems (MOPs) and obtaining superior performance on both convergence and diversity.