Multi-objective optimization revisited

Optimization design of heat recovery systems on rotary kilns using genetic algorithms

Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker′s subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision‐making processing is implemented after Pareto optimality. In this paper, we attempted to incorporate the decider′s subjective sense with Pareto optimality for chromosomes ranking. A new ranking method based on subjective probability theory was thus proposed in order to explore and comprehend the true nature of the chromosomes on the Pareto optimal front. The properties of the ranking rule were proven, and its transitivity was presented as well. Simulation results compared the performance of the proposed ranking approach with the Pareto‐based ranking method for two multiobjective optimization cases, which demonstrated the effectiveness of the new ranking approach.

The optimization of grinding is a multi-objective problem characterized by high dimensionality, non-linearity, and complexity. Solving this multi-objective optimization (MOO) problem is one of the most challenging tasks in the field of mechanical engineering. In-depth research on multi-objective parameter optimization technology for grinding is of great significance for improving processing efficiency, optimizing product quality, and reducing energy consumption. This paper takes the multi-objective optimization problem of grinding as its starting point. First, it introduces the basic theory of multi-objective optimization and two primary methods for solving such problems: optimization target dimension reduction and multi-objective optimization. Second, the key technologies of the two methods are reviewed, including the modeling method of the optimization problem, the multi-objective optimization algorithm for solving the optimization model, and the prior and posterior trade-off methods used to obtain the compromised optimal solutions. Finally, the existing problems of the multi-objective optimization methods in grinding processing are summarized and the future development trends are predicted. This paper aims to provide researchers with a comprehensive understanding of the multi-objective optimization technology in grinding processing, enabling them to make more reasonable decisions when dealing with actual multi-objective optimization problems.

Multi-objective optimization of CO2 emission and thermal efficiency for on-site steam methane reforming hydrogen production process using machine learning

This paper presents an interactive graphical user interface (GUI) based multiobjective evolutionary algorithm (MOEA) toolbox for effective computer-aided multiobjective (MO) optimization. Without the need of aggregating multiple criteria into a compromise function, it incorporates the concept of Pareto's optimality to evolve a family of nondominated solutions distributing along the tradeoffs uniformly. The toolbox is also designed with many useful features such as the goal and priority settings to provide better support for decision-making in MO optimization, dynamic population size that is computed adaptively according to the online discovered Pareto-front, soft/hard goal settings for constraint handlings, multiple goals specification for logical "AND"/"OR" operation, adaptive niching scheme for uniform population distribution, and a useful convergence representation for MO optimization. The MOEA toolbox is freely available for download at http://vlab.ee.nus.edu.sg/-kctan/moea.htm which is ready for immediate use with minimal knowledge needed in evolutionary computing. To use the toolbox, the user merely needs to provide a simple "model" file that specifies the objective function corresponding to his/her particular optimization problem. Other aspects like decision variable settings, optimization process monitoring and graphical results analysis can be performed easily through the embedded GUIs in the toolbox. The effectiveness and applications of the toolbox are illustrated via the design optimization problem of a practical ill-conditioned distillation system. Performance of the algorithm in MOEA toolbox is also compared with other well-known evolutionary MO optimization methods upon a benchmark problem.

Chapter 17 - Multi-objective Optimum Design Concepts and Methods

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.

Many real-world design problems involve simultaneous optimisation of multiple objectives. The considered grillage design is a multi-objective optimisation problem since there are two objective functions, namely: the volume design and the cost design. Thus, the solution of this optimisation problem requires specialised method suitable for multi-objective problems. In this article, a multi-objective design optimisation using real-coded genetic algorithm is proposed for the Pareto-optimality of grillage system. The objective functions in the optimisation problem measure the design sensitivities in grillage system. The non-linear constrained multi-objective optimisation is very important from the point of view of practical problem solving. Therefore, the real-coded genetic algorithm with multiple genetic operators is proposed to find the optimum grillage system without handling any of the penalty functions. Direct strength calculation defined from the class rules of DNV was applied for structural design of grillage system. The hybrid method (real-coded genetic algorithm including the non-dominated sorting and sharing approaches) performs a marvellous explorability in finding a diverse set of solutions and in converging near the true Pareto-optimal set. The results obtained are very encouraging since they show that we can produce an important portion of the Pareto-front at a very low computational time frame.

A rational approach to terminal airport management is not a trivial task due to relatively complex interactions between passengers and terminal infrastructure. Such infrastructure may be represented or modelled as a network of service nodes. To make a decision about such a network structure, one has to take into account not only the cost of terminal infrastructure, but also a set of quality indicators depicting passenger service level. Such decision problems may be formulated in the multiple criteria setting. We propose a bi-criteria decision making problem with a discrete-event simulation model of a terminal airport as a base model. The simulation model is used to evaluate a finite set of configurations representing a network of service nodes. To point out the most preferred Pareto optimal configuration, we propose to use an interactive decision making method to navigate Pareto optimal solutions with so-called vectors of concessions and reference points as preference carriers. Such versatile decision making scheme may be used to solve practical multiple criteria decision problems with values of criteria functions obtained by simulation runs.

Harmonic distortion in power systems is a significant problem, and it is thus necessary to mitigate critical harmonics. This study proposes an optimal method for designing passive power filters (PPFs) to suppress these harmonics. The design of a PPF involves multi-objective optimization. A multi-objective bee swarm optimization (MOBSO) with Pareto optimality is implemented, and an external archive is used to store the non-dominated solutions obtained. The minimum Manhattan distance strategy was used to select the most balanced solution in the Pareto solution set. A series of case studies are presented to demonstrate the efficiency and superiority of the proposed method. Therefore, the proposed method has a very promising future not only in filter design but also in solving other multi-objective optimization problems.

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 presents a Multi Objective Evolutionary Algorithm (MOEA) to solve nonlinear power system optimization problem. The optimization is done with three variables; choice, location and rating of FACTS devices. The targeted technical objectives are; to control the power flow, increase the transmission line capability to its maximum thermal limits, to keep the voltages within limits while minimizing losses. The parameters of objectives are optimized independently and then the formulation of a nonlinear constrained multi-objective optimization problem is done while carrying out concurrent optimization taking two and three objectives. A Fuzzy min max approach is incorporated to reduce the best solution out of non dominated Pareto optimal set. Assessments have been done on IEEE 14 and IEEE 30 bus system for different loading conditions with two devices SVC and TCSC modeled in steady state and the results affirm the potency of the propound approach.

Multi-Objective Reactive Power Optimization Based On The Fuzzy Adaptive Particle Swarm Algorithm

Chapter 5 - Multiobjective Optimization and Advanced Topics