Progressively interactive evolutionary multiobjective optimization

A complete optimization procedure for a multi-objective problem essentially comprises of search and decision making. Depending upon how the search and decision making task is integrated, algorithms can be classified into various categories. Following `a decision making after search' approach, which is common with evolutionary multi-objective optimization algorithms, requires to produce all the possible alternatives before a decision can be taken. This, with the intricacies involved in producing the entire Pareto-front, is not a wise approach for high objective problems. Rather, for such kind of problems, the most preferred point on the front should be the target. In this study we propose and evaluate algorithms where search and decision making tasks work in tandem and the most preferred solution is the outcome. For the two tasks to work simultaneously, an interaction of the decision maker with the algorithm is necessary, therefore, preference information from the decision maker is accepted periodically by the algorithm and progress towards the most preferred point is made. Two different progressively interactive procedures have been suggested in the dissertation which can be integrated with any existing evolutionary multi-objective optimization algorithm to improve its effectiveness in handling high objective problems by making it capable to accept preference information at the intermediate steps of the algorithm. A number of high objective un-constrained as well as constrained problems have been successfully solved using the procedures. One of the less explored and difficult domains, i.e., bilevel multiobjective optimization has also been targeted and a solution methodology has been proposed. Initially, the bilevel multi-objective optimization problem has been solved by developing a hybrid bilevel evolutionary multi-objective optimization algorithm. Thereafter, the progressively interactive procedure has been incorporated in the algorithm leading to an increased accuracy and savings in computational cost. The efficacy of using a progressively interactive approach for solving difficult multi-objective problems has, therefore, further been justifie

Solving bilevel multi-objective optimization problems using evolutionary algorithms

Bilevel optimization problems require every feasible upper-level solution to satisfy optimality of a lower-level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy development, transportation problems, and others. In the context of a bilevel single objective problem, there exists a number of theoretical, numerical, and evolutionary optimization results. However, there does not exist too many studies in the context of having multiple objectives in each level of a bilevel optimization problem. In this paper, we address bilevel multi-objective optimization issues and propose a viable algorithm based on evolutionary multi-objective optimization (EMO) principles. Proof-of-principle simulation results bring out the challenges in solving such problems and demonstrate the viability of the proposed EMO technique for solving such problems. This paper scratches the surface of EMO-based solution methodologies for bilevel multi-objective optimization problems and should motivate other EMO researchers to engage more into this important optimization task of practical importance

Solving Bilevel Multiobjective Programming Problem by Elite Quantum Behaved Particle Swarm Optimization

An elite quantum behaved particle swarm optimization (EQPSO) algorithm is proposed, in which an elite strategy is exerted for the global best particle to prevent premature convergence of the swarm. The EQPSO algorithm is employed for solving bilevel multiobjective programming problem (BLMPP) in this study, which has never been reported in other literatures. Finally, we use eight different test problems to measure and evaluate the proposed algorithm, including low dimension and high dimension BLMPPs, as well as attempt to solve the BLMPPs whose theoretical Pareto optimal front is not known. The experimental results show that the proposed algorithm is a feasible and efficient method for solving BLMPPs

Optimal design of a Low-Cost SAE JA2954 compliant WPT system using NSGA-II

Wireless Power Transfer (WPT) systems for electric vehicle charging are one of the most promising methods that, given the advantages they bring, will help the desired deployment of electric vehicles. This paper presents a mathematical optimisation method applied to the design of an 11 kW S-S system that complies with the SAE J2954 standard. A proposal is made to calculate the electrical parameters of the circuit based on equations that are compared with the results obtained by simulation with finite elements and experimental measurements, achieving very tight results with a reduced computational time. The NSGA-II multi-objective genetic algorithm is then applied together with the secant method, defining three different scenarios: minimisation of the primary copper volume, minimisation of the secondary copper volume and a compromise solution optimising the total primary and secondary copper volume. The result is a set of Pareto optimal solutions, from which the one that meets the standard can be extracted that suits the designer’s needs

Quality Representation in Multiobjective Programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along the way, several interesting results about obtuse, simplicial cones are also proved. Both the BCS and CCS methods are tested and show promise on a variety of problems: linear, convex, nonconvex (CCS only), two-dimensional, and three-dimensional. Sample Matlab code for two of these examples can be found in the appendices as well as tables containing the generated solution points. The manuscript closes with conclusions and ideas for further research in this field

Development of Methods for Solving Bilevel Optimization Problems

Bilevel optimization, also referred to as bilevel programming, involves solving an upper level problem subject to the optimality of a corresponding lower level problem. The upper and lower level problems are also referred to as the leader and follower problems, respectively. Both levels have their associated objective(s), variable(s) and constraint(s). Such problems model real-life scenarios of cases where the performance of an upper level authority is realizable/sustainable only if the corresponding lower level objective is optimum. A number of practical applications in the field of engineering, logistics, economics and transportation have inherent nested structure that are suited to this type of modelling. The range of applications as well as a rapid increase in the size and complexity of such problems has prompted active interest in the design of efficient algorithms for bilevel optimization. Bilevel optimization problems present a number of unique and interesting challenges to algorithm design. The nested nature of the problem requires optimization of a lower level problem to evaluate each upper level solution, which makes it computationally exorbitant. Theoretically, an upper level solution is considered valid/feasible only if the corresponding lower level variables are the true global optimum of the lower level problem. Global optimality can be reliably asserted in very limited cases, for example convex and linear problems. In deceptive cases, an inaccurate lower level optimum may result in an objective value better than true optimum at the upper level, which poses a severe challenge for ranking/selection strategies used within any optimization technique. In turn, this also makes the performance evaluation very difficult since the performance cannot be judged based on the objective values alone. While the area of bilevel (or more generally, multilevel) programming itself is not very new, most reports in this direction up until about a decade ago considered solving linear or at most quadratic problems at both levels. Correspondingly, the focus on was on development of exact methods to solve such problems. However, such methods typically require assumptions on mathematical properties, which may not always hold in practical applications. With increasing use of computer simulation-based evaluations in a number of disciplines in science and engineering, there is more need than ever to handle problems that are highly nonlinear or even black-box in nature. Metaheuristic algorithms, such as evolutionary algorithms are more suited to this emerging paradigm. The foray of evolutionary algorithms in bilevel programming is relatively recent and there remains scope of substantial development in the field in terms of addressing the aforementioned challenges. The work presented in this thesis is directed towards improving evolutionary techniques to enable them solve generic bilevel problems more accurately using lower number of function evaluations compared to the existing methods. Three key approaches are investigated towards accomplishing this: (a) e active hybridization of global and local search methods during dierent stages of the overall search; (b) use of surrogate models to guide the search using approximations in lieu of true function evaluations, and (c) use of a non-nested re-formulation of the problem. While most of the work is focused on single-objective problems, preliminary studies are also presented on multi-objective bilevel problems. The performance of the proposed approaches is evaluated on a comprehensive suite of mathematical test problems available in the literature, as well as some practical problems. The proposed approaches are observed to achieve a favourable balance between accuracy and computational expense for solving bilevel optimization problems, and thus exhibit suitability for use in real-life applications

Non-weighted aggregate evaluation function of multi-objective optimization for knock engine modeling

In decision theory, the weighted sum model (WSM) is the best known Multi-Criteria Decision Analysis (MCDA) approach for evaluating a number of alternatives in terms of a number of decision criteria. Assigning weights is a difficult task, especially if the number of criteria is large and the criteria are very different in character. There are some problems in the real world which utilize conflicting criteria and mutual effect. In the field of automotive, the knocking phenomenon in internal combustion or spark ignition engines limits the efficiency of the engine. Power and fuel economy can be maximized by optimizing some factors that affect the knocking phenomenon, such as temperature, throttle position sensor, spark ignition timing, and revolution per minute. Detecting knocks and controlling the above factors or criteria may allow the engine to run at the best power and fuel economy. The best decision must arise from selecting the optimum trade-off within the above criteria. The main objective of this study was to proposed a new Non-Weighted Aggregate Evaluation Function (NWAEF) model for non-linear multi-objectives function which will simulate the engine knock behavior (non-linear dependent variable) in order to optimize non-linear decision factors (non-linear independent variables). This study has focused on the construction of a NWAEF model by using a curve fitting technique and partial derivatives. It also aims to optimize the nonlinear nature of the factors by using Genetic Algorithm (GA) as well as investigate the behavior of such function. This study assumes that a partial and mutual influence between factors is required before such factors can be optimized. The Akaike Information Criterion (AIC) is used to balance the complexity of the model and the data loss, which can help assess the range of the tested models and choose the best ones. Some statistical tools are also used in this thesis to assess and identify the most powerful explanation in the model. The first derivative is used to simplify the form of evaluation function. The NWAEF model was compared to Random Weights Genetic Algorithm (RWGA) model by using five data sets taken from different internal combustion engines. There was a relatively large variation in elapsed time to get to the best solution between the two model. Experimental results in application aspect (Internal combustion engines) show that the new model participates in decreasing the elapsed time. This research provides a form of knock control within the subspace that can enhance the efficiency and performance of the engine, improve fuel economy, and reduce regulated emissions and pollution. Combined with new concepts in the engine design, this model can be used for improving the control strategies and providing accurate information to the Engine Control Unit (ECU), which will control the knock faster and ensure the perfect condition of the engine

Evolutionary Algorithms in Engineering Design Optimization

Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc