Improving a multi-objective differential evolution optimizer using fuzzy adaptation and $$K$$ K -medoids clustering

Hybrid Stepper Motors (HSMs) have received enormous industrial applications due to their higher efficiency, better resolution, better detent torque and smoother operation as compared to other stepper motors and servomotors. HSM conventional control schemes however could not overcome poor damping characteristics at increasing load inertia, high overshoot, undershoot and settling time which compromise motor integrity in terms of efficiency and precise positioning. In this paper, a PI-based Mamdani type Fuzzy Logic Controller (FLC) was designed for an HSM. Triangular and trapezoidal membership functions for input and output linguistic variables were employed giving 49 rules in the rule base of the FLC. Matlab fuzzy logic toolbox was used for the FLC design. The FLC was used to model a position controller for the HSM in Simulink. The dynamic response for a unit step input for the HSM position control system presented better characteristics in terms of overshoot and undershoot but higher settling time and rise time as compared to the system without FLC. With the FLC, overshoot and undershoot were 0.454% and 1.892% as against 0.562% and 4.069% for the non-FLC respectively. The settling time and rise time were 15.36 ms and 9.83 ms for the FLC as against 13.727 ms and 5.306 ms for the non-FLC respectively. Further, the FLC response had almost no ripples. The FLC could be considered for the control of the HSM.

Due to increased search complexity in multi-objective optimization, premature convergence becomes a problem. Complex engineering problems poses high number of variables with many constraints. Hence, more difficult benchmark problems must be utilized to validate new algorithms performance. A well-known optimizer, Multi-Objective Particle Swarm Optimizer (MOPSO), has a few weakness that needs to be addressed, specifically its convergence in high dimensional problems and its constraints handling capability. For these reasons, we propose a modified MOPSO (M-MOPSO) to improve upon these aspects. M-MOPSO is compared with four other algorithms namely, MOPSO, Multi-Objective Grey Wolf Optimizer (MOGWO), Multi-Objective Evolutionary Algorithm based on Decompositions (MOEA/D) and Multi-Objective Differential Evolution (MODE). M-MOPSO emerged as the best algorithm in eight out of the ten constrained benchmark problems. It also shows promising results in bioprocess application problems and tumor treatment problems. In overall, M-MOPSO was able to solve multi-objective problems with good convergence and is suitable to be used in real world problem.

In this study, a problem space genetic algorithm (PSGA) is used to solve bicriteria tool management and scheduling problems simultaneously in flexible manufacturing systems. The PSGA is used to generate approximately efficient solutions minimizing both the manufacturing cost and total weighted tardiness. This is the first implementation of PSGA to solve a multiobjective optimization problem (MOP). In multiobjective search, the key issues are guiding the search towards the global Pareto-optimal set and maintaining diversity. A new fitness assignment method, which is used in PSGA, is proposed to find a well-diversified, uniformly distributed set of solutions that are close to the global Pareto set. The proposed fitness assignment method is a combination of a nondominated sorting based method which is most commonly used in multiobjective optimization literature and aggregation of objectives method which is popular in the operations research literature. The quality of the Pareto-optimal set is evaluated by using the performance measures developed for multiobjective optimization problems.

Differential evolution (DE) research for multi-objective optimization can be divided into proposals that either consider DE as a stand-alone algorithm, or see DE as an algorithmic component that can be coupled with other algorithm components from the general evolutionary multiobjective optimization (EMO) literature. Contributions of the latter type have shown that DE components can greatly improve the performance of existing algorithms such as NSGA-II, SPEA2, and IBEA. However, several experimental factors have been left aside from that type of algorithm design, compromising its generality. In this work, we revisit the research on the effectiveness of DE for multi-objective optimization, improving it in several ways. In particular, we conduct an iterative analysis on the algorithmic design space, considering DE and environmental selection components as factors. Results show a great level of interaction between algorithm components, indicating that their effectiveness depends on how they are combined. Some designs present state-of-the-art performance, confirming the effectiveness of DE for multi-objective optimization.

In multi-objective Bayesian optimization, an infill criterion is an important part, as it is the indicator to evaluate how much good a new set of solutions is, compared to a Pareto-front approximation set. This paper presents a deterministic algorithm for computing the Expected R2 Indicator for bi-objective problems and studies its use as an infill criterion in Bayesian Global Optimization. The R2-Indicator was introduced in 1998 by M. Hansen and A. Jaszkiewicz for performance assessment in multi-objective optimization and is more recently also used in indicator-based multi-criterion evolutionary algorithms (IBEAs). In Bayesian Global Optimization, we propose the Expected R2-indicator Improvement (ER2I) as an infill criterion. It is defined as the expected decrease of the R2 indicator by a point that is sampled from a predictive Gaussian distribution. The ER2I can also be used as a pre-selection criterion in surrogate-assisted IBEAs. It provides an alternative to the Expected Hypervolume-Indicator Improvement (EHVI) that requires a reference point, bounding the Pareto front from above. In contrast, the ER2I works with a utopian reference point that bounds the Pareto front from below. In addition, the ER2I supports preference modelling with utility functions and its computation time grows only linearly with the number of considered weight combinations. It is straightforward to approximate the ER2I by Monte Carlo Integration, but so far a deterministic algorithm to solve the non-linear integral remained unknown. We outline a deterministic algorithm for the computation of the bi-objective ER2I with Chebychev utility functions. Moreover, we study monotonicity properties of the ER2I w.r.t. parameters of the predictive distribution and numerical simulations demonstrate fast convergence to Pareto fronts of different shapes and the ability of the ER2I Bayesian optimization to fill gaps in the Pareto front approximation.

Radiation therapy treatment planning is inherently a multiobjective problem, aiming to obtain the best tradeoffs between irradiating the tumor with the prescribed dose and sparing as much as possible the surrounding healthy organs. Many different multiobjective approaches have been proposed for the optimization of radiation intensities for fixed beam irradiation directions. However, multiobjective beam angle optimization is seldom considered. The purpose of this paper is to introduce a new multiobjective optimization framework that explicitly and simultaneously considers the optimization of intensities and also beam directions. Whilst multiobjective optimization of radiation intensities considering a fixed set of beam directions gives rise to a single Pareto front, beam angle optimization gives rise to the appearance of multiple Pareto fronts, each one associated with a given beam angle set. Our framework proposes a beam angle set choice based on the evaluation of non-dominated solutions belonging to different Pareto fronts, using a tree-based approach and a performance indicator to assess the quality of each Pareto front. The proposed approach, illustrated by head-and-neck cancer cases, allows for more flexibility in the calculation of solutions and a better understanding of the existing compromises between different objectives.

In this paper a two-step design methodology of the near optimal Mamdani type fuzzy logic controller (FLC) has been applied to three types of systems: a linear time invariant system (LTI), a LTI system with time delay and an nonlinear system. In the first step, the tuning/learning procedure of a data base/knowledge base of the FLC is based on the model of the system using genetic algorithms (GA). The achieved solution is the optimal one with regard to the model of the system. In the second step experiments are performed on the real system at the vicinity of the optimum (achieved by GA) and using response surface methodology (RSM) control parameters are readjusted in order to achieve the near optimal solution for the real system. The proposed two step methodology gives a systematic way of the near optimal FLC tuning/learning when confronted with the real system and a very efficient combination of off-line and online part of design procedure.

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.

In recent decade, the vehicle to grid (V2G) technology makes the electric vehicles (EVs) become the potential energy storage capacity for alleviating the random fluctuation of the renewable energy power. The EV aggregator is the promising solution to aggregate enough capacity for the V2G. In this paper, a preliminary study of the multi-objective optimal dispatch of smart grid by estimating available capacity of EV aggregators is proposed. The behavior of EVs is described by a statistical model to estimate the maximum available capacity of EVs. Then, the multi-objectives and constrains are defined for the multi-objective optimal dispatch. The multi-objective genetic particle swarm optimizer is used to solve the high dimensional multi-objective optimization problem to obtain the Pareto front. The multi-objective optimization results show that the charging period of EVs is shifted to avoid load peak for the solved optimal dispatch.

Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multi-objective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework, which integrates three steps. In the first step, we establish surrogate models for the constraints using Gaussian processes (GPs) and employ multi-objective Bayesian optimization to search for feasible points that satisfy the constraints. In the second step, we establish surrogate models for the objective function and constraints using GPs and utilize constrained multi-objective Bayesian optimization to search for an approximate Pareto front. In the third step, we perform a local search based on the approximate Pareto front. By employing the trust region filter method, we construct quadratic models for each constraint and objective function and refine the Pareto front to achieve local optimality. This framework demonstrates the efficiency of Bayesian optimization and the local optimality of the trust region method. A comparison with the popular evolutionary algorithm, Nondominated Sorting Genetic Algorithm II (NSGA-II), showed that this framework had a higher hypervolume of the Pareto front while halving the runtime and reducing the number of simulations by a factor of 20.

Surrogate-based method can dramatically reduce the number of expensive function evaluations in real-world multi- objective optimization problems (MOP). When the number of objectives is small, using surrogate models combined with expected hypervolume improvement (EHVI) infill sampling criterion (ISC) has been proved to be efficient to provide a set of solutions with good diversity and good proximity to the Pareto front (PF) in aerodynamic shape optimization. However, traditional hypervolume-based infilling strategies use only one kind of ISC to generate one or multiple sample points, the advantages of various kinds of ISC cannot be comprehensively utilized and the parallelization is not easy to implement. This paper proposes a combined multi-point infilling strategy based on Kriging models and develops an efficient global multi-objective constrained optimization method (EGMOCO) to solve multi- objective aerodynamic shape optimization with complex constraints. Multiple sample points are generated by using four ISC considering hypervolume at each iteration and then evaluated in parallel. Firstly, the performance of EGMOCO is compared with that of single criterion EHVI strategy on six benchmarks within the same computational budget to prove its effectiveness, and then EGMOCO is implemented in an aerodynamic shape optimization problem with complex constraints. The result shows that EGMOCO has good performance in balancing local exploitation and global exploration with faster convergence rate and high robustness, the whole PF can be fully explored in limited evaluations and the constraint handling is effective especially for real-world problems with complex and nonlinear constraints, the comprehensive aerodynamic performance of the airfoil is greatly improved. It can be confirmed that Kriging-based multi-objective optimization method combined with multi-point infilling strategy performs better than single infilling criterion EHVI, since different sample infilling criteria can complement with each other, both local exploitation and global exploration can be considered and well balanced.

This paper presents a fuzzy adaptive differential evolution (DE) for 3D UAV path planning. The path-planning problem is formulated as a multi-objective unconstrained optimization problem in the aim of minimizing the fuel and the threat cost as well as finding the shortest path. A fuzzy logic controller is used to find the parameter values of DE during this optimization process. The mutation operation of DE is modified in a way to strike a balance between the DE/rand/1 and DE/best/1 strategies. This method is compared with both DE/rand/1 and DE/best/1 and it relatively outperformed both the classical variations. As it is often tedious to find the right parameter values for DE, this method will give freedom from the process of finding the parameter values for the acceptable performance in 3D path planning optimization.

Two step design methodology of near optimal fuzzy logic controller

Summary CO2-water-alternating-gas (CO2-WAG) is a reservoir development method that can simultaneously enhance oil recovery and achieve CO2 storage. However, improperly designed parameters for CO2 injection and oil production may significantly reduce the oil displacement efficiency and CO2 storage. Furthermore, optimizing the injection parameters is computationally expensive due to the high computational cost of the compositional simulation. This work aims to propose an efficient optimization method to obtain a series of well-control schemes that balance maximizing net present value (NPV) and CO2 storage for decision-makers. Given the number of CO2-WAG cycles and the duration of each cycle, we optimize the water injection rate, gas injection rate, and half-cycle for the injection well and the bottomhole pressure (BHP) for the production well. In this paper, a two-stage optimization strategy is proposed to enhance the optimization efficiency. The first stage performs the surrogate-assisted single-objective optimizations of each considered objective. It is designed to find the endpoints of the Pareto front that connect all solutions of the multiobjective optimization; this stage not only provides important search directions for the subsequent multiobjective optimization but also improves the accuracy of the surrogate model near the Pareto front. The second stage is the surrogate-assisted multiobjective optimization, which aims to find all the solutions along the Pareto front based on the Pareto endpoints obtained from the first stage. In addition, this study successfully combines the gradient of the objective functions with the meta-heuristic algorithm during the multiobjective optimization, which ensures a faster convergence to the global optimum. The proposed multiobjective optimization algorithm shows faster convergence than the conventional optimization methods when applied to the three multiobjective optimization test functions. Finally, a comparison with the conventional multiobjective optimization is conducted based on one test function and two benchmark reservoir simulation models to verify the correctness and efficiency of the proposed method. It is confirmed that the proposed method outperforms the conventional ones for the optimization of CO2-WAG injection.

Thermodynamic modeling and multi-objective evolutionary-based optimization of a new multigeneration energy system