A New Approach to Design Multi-loop Control Systems with Multiple Controllers

In this contribution, the control of a reverse osmosis desalination plant by using an optimal multi-loop approach is presented. Controllers are assumed to be players of a cooperative game, whose solution is obtained by multi-objective optimization (MOO). The MOO problem is solved by applying a genetic algorithm and the final solution is found from this Pareto set. For the reverse osmosis plant a control scheme consisting of two PI control loops are proposed. Simulation results show that in some cases, as for example this desalination plant, multi-loop control with several controllers, which have been obtained by join multi-objective optimization, perform as good as more complex controllers but with less implementation effort.

Genetic algorithms (GAs) have the characteristic of maintaining a population of solutions and can search in a parallel manner for many nondominated solutions. These features coincide with the requirement of seeking a Pareto optimal set in a multiobjective (multicriteria, vector) optimization problem. The rationale for multiobjective optimization via GAs is that at each generation, the fitness of each individual is defined according to its nondominated property. Because nondominated individuals are assigned the highest fitness values, the convergence of a population will go to the nondominated zone: the Pareto optimal set. Based on this concept, a Pareto GA, whose goal is to locate the Pareto optimal set of a multiobjective optimization problem, is developed. In this GA, to avoid missing Pareto optimal points during evolutionary processes, a new concept called Pareto-set filter is adopted. At each generation, the points of rank 1 are put into the filter and undergo a nondominated check. In addition, a niche technique is provided to prevent genetic drift in population evolution. This technique sets a replacement rule for reproduction procedures. For a constrained optimization problem, a revised penalty function method is introduced to transfer a constrained problem into a nonconstralned one. The transferred function of a point contains information on a point's status (feasible or infeasible), position in a search region, and distance to the Pareto optimal set Two multiobjective optimization examples, a 25-bar space truss optimal design (objectives: structural weight and virtual work, constraints: stresses) and a four-bar pyramid truss with control system (objectives: structural weight and control effort, constraints: closed-loop frequencies) are provided to demonstrate analysis procedures of the proposed Pareto GA.

A process of compromise that addresses conflicting objective functions such as performance and cost is often involved in real-world engineering design activities. If such conflicting relationships among objective functions exist in a multiobjective design optimization problem, no single solution can simultaneously minimize all objective functions, and the solutions of the optimization problem are obtained as a set of design alternatives called a Pareto optimal solution set. This paper proposes a new gradient-based multiobjective c that incorporates a population-based aggregative strategy for obtaining a Pareto optimal solution set. In this method, the objective functions and constraints are evaluated at multiple points in the objective function space, and design variables at each point are updated using information aggregatively obtained from all other points. In the proposed method, a multiobjective optimization problem is converted to a single objective optimization problem using a weighting method, with weighting coefficients adaptively determined by solving a linear programming problem. A sequential approximate optimization-based technique is used to update the design variables, since it allows effective use of design sensitivities that can be easily obtained in many engineering optimization problems. Several numerical examples, including a structural optimization problem, are provided to illustrate the effectiveness and utility of the proposed method.

Chapter 17 - Multi-objective Optimum Design Concepts and Methods

Study of a hull form optimization system based on a Gaussian process regression algorithm and an adaptive sampling strategy, Part II: Multi-objective optimization

Independent control mode of automatic generation control (AGC) and automatic voltage control (AVC) has exposed a lot of problems, including mutual influences between the control effect of each other and repeated adjustments of generators. In this paper, a coordinated automatic control system (CACS) of AGC and AVC is built, which can be described as a highly constrained multi-objective optimization problem (MOP). Indexes of economy, safety and quality are taken into account as the objective targets and the active power output and voltage magnitude of generators are selected as the control variables. Multi-objective particle swarm optimization (MOPSO) is used to solve this MOP and get the Pareto optimal set. Moreover, an approach of fuzzy decision making is presented to extract the best compromise solution from the Pareto optimal set. The proposed control strategy has been applied to New England 10-generator 39-bus system and several optimization simulations have been carried out on different control strategies. Results show the effectiveness of the proposed control system and strategy, which can obtain high quality solutions and is able to provide a satisfactory best compromise solution compared to the traditional techniques.

A dual level searching approach for multi objective optimisation problems using particle swarm optimisation and modified adaptive bats sonar algorithm is presented. The concept of echolocation of a colony of bats to find prey in the modified adaptive bats sonar algorithm is integrated with the established particle swarm optimisation algorithm. The proposed algorithm incorporates advantages of both particle swarm optimisation and modified adaptive bats sonar algorithm approach to handle the complexity of multi objective optimisation problems. These include swarm flight attitude and swarm searching strategy. The performance of the algorithm is verified through several multi objective optimisation benchmark test functions and problem. The acquired results show that the proposed algorithm perform well to produce a reliable Pareto front. The proposed algorithm can thus be an effective method for solving of multi objective optimisation problems.

Multi-objective optimization and multi-attribute decision-making support for optimal operation of multi stakeholder integrated energy systems

In this paper, the combined power management/design optimization problem is investigated for a fuel cell/Liion battery PHEV. Formulated as a constrained multi-objective optimization problem (MOP), the combined optimization problem simultaneously minimizes the vehicle cost and fuel consumption subject to the vehicle performance requirements. With an emphasis on developing a generic optimization algorithm to find the Pareto front for the synthesized MOP, the Pareto based multi-objective particle swarm optimization (PMOPSO) algorithm is developed, which solely depends on the concept of Pareto dominance. Three approaches are introduced to the PMOPSO method to address the constrained MOP. They are: (i) by incorporating system constraints in the original objective functions, the constrained MOP is transformed to an unconstrained MOP; (ii) to avoid being trapped in local minima, a disturbance operator with a decaying mutation possibility is introduced; (iii) to generate a sparsely distributed Pareto front, the concept of crowding distance is utilized to determine the global guidance for the particles. Finally, under the Matlab/Simulink software environment, simulation results are presented to demonstrate the effectiveness of the PMOPSO in the derivation of the true Pareto front.

Pareto Set Learning (PSL) is an emerging research area in multi-objective optimization, focusing on training neural networks to learn the mapping from preference vectors to Pareto optimal solutions. However, existing PSL methods are limited to addressing a single Multi-objective Optimization Problem (MOP) at a time. When faced with multiple MOPs, this limitation results in significant inefficiencies and hinders the ability to exploit potential synergies across varying MOPs. In this paper, we propose a Collaborative Pareto Set Learning (CoPSL) framework, which learns the Pareto sets of multiple MOPs simultaneously in a collaborative manner. CoPSL particularly employs an architecture consisting of shared and MOP-specific layers. The shared layers are designed to capture commonalities among MOPs collaboratively, while the MOP-specific layers tailor these general insights to generate solution sets for individual MOPs. This collaborative approach enables CoPSL to efficiently learn the Pareto sets of multiple MOPs in a single execution while leveraging the potential relationships among various MOPs. To further understand these relationships, we experimentally demonstrate that shareable representations exist among MOPs. Leveraging these shared representations effectively improves the capability to approximate Pareto sets. Extensive experiments underscore the superior efficiency and robustness of CoPSL in approximating Pareto sets compared to state-of-the-art approaches on a variety of synthetic and real-world MOPs. Code is available at https://github.com/ckshang/CoPSL.

The main reason for applying evolutionary algorithms in multi-objective optimization problems is to obtain near-optimal nondominated solutions/Pareto fronts, from which decision-makers can choose a suitable solution. The efficiency of multi-objective optimization algorithms depends on the quality and quantity of Pareto fronts produced by them. To compare different Pareto fronts resulting from different algorithms, criteria are considered and applied in multi-objective problems. Each criterion denotes a characteristic of the Pareto front. Thus, ranking approaches are commonly used to evaluate different algorithms based on different criteria. This paper presents three multi-objective optimization methods based on the multi-objective particle swarm optimization (MOPSO) algorithm. To evaluate these methods, bi-objective mathematical benchmark problems are considered. Results show that all proposed methods are successful in finding near-optimal Pareto fronts. A ranking method is used to compare the capability of the proposed methods and the best method for further study is suggested. Moreover, the nominated method is applied as an optimization tool in real multi-objective optimization problems in multireservoir system operations. A new technique in multi-objective optimization, called warm-up, based on the PSO algorithm is then applied to improve the quality of the Pareto front by single-objective search. Results show that the proposed technique is successful in finding an optimal Pareto front.

The multi-objective flexible job-shop scheduling optimization model was conducted in order to solve multi-objective optimization problem of flexible job-shop small batch lot-splitting scheduling.The model was concerned with makespan,tardiness penalty,manufacturing cost,count of batch and total workload.The optimal solutions were obtained by using improved strength Pareto evolutionary algorithm(SPEA).The algorithm was improved by using the fuzzy c-means clustering algorithm to accelerate the clustering procedure within the external population.A self-adaptive mutation operator was also introduced to enhance the diversity of solutions.A Pareto optimal set can be achieved in a single run with the constraint Pareto domination concept and the flexible representation schema.Then the preference sequence of Pareto solutions was achieved and a solution was extracted as the best compromise one based on set theory.The jobs were split into flexible size batch,and the batch routing and sequencing were simultaneously optimized by the method.The performance of the method was evaluated through simulation.The feasibility and validity of the method were proved in a workshop scheduling.

In this paper, we propose a sufficient condition for a solution to be optimal for a 2-additive Choquet integral in the context of multiobjective combinatorial optimization problems. A 2-additive Choquet optimal solution is a solution that optimizes at least one set of parameters of the 2-additive Choquet integral. We also present a method to generate 2-additive Choquet optimal solutions of multiobjective combinatorial optimization problems. The method is experimented on some Pareto fronts and the results are analyzed.

Conflicting interrelationships among objective functions are often encountered in real-world engineering design problems. If such exist in a multiobjective optimization problem, no unique solution can simultaneously minimize all of the objective functions. Instead, the solutions of a multiobjective optimization problem are obtained as non-dominated solutions called a Pareto optimal solution set. Since a comprehensive Pareto optimal solution set enables the analysis of the trade-off relationships between conflicting objective functions, obtaining such a solution set can be highly beneficial because it increases flexibility when making engineering design decisions. Therefore, this paper proposes an aggregative gradient-based multiobjective optimization method for bi-objective optimization problems, which can ensure the diversity of the Pareto optimal solution set. The proposed method utilizes an aggregative optimization approach where multiple points are concurrently updated during the optimization process. First, an appropriate searching direction for each point is calculated by solving a linear programming problem considering point distribution. Next, design sensitivities are calculated at each point for use as gradient information in the objective functions and constraints. Then, the design variables of all points are updated using a local optimization technique that considers the previously calculated searching direction. During this update process, the proposed method introduces distance constraints among all the points in the objective function space in order to maintain their diversity, which ensures the diversity of the obtained Pareto optimal solution set. These steps are iteratively conducted until the optimization process is converged. Several numerical examples, including a topology optimization problem, are provided to confirm the usefulness of the proposed bi-objective optimization method.

Particle swarm optimization(PSO) algorithm has been widely applied in solving multi-objective optimization problems(MOPs) since it was proposed. However, PSO algorithms updated the velocity of each particle using a single search strategy, which may be difficult to obtain approximate Pareto front for complex MOPs. In this paper, inspired by the theory of P system, a multi-objective particle swarm optimization (PSO) algorithm based on the framework of membrane system(PMOPSO) is proposed to solve MOPs. According to the hierarchical structure, objects and rules of P system, the PSO approach is used in elementary membranes to execute multiple search strategy. And non-dominated sorting and crowding distance is used in skin membrane for improving speed of convergence and maintaining population diversity by evolutionary rules. Compared with other multi-objective optimization algorithm including MOPSO, dMOPSO, SMPSO, MMOPSO, MOEA/D, SPEA2, PESA2, NSGAII on a benchmark series function, the experimental results indicate that the proposed algorithm is not only feasible and effective but also have a better convergence to true Pareto front.