Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems. (C) 2004 Elsevier Ltd. All rights reserved.

Decentralized Computation of Pareto Optimal Pure Nash Equilibria of Boolean Games with Privacy Concerns

In Boolean games, agents try to reach a goal formulated as a Boolean formula. These games are attractive because of their compact representations. However, few methods are available to compute the solutions and they are either limited or do not take privacy or communication concerns into account. In this paper we propose the use of an algorithm related to reinforcement learning to address this problem. Our method is decentralized in the sense that agents try to achieve their goals without knowledge of the other agents’ goals. We prove that this is a sound method to compute a Pareto optimal pure Nash equilibrium for an interesting class of Boolean games. Experimental results are used to investigate the performance of the algorithm.

The Pareto regret frontier

Performance guarantees for online learning algorithms typically take the form of regret bounds, which express that the cumulative loss overhead compared to the best expert in hindsight is small. In the common case of large but structured expert sets we typically wish to keep the regret especially small compared to simple experts, at the cost of modest additional overhead compared to more complex others. We study which such regret trade-offs can be achieved, and how. We analyse regret w.r.t. each individual expert as a multi-objective criterion in the simple but fundamental case of absolute loss. We characterise the achievable and Pareto optimal trade-offs, and the corresponding optimal strategies for each sample size both exactly for each finite horizon and asymptotically.

基于QoS的Pareto最优的服务选择

随着越来越多的服务能够满足用户的功能需求,需要一种策略基于服务的多种QoS属性来帮助用户选择合适的服务。以XML描述服务的QoS属性,提出了一种基于QoS的Pareto最优的服务选择策略,选择出那些不在所有的QoS属性上劣于其它服务的服务。实验结果表明,与随机选择和偏好导向的选择策略相比,Pareto最优策略有独特的效果。

«Constrained-optimal strategy-proof assignment: beyond the groves mechanisms»

A single object must be allocated to at most one of n agents. Money transfers are possible and preferences are quasilinear. We offer an explicit description of the individually rational mechanisms which are Pareto-optimal in the class of feasible, strategy-proof, anonymous and envy-free mechanisms. These mechanisms form a one-parameter infinite family; the Vickrey mechanism is the only Groves mechanism in that family.

Pareto archived simulated annealing for single machine job shop scheduling with multiple objectives

In this paper, the single machine job shop scheduling problem is studied with the objectives of minimizing the tardiness and the material cost of jobs. The simultaneous consideration of these objectives is the multi-criteria optimization problem under study. A metaheuristic procedure based on simulated annealing is proposed to find the approximate Pareto optimal (non-dominated) solutions. The two objectives are combined in one composite utility function based on the decision maker’s interest in having a schedule with weighted combination. In view of the unknown nature of the weights for the defined objectives, a priori approach is applied to search for the non-dominated set of solutions based on the Pareto dominance. The obtained solutions set is presented to the decision maker to choose the best solution according to his preferences. The performance of the algorithm is evaluated in terms of the number of non-dominated schedules generated and the proximity of the obtained non-dominated front to the true Pareto front. Results show that the produced solutions do not differ significantly from the optimal solutions.

Solving a multiobjective job shop scheduling problem using Pareto Archived Cuckoo Search

This paper investigates a new approach for solving the multiobjective job shop scheduling problem, namely the Cuckoo Search ( CS) approach. The requirement is to schedule jobs on a single machine so that the total material waste is minimised as well as the total tardiness time. The material waste is quantified in terms of saving factors to show the reduction in material that can be achieved when producing two jobs with the same materials in sequence. The estimated saving factor is used to calculate a cost savings for each job based on its material type. A formulation of multiobjective optimisation problems is adopted to generate the set of schedules that maximise the overall cost savings and minimise the total tardiness time. where all trade-offs are considered for the two conflicting objectives. A Pareto Archived Multiobjective Cuckoo Search (PAMOCS) is developed to find the set ofnondominated Pareto optimal solutions. The solution accuracy of PAMOCS is shown by comparing the closeness of the obtained solutions to the true Pareto front generated by the complete enumeration methad. Results shaw that CS is a very effective and promising technique to solve job shop scheduling problems.

Optimal Rehabilitation Strategy In Water Distribution Systems Considering Reduction In Greenhouse Gas Emissions

Most of water distribution systems (WDS) need rehabilitation due to aging infrastructure leading to decreasing capacity, increasing leakage and consequently low performance of the WDS. However an appropriate strategy including location and time of pipeline rehabilitation in a WDS with respect to a limited budget is the main challenge which has been addressed frequently by researchers and practitioners. On the other hand, selection of appropriate rehabilitation technique and material types is another main issue which has yet to address properly. The latter can affect the environmental impacts of a rehabilitation strategy meeting the challenges of global warming mitigation and consequent climate change. This paper presents a multi-objective optimization model for rehabilitation strategy in WDS addressing the abovementioned criteria mainly focused on greenhouse gas (GHG) emissions either directly from fossil fuel and electricity or indirectly from embodied energy of materials. Thus, the objective functions are to minimise: (1) the total cost of rehabilitation including capital and operational costs; (2) the leakage amount; (3) GHG emissions. The Pareto optimal front containing optimal solutions is determined using Non-dominated Sorting Genetic Algorithm NSGA-II. Decision variables in this optimisation problem are classified into a number of groups as: (1) percentage proportion of each rehabilitation technique each year; (2) material types of new pipeline for rehabilitation each year. Rehabilitation techniques used here includes replacement, rehabilitation and lining, cleaning, pipe duplication. The developed model is demonstrated through its application to a Mahalat WDS located in central part of Iran. The rehabilitation strategy is analysed for a 40 year planning horizon. A number of conventional techniques for selecting pipes for rehabilitation are analysed in this study. The results show that the optimal rehabilitation strategy considering GHG emissions is able to successfully save the total expenses, efficiently decrease the leakage amount from the WDS whilst meeting environmental criteria.

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

On Pareto Sets in Multi-Criteria Optimization

Здравко Д. Славов - В тази работа се разглеждат Паретовските решения в непрекъсната многокритериална оптимизация. Обсъжда се ролята на някои предположения, които влияят на характеристиките на Паретовските множества. Авторът се е опитал да премахне предположенията за вдлъбнатост на целевите функции и изпъкналост на допустимата област, които обикновено се използват в многокритериалната оптимизация. Резултатите са на базата на конструирането на ретракция от допустимата област върху Парето-оптималното множество.

Knowledge discovery for adaptive negotiation agents in e-marketplaces

Intelligent software agents are promising in improving the effectiveness of e-marketplaces for e-commerce. Although a large amount of research has been conducted to develop negotiation protocols and mechanisms for e-marketplaces, existing negotiation mechanisms are weak in dealing with complex and dynamic negotiation spaces often found in e-commerce. This paper illustrates a novel knowledge discovery method and a probabilistic negotiation decision making mechanism to improve the performance of negotiation agents. Our preliminary experiments show that the probabilistic negotiation agents empowered by knowledge discovery mechanisms are more effective and efficient than the Pareto optimal negotiation agents in simulated e-marketplaces.

Active transonic aerofoil design optimization using robust multiobjective evolutionary algorithms

The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary-layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. Two test cases are conducted: the first test assumes the boundary-layer transition position is at 45% of chord from the leading edge, and the second test considers robust design optimization for the shock control bump at the variability of boundary-layer transition positions. The numerical result shows that the optimization method coupled to uncertainty design techniques produces Pareto optimal shock-control-bump shapes, which have low sensitivity and high aerodynamic performance while having significant total drag reduction.

Adaptive wing/aerofoil design optimisation using MOEA coupled to uncertainty design method

The use of adaptive wing/aerofoil designs is being considered as promising techniques in aeronautic/aerospace since they can reduce aircraft emissions, improve aerodynamic performance of manned or unmanned aircraft. The paper investigates the robust design and optimisation for one type of adaptive techniques; Active Flow Control (AFC) bump at transonic flow conditions on a Natural Laminar Flow (NLF) aerofoil designed to increase aerodynamic efficiency (especially high lift to drag ratio). The concept of using Shock Control Bump (SCB) is to control supersonic flow on the suction/pressure side of NLF aerofoil: RAE 5243 that leads to delaying shock occurrence or weakening its strength. Such AFC technique reduces total drag at transonic speeds due to reduction of wave drag. The location of Boundary Layer Transition (BLT) can influence the position the supersonic shock occurrence. The BLT position is an uncertainty in aerodynamic design due to the many factors, such as surface contamination or surface erosion. The paper studies the SCB shape design optimisation using robust Evolutionary Algorithms (EAs) with uncertainty in BLT positions. The optimisation method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing and asynchronous evaluation. Two test cases are conducted; the first test assumes the BLT is at 45% of chord from the leading edge and the second test considers robust design optimisation for SCB at the variability of BLT positions and lift coefficient. Numerical result shows that the optimisation method coupled to uncertainty design techniques produces Pareto optimal SCB shapes which have low sensitivity and high aerodynamic performance while having significant total drag reduction.

Hierarchical robust design optimisation of shock control bump devices for airfoil drag reduction

The paper investigates a detailed Active Shock Control Bump Design Optimisation on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 to reduce cruise drag at transonic flow conditions using Evolutionary Algorithms (EAs) coupled to a robust design approach. For the uncertainty design parameters, the positions of boundary layer transition (xtr) and the coefficient of lift (Cl) are considered (250 stochastic samples in total). In this paper, two robust design methods are considered; the first approach uses a standard robust design method, which evaluates one design model at 250 stochastic conditions for uncertainty. The second approach is the combination of a standard robust design method and the concept of hierarchical (multi-population) sampling (250, 50, 15) for uncertainty. Numerical results show that the evolutionary optimization method coupled to uncertainty design techniques produces useful and reliable Pareto optimal SCB shapes which have low sensitivity and high aerodynamic performance while having significant total drag reduction. In addition,it also shows the benefit of using hierarchical robust method for detailed uncertainty design optimization.