Adaptive modelling strategy for continuous multi-objective optimization

The Pareto optimal set of a continuous multi-objective optimization problem is a piecewise continuous manifold under some mild conditions. We have recently developed several multi-objective evolutionary algorithms based on this property. However, the modelling methods used in these algorithms are rather costly. In this paper, a cheap and effective modelling strategy is proposed for building the probabilistic models of promising solutions. A new criterion is proposed for measuring the convergence of the algorithm. The locality degree of each local model is adjusted according to the proposed convergence criterion. Experimental results show that the algorithm with the proposed strategy is very promising. © 2007 IEEE

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Sampling CAD models via an extended teaching–learning-based optimization technique

The Teaching–Learning-Based Optimization (TLBO) algorithm of Rao et al. has been presented in recent years, which is a population-based algorithm and operates on the principle of teaching and learning. This algorithm is based on the influence of a teacher on the quality of learners in a population. In this study, TLBO is extended for constrained and unconstrained CAD model sampling which is called Sampling-TLBO (S-TLBO). Sampling CAD models in the design space can be useful for both designers and customers during the design stage. A good sampling technique should generate CAD models uniformly distributed in the entire design space so that designers or customers can well understand possible design options. To sample designs in a predefined design space, sub-populations are first generated each of which consists of separate learners. Teaching and learning phases are applied for each sub-population one by one which are based on a cost (fitness) function. Iterations are performed until change in the cost values becomes negligibly small. Teachers of each sub-population are regarded as sampled designs after the application of S-TLBO. For unconstrained design sampling, the cost function favors the generation of space-filling and Latin Hypercube designs. Space-filling is achieved using the Audze and Eglais’ technique. For constrained design sampling, a static constraint handling mechanism is utilized to penalize designs that do not satisfy the predefined design constraints. Four CAD models, a yacht hull, a wheel rim and two different wine glasses, are employed to validate the performance of the S-TLBO approach. Sampling is first done for unconstrained design spaces, whereby the models obtained are shown to users in order to learn their preferences which are represented in the form of geometric constraints. Samples in constrained design spaces are then generated. According to the experiments in this study, S-TLBO outperforms state-of-the-art techniques particularly when a high number of samples are generated

A hybrid multiagent approach for global trajectory optimization

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers(corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with existing deterministic and stochastic global optimization methods

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo

Enhanced evolutionary algorithm with cuckoo search for nurse scheduling and rescheduling problem

Nurse shortage, uncertain absenteeism and stress are the constituents of an unhealthy working environment in a hospital. These matters have impact on nurses' social lives and medication errors that threaten patients' safety, which lead to nurse turnover and low quality service. To address some of the issues, utilizing the existing nurses through an effective work schedule is the best alternative. However, there exists a problem of creating undesirable and non-stable nurse schedules for nurses' shift work. Thus, this research attempts to overcome these challenges by integrating components of a nurse scheduling and rescheduling problem which have normally been addressed separately in previous studies. However, when impromptu schedule changes are required and certain numbers of constraints need to be satisfied, there is a lack of flexibility element in most of scheduling and rescheduling approaches. By embedding the element, this gives a potential platform for enhancing the Evolutionary Algorithm (EA) which has been identified as the solution approach. Therefore, to minimize the constraint violations and make little but attentive changes to a postulated schedule during a disruption, an integrated model of EA with Cuckoo Search (CS) is proposed. A concept of restriction enzyme is adapted in the CS. A total of 11 EA model variants were constructed with three new parent selections, two new crossovers, and a crossover-based retrieval operator, that specifically are theoretical contributions. The proposed EA with Discovery Rate Tournament and Cuckoo Search Restriction Enzyme Point Crossover (DᵣT_CSREP) model emerges as the most effective in producing 100% feasible schedules with the minimum penalty value. Moreover, all tested disruptions were solved successfully through preretrieval and Cuckoo Search Restriction Enzyme Point Retrieval (CSREPᵣ) operators. Consequently, the EA model is able to fulfill nurses' preferences, offer fair on-call delegation, better quality of shift changes for retrieval, and comprehension on the two-way dependency between scheduling and rescheduling by examining the seriousness of disruptions

Optimal experimental design and its applications to biochemical engineering systems

This work is motivated by challenges in data-based modelling of complex systems due to limited information of sparse and noisy experimental data. Optimal experimental design (OED) techniques, which aim at devising necessary experiments to generate informative measurement data to facilitate model identification, have been investigated comprehensively.The limitations of existing experimental design approaches have been extensively discussed, based on which advanced experimental design methods and efficient numerical strategies have been developed for improved solutions.;Two case study biochemical systems have been used through the research investigation, one is an enzyme reaction system, the other one is a lab-scale enzymatic biodiesel production system. The main contributions of this PhD work can be summarised as follows:;Single objective experimental designs by considering one type of design factors, i.e. input intensity, measurement set selection, sampling profile design, respectively, has been formulated and numerical strategies to solve these optimisation problems have been described in detail. Implementations of these design methods to biochemical systems have demonstrated its efficiency in reducing parameter estimation errors.;A new OED strategy has been proposed to cope with OED problems including multiple design factors in one optimisation framework. An iterative two-layer design structure is developed. In the lower layer for observation design, the sampling profile and the measurement set selection are combined and formulated as a single integrated observation design problem, which is relaxed to a convex optimization problem that can be solved with a local method.;Thus the measurement set selection and the sampling profile can be determined simultaneously. In the upper layer for input design, the optimisation of input intensities is obtained through stochastic global searching. In this way, the multi-factor optimisation problem is solved through the integration of a stochastic method, for the upper layer, and a deterministic method, for the lower layer.;A new enzyme reaction model has been established which represents a typical class of enzymatic kinetically controlled synthesis process. This model contains important kinetic reaction features, moderate complexity, and complete model information. It can be used as a benchmark problem for development and comparison of OED algorithms. Systematic analysis has been performed in order to examine the system behaviours, and the dependence on model parameters, initial operation conditions.;Structural identifiability and practical identifiability of this system have been analysed and identifiable parameters determined. The design of experiment for the enzyme reactionsystem by considering different types of design variables have been investigated. The parameter estimation precision can be improved significantly by using the proposed OED techniques, compared to the non-designed condition.;The OED techniques are numerically investigated based on a lab-scale biodiesel production process with real experimental data through research collaboration with DTU in Denmark. The OED applications on this real system model allow to examine the effectiveness and efficiency of those new proposed OED methods. The measurement set selection and the sampling design of this system are developed which provide detailed instructions on how to improve experiments through OED.;Also, the sensitivity analysis and parameter identifiability analysis are conducted; and their impacts to experimental design are clearly identified.This work is motivated by challenges in data-based modelling of complex systems due to limited information of sparse and noisy experimental data. Optimal experimental design (OED) techniques, which aim at devising necessary experiments to generate informative measurement data to facilitate model identification, have been investigated comprehensively.The limitations of existing experimental design approaches have been extensively discussed, based on which advanced experimental design methods and efficient numerical strategies have been developed for improved solutions.;Two case study biochemical systems have been used through the research investigation, one is an enzyme reaction system, the other one is a lab-scale enzymatic biodiesel production system. The main contributions of this PhD work can be summarised as follows:;Single objective experimental designs by considering one type of design factors, i.e. input intensity, measurement set selection, sampling profile design, respectively, has been formulated and numerical strategies to solve these optimisation problems have been described in detail. Implementations of these design methods to biochemical systems have demonstrated its efficiency in reducing parameter estimation errors.;A new OED strategy has been proposed to cope with OED problems including multiple design factors in one optimisation framework. An iterative two-layer design structure is developed. In the lower layer for observation design, the sampling profile and the measurement set selection are combined and formulated as a single integrated observation design problem, which is relaxed to a convex optimization problem that can be solved with a local method.;Thus the measurement set selection and the sampling profile can be determined simultaneously. In the upper layer for input design, the optimisation of input intensities is obtained through stochastic global searching. In this way, the multi-factor optimisation problem is solved through the integration of a stochastic method, for the upper layer, and a deterministic method, for the lower layer.;A new enzyme reaction model has been established which represents a typical class of enzymatic kinetically controlled synthesis process. This model contains important kinetic reaction features, moderate complexity, and complete model information. It can be used as a benchmark problem for development and comparison of OED algorithms. Systematic analysis has been performed in order to examine the system behaviours, and the dependence on model parameters, initial operation conditions.;Structural identifiability and practical identifiability of this system have been analysed and identifiable parameters determined. The design of experiment for the enzyme reactionsystem by considering different types of design variables have been investigated. The parameter estimation precision can be improved significantly by using the proposed OED techniques, compared to the non-designed condition.;The OED techniques are numerically investigated based on a lab-scale biodiesel production process with real experimental data through research collaboration with DTU in Denmark. The OED applications on this real system model allow to examine the effectiveness and efficiency of those new proposed OED methods. The measurement set selection and the sampling design of this system are developed which provide detailed instructions on how to improve experiments through OED.;Also, the sensitivity analysis and parameter identifiability analysis are conducted; and their impacts to experimental design are clearly identified

Information and decentralization in inventory, supply chain, and transportation systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2006.Includes bibliographical references (p. 199-213).This thesis investigates the impact of lack of information and decentralization of decision-making on the performance of inventory, supply chain, and transportation systems. In the first part of the thesis, we study two extensions of a classic single-item, single-period inventory control problem: the "newsvendor problem." We first analyze the newsvendor problem when the demand distribution is only partially specified by some moments and shape parameters. We determine order quantities that are robust, in the sense that they minimize the newsvendor's maximum regret about not acting optimally, and we compute the maximum value of additional information. The minimax regret approach is scalable to solve large practical problems, such as those arising in network revenue management, since it combines an efficient solution procedure with very modest data requirements. We then analyze the newsvendor problem when the inventory decision-making is decentralized. In supply chains, inventory decisions often result from complex negotiations among supply partners and might therefore lead to a loss of efficiency (in terms of profit loss).(cont.) We quantify the loss of efficiency of decentralized supply chains that use price-only contracts under the following configurations: series, assembly, competitive procurement, and competitive distribution. In the second part of the thesis, we characterize the dynamic nature of traffic equilibria in a transportation network. Using the theory of kinematic waves, we derive an analytical model for traffic delays capturing the first-order traffic dynamics and the impact of shock waves. We then incorporate the travel-time model within a dynamic user equilibrium setting and illustrate how the model applies to solve a large network assignment problem.by Guillaume Roels.Ph.D