A hybrid integrated multi-objective optimization procedure for estimating nadir point

A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure

A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point

Abstract. A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure

A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point

Abstract. A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly, estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure

Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches

A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

A Multi-Objective Optimization Approach for Multi-Head Beam-Type Placement Machines

This paper addresses a highly challenging scheduling problem in the field of printed circuit board (PCB) assembly systems using Surface Mounting Devices (SMD). After describing some challenging optimization sub-problems relating to the heads of multi-head surface mounting placement machines, we formulate an integrated multi-objective mathematical model considering of two main sub-problems simultaneously. The proposed model is a mixed integer nonlinear programming one which is very complex to be solved optimally. Therefore, it is first converted into a linearized model and then solved using an efficient multi-objective approach, i.e., the augmented epsilon constraint method. An illustrative example is also provided to show the usefulness and applicability of the proposed model and solution method.PCB assembly. Multi-head beam-type placement machine. Multi-objective mathematical programming. Augmented epsilon-constraint method

Determining Feasibility Resilience: Set Based Design Iteration Evaluation Through Permutation Stability Analysis

The goal of robust design is to select a design that will still perform satisfactorily even with unexpected variation in design parameters. A resilient design will accommodate unanticipated future system requirements. Through studying the variations of system parameters through the use of multi objective optimization, a designer hopes to locate a robustly resilient design, which performs current mission well even with varying system parameters and is able to be easily repurposed to new missions. This ability to withstand changes is critical because it is common for the product of a design to undergo changes throughout its life cycle. This subject has been an active area of research in industrial design and systems engineering but most methodologies rest upon exhaustive understanding of design, manufacturing and mission variance. The thrust of this research is to develop new methodologies for estimating robust resilience given imperfect information. In this work we will apply new methodologies for locating resilient designs within a dataset derive from a study performed by the Small Surface Combatant Task Force in order to improve upon a state of the art design process. Two new methodologies, permutation stability analysis and mutation stability analysis, are presented along with results and discussion as applied to the SSCTF dataset. It is demonstrated that these new methods improve upon the state of the art by providing insight into the robustness and resilience of selected system properties. These methodologies, although applied to the SSCTF dataset are posed more generally for wider application in system design

Multi-Objective Optimization of Mixed-Variable, Stochastic Systems Using Single-Objective Formulations

Many problems exist where one desires to optimize systems with multiple, often competing, objectives. Further, these problems may not have a closed form representation, and may also have stochastic responses. Recently, a method expanded mixed variable generalized pattern search/ranking and selection (MVPS-RS) and Mesh Adaptive Direct Search (MADS) developed for single-objective, stochastic problems to the multi-objective case by using aspiration and reservation levels. However, the success of this method in approximating the true Pareto solution set can be dependent upon several factors. These factors include the experimental design and ranges of the aspiration and reservation levels, and the approximation quality of the nadir point. Additionally, a termination criterion for this method does not yet exist. In this thesis, these aspects are explored. Furthermore, there may be alternatives or additions to this method that can save both computational time and function evaluations. These include the use of surrogates as approximating functions and the expansion of proven singleobjective formulations. In this thesis, two new approaches are developed that make use of all of these previous existing methods in combination