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-criteria optimization and decision-making approach for improvement of food engineering processes.

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demostrated using experimental data obtained on osmotic dehydratation of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes

A multi-criteria optimization and decision-making approach for improvement of food engineering processes

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demonstrated using experimental data obtained on osmotic dehydration of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.Facultad de IngenieríaCentro de Investigación y Desarrollo en Criotecnología de Alimento

A multi-criteria optimization and decision-making approach for improvement of food engineering processes

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demonstrated using experimental data obtained on osmotic dehydration of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.Facultad de IngenieríaCentro de Investigación y Desarrollo en Criotecnología de Alimento

Methodological review of multicriteria optimization techniques: aplications in water resources

Multi-criteria decision analysis (MCDA) is an umbrella approach that has been applied to a wide range of natural resource management situations. This report has two purposes. First, it aims to provide an overview of advancedmulticriteriaapproaches, methods and tools. The review seeks to layout the nature of the models, their inherent strengths and limitations. Analysis of their applicability in supporting real-life decision-making processes is provided with relation to requirements imposed by organizationally decentralized and economically specific spatial and temporal frameworks. Models are categorized based on different classification schemes and are reviewed by describing their general characteristics, approaches, and fundamental properties. A necessity of careful structuring of decision problems is discussed regarding planning, staging and control aspects within broader agricultural context, and in water management in particular. A special emphasis is given to the importance of manipulating decision elements by means ofhierarchingand clustering. The review goes beyond traditionalMCDAtechniques; it describes new modelling approaches. The second purpose is to describe newMCDAparadigms aimed at addressing the inherent complexity of managing water ecosystems, particularly with respect to multiple criteria integrated with biophysical models,multistakeholders, and lack of information. Comments about, and critical analysis of, the limitations of traditional models are made to point out the need for, and propose a call to, a new way of thinking aboutMCDAas they are applied to water and natural resources management planning. These new perspectives do not undermine the value of traditional methods; rather they point to a shift in emphasis from methods for problem solving to methods for problem structuring. Literature review show successfully integrations of watershed management optimization models to efficiently screen a broad range of technical, economic, and policy management options within a watershed system framework and select the optimal combination of management strategies and associated water allocations for designing a sustainable watershed management plan at least cost. Papers show applications in watershed management model that integrates both natural and human elements of a watershed system including the management of ground and surface water sources, water treatment and distribution systems, human demands,wastewatertreatment and collection systems, water reuse facilities,nonpotablewater distribution infrastructure, aquifer storage and recharge facilities, storm water, and land use

04461 Abstracts Collection -- Practical Approaches to Multi-Objective Optimization

From 07.11.04 to 12.11.04, the Dagstuhl Seminar 04461 ``Practical Approaches to Multi-Objective Optimization\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Multicriteria Optimization Techniques for Understanding the Case Mix Landscape of a Hospital

Various medical and surgical units operate in a typical hospital and to treat their patients these units compete for infrastructure like operating rooms (OR) and ward beds. How that competition is regulated affects the capacity and output of a hospital. This article considers the impact of treating different patient case mix (PCM) in a hospital. As each case mix has an economic consequence and a unique profile of hospital resource usage, this consideration is important. To better understand the case mix landscape and to identify those which are optimal from a capacity utilisation perspective, an improved multicriteria optimization (MCO) approach is proposed. As there are many patient types in a typical hospital, the task of generating an archive of non-dominated (i.e., Pareto optimal) case mix is computationally challenging. To generate a better archive, an improved parallelised epsilon constraint method (ECM) is introduced. Our parallel random corrective approach is significantly faster than prior methods and is not restricted to evaluating points on a structured uniform mesh. As such we can generate more solutions. The application of KD-Trees is another new contribution. We use them to perform proximity testing and to store the high dimensional Pareto frontier (PF). For generating, viewing, navigating, and querying an archive, the development of a suitable decision support tool (DST) is proposed and demonstrated.Comment: 38 pages, 17 figures, 11 table

Feasibility of Multisolutions Optimization Technique for Real-Time HDR Brachytherapy of Prostate

The purpose of this study was to evaluate the efficacy of multisolutions optimization algorithm for High Dose Rate (HDR) brachytherapy of prostate. In this retrospective study, we included data from 20 prostate cancer patients who underwent ultrasound based real time HDR Brachytherapy at institution. The treatment plans of all 20 patients were optimized in Oncentra Prostate treatment planning system (TPS) using inverse dose volume histogram based optimization followed by graphical optimization (GRO) in real time. The data of all the patients were retrieved later, and the treatment plans were re-optimized using multisolutions dose volume histogram based optimization (MDVHO) and multisolutions variance based optimization (MVBO) algorithms with same set of dose constraints, same number of catheters, and same contour set as in GRO. Several Pareto optimal solutions were obtained by varying the weighting factors of composite objective function in finite steps of adequate resolutions.  These solutions were then stored in the database of TPS and same decision criteria was employed to pick the final solution using a decision engine. The average values for planning target volume receiving 100% of prescribed dose (V100) for MDVHO, MVBO, and GRO were 95.03%, 86.72% and 97.56%, respectively. The average V100 due to MDVHO was statistically significant (P = 0.002) in comparison to MVBO, whereas the average V100 due to MDVHO and GRO was not statistically significant (P = 0.066). In conclusion, the MDVHO can provide comparable solutions to typical clinical optimizations using GRO within clinically reasonable amount of time. In most of the cases, the plans created by MVBO were not clinically acceptable without users’ further manual intervention

Increasing the density of available pareto optimal solutions

The set of available multi-objective optimization algorithms continues to grow. This fact can be partially attributed to their widespread use and applicability. However this increase also suggests several issues remain to be addressed satisfactorily. One such issue is the diversity and the number of solutions available to the decision maker (DM). Even for algorithms very well suited for a particular problem, it is difficult - mainly due to the computational cost - to use a population large enough to ensure the likelihood of obtaining a solution close to the DMs preferences. In this paper we present a novel methodology that produces additional Pareto optimal solutions from a Pareto optimal set obtained at the end run of any multi-objective optimization algorithm. This method, which we refer to as Pareto estimation, is tested against a set of 2 and 3-objective test problems and a 3-objective portfolio optimization problem to illustrate its’ utility for a real-world problem