Method of Group Decision Making for Production Planning of the Oil Refinery Plant

This article is devoted to the problem of decision making under uncertainty. An aggregated approach is used that combines optimization and choice of a solution, which makes it possible to obtain a more realistic solution. The criteria in the vector optimization problem are: profit, product quality, employee satisfaction. To solve the optimization problem, 3 methods were used: "Goal programming", "Interactive", "FMOLP". The task of group decision making is implemented on the basis of the package FGDSS-CD (Fuzzy group Decision Support System).

Method of Group Decision Making for Production Planning of the Oil Refinery Plant

This article is devoted to the problem of decision making under uncertainty. An aggregated approach is used that combines optimization and choice of a solution, which makes it possible to obtain a more realistic solution. The criteria in the vector optimization problem are: profit, product quality, employee satisfaction. To solve the optimization problem, 3 methods were used: “Goal programming”, “Interactive”, “FMOLP”. The task of group decision making is implemented on the basis of the package FGDSS-CD (Fuzzy group Decision Support System).

Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

In this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

Resolution of the Min-Max Optimization Problem Applied in the Agricultural Sector with the Estimation of Yields by Nonparametric Statistical Approaches

The ultimate objective of the problem under study is to apply the min-max tool, thus making it possible to optimize the default risks linked to several areas: the agricultural sector, for example, which requires the optimization of the default risk using the following elements: silage crops, annual consumption requirements, and crops produced for a given year. To minimize the default risk in the future, we start, in the first step, by forecasting the total budget of agriculture investment for the next 20 years, then distribute this budget efficiently between the irrigation and construction of silos. To do this, Bangladesh was chosen as an empirical case study given the availability of its data on the FAO website; it is considered a large agricultural country in South Asia. In this article, we give a detailed and original in-depth study of the agricultural planning model through a calculating algorithm suggested to be coded on the R software thereafter. Our approach is based on an original statistical modeling using nonparametric statistics and considering an example of a simulation involving agricultural data from the country of Bangladesh. We also consider a new pollution model, which leads to a vector optimization problem. Graphs illustrate our quantitative analysis.

Time Consistency of the Mean-Risk Problem

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through a backward recursion. The mean-risk problem is known to be time inconsistent when considered in its scalarized form. However, when left in its original bi-objective form, it turns out to satisfy a more general time consistency property that seems better suited to a vector optimization problem. In “Time Consistency of the Mean-Risk Problem,” Kováĉova and Rudloff introduce a set-valued version of the famous Bellman principle and show that the bi-objective mean-risk problem does satisfy it. Then, the upper image, a set that contains the efficient frontier on its boundary, recurses backward in time. Kováĉova and Rudloff present conditions under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. This opens the door for a new branch in mathematics: dynamic multivariate programming.

Path-Planning for Mobile Robots Using a Novel Variable-Length Differential Evolution Variant

Mobile robots are currently exploited in various applications to enhance efficiency and reduce risks in hard activities for humans. The high autonomy in those systems is strongly related to the path-planning task. The path-planning problem is complex and requires in its formulation the adjustment of path elements that take the mobile robot from a start point to a target one at the lowest cost. Nevertheless, the identity or the number of the path elements to be adjusted is unknown; therefore, the human decision is necessary to determine this information reducing autonomy. Due to the above, this work conceives the path-planning as a Variable-Length-Vector optimization problem (VLV-OP) where both the number of variables (path elements) and their values must be determined. For this, a novel variant of Differential Evolution for Variable-Length-Vector optimization named VLV-DE is proposed to handle the path-planning VLV-OP for mobile robots. VLV-DE uses a population with solution vectors of different sizes adapted through a normalization procedure to allow interactions and determine the alternatives that better fit the problem. The effectiveness of this proposal is shown through the solution of the path-planning problem in complex scenarios. The results are contrasted with the well-known A* and the RRT*-Smart path-planning methods.

Duality Theorem for a Minimax Vector Optimization Problem

A duality theorem is stated and proved for a minimax vector optimization problem where the vectors are elements of the set of products of compact Polish spaces. A special case of this theorem is derived to show that two metrics on the space of probability distributions on countable products of Polish spaces are identical. The appendix includes a proof that, under the appropriate conditions, the function studied in the optimisation problem is indeed a metric. The optimisation problem is comparable to multi-commodity optimal transport where there is dependence between commodities. This paper builds on the work of R.S. MacKay who introduced the metrics in the context of complexity science in [4] and [5]. The metrics have the advantage of measuring distance uniformly over the whole network while other metrics on probability distributions fail to do so (e.g total variation, Kullback–Leibler divergence, see [5]). This opens up the potential of mathematical optimisation in the setting of complexity science.

Stability kernel of vector optimization problems under perturbations of criterion functions

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of optimiza-tion multicriterial problems. In the optimization problems, including problems with vector criterion, small per-turbations in initial data can result in solutions strongly different from the true ones. The results of the con-ducted researches allow us to extend the known class of vector optimization problems, stable with respect to in-put data perturbations in vector criterion. We are talking about stability in the sense of Hausdorff lower semicontinuity for point-set mapping that characterizes the dependence of the set of optimal solutions on the input data of the vector optimization problem. The conditions of stability against input data perturbations in vector criterion for the problem of finding Pareto optimal solutions with continuous partial criterion func-tions and feasible set of arbitrary structure are obtained by studying the sets of points that are stable belonging and stable not belonging to the Pareto set.

A study on vector variational-like inequalities using convexificators and application to its bi-level form

<p style='text-indent:20px;'>This paper deals with the weak versions of the vector variational-like inequalities, namely Stampacchia and Minty type under invexity in the framework of convexificators. The connection between both the problems along with the link to vector optimization problem are analyzed. An application to nonconvex mathematical programming has also been presented. Further, the bi-level version of these problems is formulated and a procedure to obtain the solution involving the auxiliary principle technique is described in detail. We have shown that the iterative algorithm with the help of which we get the approximate solution converges strongly to the exact solution of the problem.</p>