A Posynomial Geometric Programming Restricted to a System of Fuzzy Relation Equations

AbstractA posynomial geometric optimization problem subjected to a system of max-min fuzzy relational equations (FRE) constraints is considered. The complete solution set of FRE is characterized by unique maximal solution and finite number of minimal solutions. A two stage procedure has been suggested to compute the optimal solution for the problem. Firstly all the minimal solutions of fuzzy relation equations are determined. Then a domain specific evolutionary algorithm (EA) is designed to solve the optimization problems obtained after considering the individual sub-feasible region formed with the help of unique maximum solution and each of the minimal solutions separately as the feasible domain with same objective function. A single optimal solution for the problem is determined after solving these optimization problems. The whole procedure is illustrated with a numerical example

Geometric Programming Subject to System of Fuzzy Relation Inequalities

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on the solution process. Also, an algorithm and two practical examples are presented to abbreviate and illustrate the steps of the problem resolution

A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production

This paper addresses the problem of the optimal design of batch plants with imprecise demands and proposes an alternative treatment of the imprecision by using fuzzy concepts. For this purpose, we extended a multiobjective genetic algorithm (MOGA) developed in previousworks, taking into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The former is computed by comparing the fuzzy computed production time to a given fuzzy production time horizon and the latter is based on the additional fuzzy demand that the plant is able to produce. The methodology provides a set of scenarios that are helpful to the decision’s maker and constitutes a very promising framework for taken imprecision into account in new product development stage

Optimization Model of Fuzzy Rule Based Expert System Using Max-Min Composition and Schema Mapping Translation

Abstract— Fuzzy Decision Making involves a process of selecting one or more alternatives or solutions from a finite set of alternatives which suits a set of constraints. In the rule-based expert system, the terms following in the decision making is using knowledge based and the IF Statements of the rule are called the premises, while the THEN part of the rule is called conclusion. Membership function and knowledge based determines the performance of fuzzy rule based expert system. Membership function determines the performance of fuzzy logic as it relates to represent fuzzy set in a computer. Knowledge Based in the other side relates to capturing human cognitive and judgemental processes, such as thinking and reasoning. In this paper, we have proposed a method by using Max-Min Composition combined with Genetic Algorithm for determining membership function of Fuzzy Logic and Schema Mapping Translation for the rules assignment.Keywords— Fuzzy Decision Making, Rule-Based Expert System, Membership Function, Knowledge Based, Max-Min Composition, Schema Mapping Translatio

Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs

In this paper, we introduce a type of latticized optimization problem whose objective function is the maximum component function and the feasible region is defined as a system of fuzzy relational equalities (FRE) defined by the Dombi t-norm. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Some necessary and sufficient conditions are derived to determine the feasibility of the problem. The feasible solution set is characterized in terms of a finite number of closed convex cells. An algorithm is presented for solving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.Comment: arXiv admin note: text overlap with arXiv:2206.09716, arXiv:2207.0637

An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints

Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the generalized form of fuzzy relational inequalities (FRI) in which fuzzy inequality replaces ordinary inequality in the constraints. Fuzzy constraints enable us to attain optimal points (called super-optima) that are better solutions than those resulted from the resolution of the similar problems with ordinary inequality constraints. This paper considers the linear objective function optimization with respect to max-product FRI-FC problems. It is proved that there is a set of optimization problems equivalent to the primal problem. Based on the algebraic structure of the primal problem and its equivalent forms, some simplification operations are presented to convert the main problem into a more simplified one. Finally, by some appropriate mathematical manipulations, the main problem is transformed into an optimization model whose constraints are linear. The proposed linearization method not only provides a super-optimum (that is better solution than ordinary feasible optimal solutions) but also finds the best super-optimum for the main problem. The current approach is compared with our previous work and some well-known heuristic algorithms by applying them to random test problems in different sizes.Comment: 29 pages, 8 figures, 7 table

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems