Multi-Objective Optimization of Gas Pipeline Networks

The main goal of this paper is to prove that bi-objective optimization of high-pressure gas networks ensures grater system efficiency than scalar optimization. The proposed algorithm searches for a trade-off between minimization of the running costs of compressors and maximization of gas networks capacity (security of gas supply to customers). The bi-criteria algorithm was developed using a gradient projection method to solve the nonlinear constrained optimization problem, and a hierarchical vector optimization method. To prove the correctness of the algorithm, three existing networks have been solved. A comparison between the scalar optimization and bi-criteria optimization results confirmed the advantages of the bi-criteria optimization approach.

Second-Order Optimality Conditions: An extension to Hadamard Manifolds

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

Necessary and Sufficient Second-Order Optimality Conditions on Hadamard Manifolds

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivatives, second-order pseudoinvexity functions, and the second-order Karush–Kuhn–Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization, respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of “Higgs Boson like” potentials, among others.

Pointwise well-posedness and scalarization of optimization problems for locally convex cone-valued functions

We investigate the pointwise well-posedness of optimization problems for locally convex conevalued functions and establish some relations between the kinds of well-posedness. Via the neighborhoods and elements, we define the scalarization functions for locally convex cones and discuss their properties. We consider the scalar optimization problems and obtain some results about the well-posedness of the optimization problems.

Scalarization and well-posedness for set optimization using coradiant sets

The aim of this paper is to study scalarization and well-posedness for a set-valued optimization problem with order relations induced by a coradiant set. We introduce the notions of the set criterion solution for this problem and obtain some characterizations for these solutions by means of nonlinear scalarization. The scalarization function is a generalization of the scalarization function introduced by Khoshkhabar-amiranloo and Khorram. Moveover, we define the pointwise notions of LP well-posedness, strong DH-well-posedness and strongly B-well-posedness for the set optimization problem and characterize these properties through some scalar optimization problem based on the generalized nonlinear scalarization function respectively.

Memory-Enhanced Dynamic Multi-Objective Evolutionary Algorithm Based on Lp Decomposition

Decomposition-based multi-objective evolutionary algorithms provide a good framework for static multi-objective optimization. Nevertheless, there are few studies on their use in dynamic optimization. To solve dynamic multi-objective optimization problems, this paper integrates the framework into dynamic multi-objective optimization and proposes a memory-enhanced dynamic multi-objective evolutionary algorithm based on L p decomposition (denoted by dMOEA/D- L p ). Specifically, dMOEA/D- L p decomposes a dynamic multi-objective optimization problem into a number of dynamic scalar optimization subproblems and coevolves them simultaneously, where the L p decomposition method is adopted for decomposition. Meanwhile, a subproblem-based bunchy memory scheme that stores good solutions from old environments and reuses them as necessary is designed to respond to environmental change. Experimental results verify the effectiveness of the L p decomposition method in dynamic multi-objective optimization. Moreover, the proposed dMOEA/D- L p achieves better performance than other popular memory-enhanced dynamic multi-objective optimization algorithms.

Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

Robustness Testing of Model Based Multiple Criteria Decisions: Fundamentals and Applications

Robustness or insensitivity is a desirable property of decisions; however, most texts on robustness and/or sensitivity analysis do not define it precisely. A broad literature in this field concentrates on robust design of decisions (including robust optimization). This paper focuses on robustness testing, that is, checking whether a design has actually resulted in robust properties of the system if some of basic assumptions are changed. We propose a general framework of such robustness testing and show that robustness is a property of the relation between three (classes of) models: a basic model of the decision situation, a second model of possible perturbations of the first model, and a model of implementation of the decision, optionally taking into account some measurements of the impact of perturbations. Typical approaches to robustness or sensitivity analysis assume tacitly that the first two models can be combined and analyze parameters deviations in one combined model. However, the role of the first two models can be asymmetric if some optimization of the decision is performed on the first model. We extend this framework, intended originally for single criteria (scalar) optimization to multiple criteria (vector) optimization. The proposed approach is illustrated by diverse examples.