Solving tri-level programming problems using a particle swarm optimization algorithm

© 2015 IEEE. Tri-level programming, a special case of multilevel programming, arises to deal with decentralized decision-making problems that feature interacting decision entities distributed throughout three hierarchical levels. As tri-level programming problems are strongly NP-hard and the existing solution approaches lack universality in solving such problems, the purpose of this study is to propose an intelligence-based heuristic algorithm to solve tri-level programming problems involving linear and nonlinear versions. In this paper, we first propose a general tri-level programming problem and discuss related theoretical properties. A particle swarm optimization (PSO) algorithm is then developed to solve the tri-level programming problem. Lastly, a numerical example is adopted to illustrate the effectiveness of the proposed PSO algorithm

A solution to bi/tri-level programming problems using particle swarm optimization

© 2016 Elsevier Inc. Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems

A compromise-based particle swarm optimization algorithm for solving Bi-level programming problems with fuzzy parameters

© 2015 IEEE. Bi-level programming has arisen to handle decentralized decision-making problems that feature interactive decision entities distributed throughout a bi-level hierarchy. Fuzzy parameters often appear in such a problem in applications and this is called a fuzzy bi-level programming problem. Since the existing approaches lack universality in solving such problems, this study aims to develop a particle swarm optimization (PSO) algorithm to solve fuzzy bi-level programming problems in the linear and nonlinear versions. In this paper, we first present a general fuzzy bi-level programming problem and discuss related theoretical properties based on a fuzzy number ranking method commonly used. A PSO algorithm is then developed to solve the fuzzy bi-level programming problem based on different compromised selections by decision entities on the feasible degree for constraint conditions under fuzziness. Lastly, an illustrative numerical example and two benchmark examples are adopted to state the effectiveness of the compromise-based PSO algorithm

Particle swarm optimization for bi-level pricing problems in supply chains

With rapid technological innovation and strong competition in hi-tech industries such as computer and communication organizations, the upstream component price and the downstream product cost usually decline significantly with time. As a result, an effective pricing supply chain model is very important. This paper first establishes two bi-level pricing models for pricing problems with the buyer and the vendor in a supply chain designated as the leader and the follower, respectively. A particle swarm optimization (PSO) based algorithm is developed to solve problems defined by these bi-level pricing models. Experiments illustrate that this PSO based algorithm can achieve a profit increase for buyers or vendors if they are treated as the leaders under some situations, compared with the existing methods. © 2010 Springer Science+Business Media, LLC

Optimistic Variants of Single-Objective Bilevel Optimization for Evolutionary Algorithms

Single-objective bilevel optimization is a specialized form of constraint optimization problems where one of the constraints is an optimization problem itself. These problems are typically non-convex and strongly NP-Hard. Recently, there has been an increased interest from the evolutionary computation community to model bilevel problems due to its applicability in real-world applications for decision-making problems. In this work, a partial nested evolutionary approach with a local heuristic search has been proposed to solve the benchmark problems and have outstanding results. This approach relies on the concept of intermarriage-crossover in search of feasible regions by exploiting information from the constraints. A new variant has also been proposed to the commonly used convergence approaches, i.e., optimistic and pessimistic. It is called an extreme optimistic approach. The experimental results demonstrate the algorithm converges differently to known optimum solutions with the optimistic variants. Optimistic approach also outperforms pessimistic approach. Comparative statistical analysis of our approach with other recently published partial to complete evolutionary approaches demonstrates very competitive results

A bi-level decision model for customer churn analysis

This paper develops a bi-level decision model and a solution approach to optimizing service features for a company to reduce its customer churn rate. First, a bi-level decision model, together with its modeling approach, are developed to describe the gaming relationship between decision makers in a company (service provider) and its customers. Then, a practical solution approach to reaching solutions for the bi-level-modeled customer churn problem is developed. Finally, experiments and case studies are conducted to illustrate the bi-level decision model and the solution approach. © 2013 Wiley Periodicals, Inc