A bilevel game theoretic approach to optimum design of flywheels

Abstract

Multiobjective optimization problems arise frequently in mechanical design. One approach to solving these types of problems is to use a game theoretic formulation. This article illustrates the application of a bilevel, leader-follower model for solving an optimum design problem. In particular, the optimization problem is modelled as a Stackelberg game. The partitioning of variables between the leader and follower problem is discussed and a variable partitioning metric is introduced to compare various variable partitions. A computational procedure based on variable updating using sensitivity information is developed for exchanging information between the follower and leader problems. The proposed approach is illustrated through the design of a flywheel. The two objective functions used for the design problem include maximizing the kinetic energy stored in the flywheel while simultaneously minimizing the manufacturing cost.

Multi-objective optimization of mechanism design using a bi-level game theoretic formulation

“…The players control a subset of design variables and seek to optimize their individual objective functions. Some applications on the use of game theory in the context of mechanical design include Badhrinath and Rao (1996), Rao et al (1997), Lewis and Mistree (1998), Hernandez and Mistree (2000), and Ghotbi and Dhingra (2012).…”

“…A design of experiment-based approach (Montgomery, 2005) coupled with response surface methodology (Myers and Montgomery, 2002) has been proposed by Lewis and Mistree (1998), Marston (2000), and Hernandez and Mistree (2000) to approximate the RRS for the players. Ghotbi and Dhingra (2012) developed a new technique using sensitivity information to approximate the RRS for the players. Ghotbi et al (2014) showed that this technique is more effective than the approach developed before by Lewis and Mistree (1998) and Marston (2000).…”

Multi-objective optimization of actively controlled structures with topological considerations

“…The follower solution, or rational reaction set (RRS), depends on the choices made by the leader. Several methods have been proposed for the computation of the RRS such as response surface methods (Lewis and Mistree, 1998), monotonicity analysis (Rao et al, 1997) and sensitivity-based method (Ghotbi and Dhingra, 2012). Due to the nature of design variables for the problem considered herein, a response surface-based approach is used to construct the RRS.…”

A Game Theoretical Approach Based Bidding Strategy Optimization for Power Producers in Power Markets with Renewable Electricity

“…After receiving all bidding strategies of all power producers, the ISO determines the generating volume of each power producer at time slot h ∈ H with the goal of minimizing the total cost for utility companies purchasing electricity. The lower level of the bi-level optimization can be expressed as the following optimization problem: (30) where U denotes the total cost for utility companies purchasing electricity and q h nb denotes the generating volume of power producer n ∈ N at time slot h ∈ H, which is the decision variable of the follower's problem. Supply and demand have to be balanced in real time; hence, the following constraints have to be satisfied, (32) where q h nb max denotes the maximum generating volume of power producer n ∈ N at time slot h ∈ H. When the problem (30) is solved, optimum values of the follower's variables q h nb are determined for given values of the leader's variables b h nb , which are treated as a fixed parameter at the moment.…”

“…Accordingly, the price of power producer n ∈ N at time slot h ∈ H is determined and denoted by p h nb . The follower's optimum solution has to update while the leader's variables are changed [30].…”