Large scale problems in engineering, in the design of networks and energy systems, the biomedical fields, and finance are modeled as optimization problems. Humans and nature are constantly optimizing to minimize costs or maximize profits, to maximize the flow in a network, or to minimize the probability of a blackout in a smart grid. Due to new algorithmic developments and the computational power of machines (digital, analog, biochemical, quantum computers etc), optimization algorithms have been used to 'solve' problems in a wide spectrum of applications in science and engineering. But what do we mean by 'solving' an optimization problem? What are the limits of what machines (and humans) can compute?
Panos M. Pardalos: Center for Applied Optimization, University of Florida www.ise.ufl.edu/pardalos
During recent years the interest in Bayesian approach to global optimization is increasing. Nevertheless, some challenges deserve be investigated more intensively. In the talk the following problems will be considered discussing ways of their solution. The discussion includes the selection of a statistical model of objective functions and the estimation of its parameters, the main ideas of the corresponding global optimization algorithms, their convergence and implementation. In the talk will be presented also the recent results of the author about the bi-objective selection in global search, and about including the information on gradients in a search algorithm..
Antanas Žilinskas, Professor (Full), Principal Researcher, Department of Informatics Vilnius University, Vilnius, Lithuania.
Abstract: Real-life optimization problems typically have several conflicting objective functions to be optimized simultaneously and they often are nonlinear. Multiobjective optimization methods are needed to find the best balance between the objectives. In so-called Pareto optimal solutions, improvement in one objective function necessitates allowing impairment in at least one of the others. Because we typically have many Pareto optimal solutions, we need additional preference information from a domain expert, a decision maker, to find the most preferred Pareto optimal solution to be implemented. We can classify multiobjective optimization methods according to the role of the decision maker in the solution process. We characterize four classes with the main focus on interactive methods, where the decision maker iteratively directs the solution process with one's preference information. Simultaneously, (s)he learns and gains insight about the interdependencies of the objectives and can adjust one's preferences while learning.
In e.g. simulation based optimization, function evaluations may be time-consuming. We present three types of approaches for dealing with computationally expensive functions. The first idea is to fit a metamodel to each expensive objective function. Alternatively, we can generate a representative set of Pareto optimal solutions in advance and fit a computationally inexpensive metamodel to replace the single objective scalarizing function that the multiobjective optimization method employs. The third approach is to create a surrogate problem that is computationally inexpensive and employ different interactive multiobjective optimization methods to solve it. This approach is also based on a pre-generated representative set. We illustrate the three approaches with example methods. Finally, we share some experiences in solving real problems.
Kaisa Miettinen: University of Jyvaskyla, Industrial Optimization Group, Faculty of Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyvaskyla, Finland, kaisa.miettinen@jyu.fi http://users.jyu.fi/~miettine/engl.html
Joint work with Dmitri E. Kvasov, Daniela Lera, and Marat S. Mukhametzhanov
Deterministic Lipschitz global optimization algorithms are considered in this lecture. Derivative-free methods and methods proposed for solving problems with Lipschitz first derivatives are discussed. In both cases, a special attention is dedicated to techniques used to estimate Lipschitz constants and to balance global and local information. Several modifications are presented and compared with widely used multidimensional metaheuristic global optimization methods: genetic algorithms, differential evolution, particle swarm optimization, artificial bee colony algorithms, and firefly algorithms. For this purpose, there has been introduced a methodology allowing one to compare stochastic methods with deterministic ones by using operational characteristics originally proposed for working with deterministic algorithms only. As a result, a visual comparison of methods having different nature on classes of randomly generated test functions becomes possible. A detailed description of the new methodology for comparing, called operational zones, is given and results of broad numerical experiments are reported.
Yaroslav D. Sergeyev: Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Universita della Calabria, Rende (CS), Italy, Department of Software and Supercomputing Technologies, Lobachevsky State University of Nizhni Novgorod, Russia
Joint work with Seyedmohammadhossein Hosseinian and Dalila B.M.M. Fontes
We explore the connections between the classical maximum clique problem and its edge-weighted generalization, the maximum edge weight clique (MEWC) problem. As a result, a new analytic upper bound on the clique number of a graph is obtained and an exact algorithm for solving the MEWC problem is developed. The bound on the clique number is derived using a Lagrangian relaxation of an integer (linear) programming formulation of the MEWC problem. Furthermore, coloring-based bounds on the clique number are utilized in a novel upper-bounding scheme for the MEWC problem. This scheme is employed within a combinatorial branch-and-bound framework, yielding an exact algorithm for the MEWC problem. Results of computational experiments demonstrate a superior performance of the proposed algorithm compared to existing approaches.
Sergiy Butenko, Professor, Donna and Jim Furber '64 Faculty Fellow, A & M University, Texas, US, https://engineering.tamu.edu/industrial/profiles/sbutenko.html