Search results for "optimization problems"
showing 8 items of 8 documents
Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations
2022
AbstractWe introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires …
Logical definability of NP-optimisation problems with monadic auxiliary predicates
1993
Given a first-order formula ϕ with predicate symbols e1...el, so,...,sr, an NP-optimisation problem on -structures can be defined as follows: for every -structure G, a sequence of relations on G is a feasible solution iff satisfies ϕ, and the value of such a solution is defined to be ¦S0¦. In a strong sense, every polynomially bounded NP-optimisation problem has such a representation, however, it is shown here that this is no longer true if the predicates s1, ...,sr are restricted to be monadic. The result is proved by an Ehrenfeucht-Fraisse game and remains true in several more general situations.
On the hardness of optimization in power-law graphs
2008
Our motivation for this work is the remarkable discovery that many large-scale real-world graphs ranging from Internet and World Wide Web to social and biological networks appear to exhibit a power-law distribution: the number of nodes y"i of a given degree i is proportional to i^-^@b where @b>0 is a constant that depends on the application domain. There is practical evidence that combinatorial optimization in power-law graphs is easier than in general graphs, prompting the basic theoretical question: Is combinatorial optimization in power-law graphs easy? Does the answer depend on the power-law exponent @b? Our main result is the proof that many classical NP-hard graph-theoretic optimizati…
Assessing the Performance of Interactive Multiobjective Optimization Methods
2021
Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a …
Adaptive and Dynamic Ant Colony Search Algorithm for Optimal Distribution Systems Reinforcement Strategy
2006
The metaheuristic technique of Ant Colony Search has been revised here in order to deal with dynamic search optimization problems having a large search space and mixed integer variables. The problem to which it has been applied is an electrical distribution systems management problem. This kind of issues is indeed getting increasingly complicated due to the introduction of new energy trading strategies, new environmental constraints and new technologies. In particular, in this paper, the problem of finding the optimal reinforcement strategy to provide reliable and economic service to customers in a given time frame is investigated. Utilities indeed need efficient software tools to take deci…
A Binary Particle Swarm Optimization Algorithm for a Double Auction Market
2007
In this paper, we shall show the design of a multi-unit double auction (MDA) market. It should be enough robust, flexible and sufficiently efficient in facilitating exchanges. In a MDA market, sellers and buyers submit respectively asks and bids. A trade is made if a buyers bid exceeds a sellers ask. A sellers ask may match several buyers bids and a buyers bid may satisfy several sellers asks. The trading rule of a market defines the organization, information exchange process, trading procedure and clearance rules of the market. The mechanism is announced before the opening of the market so that every agent knows how the market will operate in advance. These autonomous agents pursue their o…
Greedy and K-Greedy algoritmhs for multidimensional data association
2011
[EN] The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension $d\in\Bbb{N}$ is to match groups of $d$ objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for $d\geq3$. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimen…
Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case
2017
Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive …