Decision Problems, Search Problems, and Counting Problems

1993 ◽  
pp. 11-50
Author(s):  
Johannes Köbler ◽  
Uwe Schöning ◽  
Jacobo Torán
Keyword(s):  
Decision Problems ◽  
Search Problems ◽  
Counting Problems

Using Evolutionary Algorithms to Generate Alternatives for Multiobjective Site-Search Problems

2002 ◽  
Vol 34 (4) ◽  
pp. 639-656 ◽  
Author(s):  
Ningchuan Xiao ◽  
David A Bennett ◽  
Marc P Armstrong
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Decision Problems ◽  
Graph Representation ◽  
Search Problems ◽  
Site Search ◽  
Conflicting Objectives ◽  
Different Types ◽  
Critical Issues ◽  
A Site

Multiobjective site-search problems are a class of decision problems that have geographical components and multiple, often conflicting, objectives; this kind of problem is often encountered and is technically difficult to solve. In this paper we describe an evolutionary algorithm (EA) based approach that can be used to address such problems. We first describe the general design of EAs that can be used to generate alternatives that are optimal or close to optimal with respect to multiple criteria. Then we define the problem addressed in this research and discuss how the EA was designed to solve it. In this procedure, called MOEA/Site, a solution (that is, a site) is encoded by using a graph representation that is operated on by a set of specifically designed evolutionary operations. This approach is applied to five different types of cost surfaces and the results are compared with 10 000 randomly generated solutions. The results demonstrate the robustness and effectiveness of this EA-based approach to geographical analysis and multiobjective decisionmaking. Critical issues regarding the representation of spatial solutions and associated evolutionary operations are also discussed.

scholarly journals Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs

2021 ◽  
Vol 21 (5) ◽  
pp. 575-592
Author(s):  
VIKTOR BESIN ◽  
MARKUS HECHER ◽  
STEFAN WOLTRAN
Keyword(s):  
Epistemic Logic ◽  
Complexity Analysis ◽  
Quantitative Reasoning ◽  
Decision Problems ◽  
Logic Programs ◽  
Counting Problems ◽  
World Views ◽  
Modal Operators ◽  
Programming Paradigm ◽  
Answer Sets

AbstractExtending the popular answer set programming paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs) where standard rules are equipped with modal operators which allow to express conditions on literals for being known or possible, that is, contained in all or some answer sets, respectively. ELPs thus deliver multiple collections of answer sets, known as world views. Employing ELPs for reasoning problems so far has mainly been restricted to standard decision problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we take a next step and contribute to epistemic logic programming in two ways: First, we establish quantitative reasoning for ELPs, where the acceptance of a certain set of literals depends on the number (proportion) of world views that are compatible with the set. Second, we present a novel system that is capable of efficiently solving the underlying counting problems required to answer such quantitative reasoning problems. Our system exploits the graph-based measure treewidth and works by iteratively finding and refining (graph) abstractions of an ELP program. On top of these abstractions, we apply dynamic programming that is combined with utilizing existing search-based solvers like (e)clingo for hard combinatorial subproblems that appear during solving. It turns out that our approach is competitive with existing systems that were introduced recently.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

Best Neighbor Heuristic Search for Finding Minimum Paths in Transportation Networks

1998 ◽  
Vol 1651 (1) ◽  
pp. 48-52 ◽  
Author(s):  
Jeffrey L. Adler
Keyword(s):  
Heuristic Search ◽  
Transportation Networks ◽  
Transportation Network ◽  
Search Problems ◽  
A Algorithm ◽  
Running Time ◽  
Search Effort ◽  
Wide Range ◽  
Path Search ◽  
Sparse Networks

For a wide range of transportation network path search problems, the A* heuristic significantly reduces both search effort and running time when compared to basic label-setting algorithms. The motivation for this research was to determine if additional savings could be attained by further experimenting with refinements to the A* approach. We propose a best neighbor heuristic improvement to the A* algorithm that yields additional benefits by significantly reducing the search effort on sparse networks. The level of reduction in running time improves as the average outdegree of the network decreases and the number of paths sought increases.

Multiobjective Hierarchical Decision Problems in C3, III.

1985 ◽  
Author(s):  
UNIVERSITY OF SOUTHERN CALIFORNIA DOWNEY
Keyword(s):  
Decision Problems ◽  
Hierarchical Decision
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