Download Ant Colony Optimization and Constraint Programming by Christine Solnon PDF

By Christine Solnon

Ant colony optimization is a metaheuristic which has been effectively utilized to quite a lot of combinatorial optimization difficulties. the writer describes this metaheuristic and stories its potency for fixing a few tough combinatorial difficulties, with a selected concentrate on constraint programming. The textual content is prepared into 3 parts.

The first half introduces constraint programming, which gives excessive point positive factors to declaratively version difficulties via constraints. It describes the most latest ways for fixing constraint pride difficulties, together with whole tree seek techniques and metaheuristics, and exhibits how they are often built-in inside of constraint programming languages.

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Extra info for Ant Colony Optimization and Constraint Programming

Example text

In the following chapters, we describe the main approaches that may be used to solve CSPs in a generic way. info Chapter 4 Exact Approaches We describe a first generic approach for solving combinatorial problems modeled as CSPs. The idea is to explore the set of all possible assignments in a systematic way until either finding a solution (if the CSP is consistent) or demonstrating that there is no solution (if the CSP is inconsistent). 1. As the number of assignments to explore may be huge (exponential), this tree-based exploration is combined with filtering techniques which propagate constraints to reduce the number of assignments to explore.

Variables that should be assigned numerical values. A numerical constraint is either an equality (=), a disequality (=) or an inequality (≤, ≥, <, >) between two arithmetic expressions. These arithmetic expressions may be linear or nonlinear functions which may contain variable products or logarithmic functions, exponentials, etc. e. variables that should be assigned to sets of values. A set constraint may be an equality (=), a disequality (=), an inclusion (⊂, ⊆) or a membership (∈) relation between set expressions that may be defined with set operators such as ∪ and ∩.

N} D(rdi ) = {2, . . , 2n} D(f di ) = {1 − n, . . , n − 1}; – the set of constraints C contains a first subset of constraints to describe the relationships between row and diagonal variables: ∀i ∈ {1, . . , n} : rdi = xi + i ∀i ∈ {1, . . , n} : f di = xi − i and there are also three global difference constraints: allDiff ({xi | i ∈ {1, . . , n}}) allDiff ({rdi | i ∈ {1, . . , n}}) allDiff ({f di | i ∈ {1, . . , n}}). 1 for four queens corresponds to the following assignment: A = {(x1 , 2), (x2 , 4), (x3 , 1), (x4 , 3), (rd1 , 3), (rd2 , 6), (rd3 , 4), (rd4 , 7), (f d1 , 1), (f d2 , 2), (f d3 , −2), (f d4 , −1)}.

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