Digraph description of k-interchange technique for optimization over permutations and adaptive algorithm system

TL;DR

This paper introduces a digraph-based framework for understanding and solving permutation optimization problems, proposing a multi-level adaptive system that analyzes problems and selects appropriate heuristics.

Contribution

It presents a novel digraph description of k-interchange techniques and develops a multi-level adaptive algorithm system for permutation optimization.

Findings

The digraph framework aids in understanding problem convexity and solvability.

Hierarchical heuristics can be designed based on the multi-level description.

The adaptive system effectively analyzes and chooses strategies for different permutation problems.

Abstract

The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization problems over permutations (e.g., ordering, scheduling, traveling salesman problem). The description is based on permutation neighborhoods of several kinds (e.g., by improvement of an objective function). Our proposed operational digraph and its kinds can be considered as a way to understand convexity and polynomial solvability for combinatorial optimization problems over permutations. Issues of an analysis of problems and a design of hierarchical heuristics are discussed. The discussion leads to a multi-level adaptive algorithm system which analyzes an individual problem and selects/designs a solving strategy (trajectory).