The 2-Opt heuristic is a very simple, easy-to-implement local search heuristic for the traveling salesman problem. While it usually provides good approximations to the optimal tour in experiments, its worst-case performance is poor. In an attempt to explain the approximation performance of 2-Opt, we analyze the smoothed approximation ratio of 2-Opt. We obtain a bound of O(log(1/σ)) for the smoo...

This article introduces two swarm intelligent algorithms, a group search optimizer (GSO) and an artificial fish swarm algorithm (AFSA). A single intelligent algorithm always has both merits in its specific formulation and deficiencies due to its inherent limitations. Therefore, we propose a mixture of these algorithms to create a new hybrid optimization algorithm known as the group search-artif...

The (1,2)-TSP is a special case of the TSP where each edge has cost either 1 or 2. In this paper we give lower bound 32 for approximation ratio 2-Opt algorithm (1,2)-TSP. Moreover, show that 3-Opt an exact 118 Furthermore, introduce 3-Opt++-algorithm, improved version (1-2)-TSP with 43.

We study fixed parameter algorithms for three problems: Kemeny rank aggregation, feedback arc set tournament, and betweenness tournament. For Kemeny rank aggregation we give an algorithm with runtime O(2 √ ), where n is the number of candidates, OPT ≤ ( n 2 ) is the cost of the optimal ranking, and O(·) hides polynomial factors. This is a dramatic improvement on the previously best known runtim...

In this article, a specific production scheduling problem (PSP), the Parallel Machine Scheduling Problem (PMSP) with Job and Sequence Setup Times, Due Dates Maintenance Times is presented. article after introduction literature review mathematical model of Machines After that Monte Carlo Tree Search Simulated Annealing are detailed. Our representation technique its evaluation also introduced. th...

We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to signiicantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, glob...

The vehicle-routing problem (VRP) has many variants, including the most accurate models of real-life transportation tasks, making it one important mathematical problems in field logistics. Our goal was to design an algorithm that can race against recent solutions for VRP and capacitated (CVRP), while also being applicable with simulations real transports. is a variant bacterial memetic (BMA), w...

We develop a novel method to improve biogeography-based optimization (BBO) for solving the traveling salesman problem (TSP). The improved is comprised of greedy randomized adaptive search procedure, 2-opt algorithm, and G2BBO. G2BBO formulation derived process flowchart shown in this article. For TSP, effectively avoids local minimum accelerates convergence by optimizing initial values. To demo...

We developed a two-stage approach (ACOLS) combining the ant colony optimization (ACO) algorithm and a 1-opt local search to solve forest transportation planning problems (FTPPs) considering fixed and variables costs and sediment yields expected to erode from road surfaces as side constraints. The ACOLS was designed for improving ACO performance and ensure the applicability to real-world, large-...