Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari

Lookahead policy and genetic algorithm for solving nurse rostering problems

Previous research has shown that value function approximation in dynamic programming does not perform too well when tackling difficult combinatorial optimisation problem such as multi-stage nurse rostering. This is because the large action space that need to be explored. This paper proposes to replace the value function approximation by a genetic algorithm in order to generate solutions to the stages before applying the lookahead policy to evaluate the future effect of decisions made in previous stages. Then, the paper proposes a hybrid approach that generates sets of weekly rosters through a genetic algorithm for consideration by the lookahead procedure that assembles a solution for the whole planning horizon of several weeks. Results indicate that this hybrid between an evolutionary algorithm and the lookahead policy mechanism from dynamic programming performs more competitive than the value function approximation dynamic programming investigated before. Results also show that the proposed algorithm is ranked well in respect of several other algorithms applied to the same set of problem instances. The intended contribution of this paper is towards a better understanding of how to successfully apply dynamic programming mechanisms to tackle difficult combinatorial optimisation problems

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

A time predefined variable depth search for nurse rostering

This paper presents a variable depth search for the nurse rostering problem. The algorithm works by chaining together single neighbourhood swaps into more effective compound moves. It achieves this by using heuristics to decide whether to continue extending a chain and which candidates to examine as the next potential link in the chain. Because end users vary in how long they are willing to wait for solutions, a particular goal of this research was to create an algorithm that accepts a user specified computational time limit and uses it effectively. When compared against previously published approaches the results show that the algorithm is very competitive

Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances

A path relinking approach for the generalized assignment problem

The generalized assignment problem is a classical combinatorial optimization problem known to be NP-hard. It can model a variety of real world applications in location, allocation, machine assignment, and supply chains. Researchers have studied the problem since the late 1960s, and computer codes for practical applications emerged in the early 1970s. We propose a new algorithm for this problem which proves to be more effective than previously existing methods. The algorithm features a path relinking approach, which is a mechanism for generating new solutions by combining two or more reference solutions. Computational comparisons on benchmark instances show that the method is not only effective in general, but is especially effective for the types D and E instances of the generalized assignment problem, which are known to be quite difficult