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This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. In Part II, we consider the computational complexity of ORPs arising in genetic algorithms for problems on permutations: the Travelling Salesman Problem, the Shortest Hamilton Path Problem and the Makespan Minimization on Single Machine and some other related problems. The analysis indicates that the corresponding ORPs are NP-hard, but solvable by faster algorithms, compared to the problems they are derived from.

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results. Part I presents the basic principles of optimal recombination with a survey of results on Boolean Linear Programming Problems. Part II (to appear in a subsequent issue) is devoted to the ORPs for problems which are naturally formulated in terms of search for an optimal permutation.

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: 1. Optimal recombination problem is solved within crossover operator. 2. A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. 3. 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.

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0000−0003−2469−023X] and Yulia V. Kovalenko 2,3[0000−0003−4791−7011]Abstract. We consider the bicriteria asymmetric traveling salesman problem (bi-ATSP). Optimal solution to a multicriteria problem is usually supposed to be the Pareto set, which is rather wide in real-world problems. We apply to the bi-ATSP the axiomatic approach of the Pareto set reduction proposed by V. Noghin. We identify series of "quanta of information" that guarantee the reduction of the Pareto set for particular cases of the bi-ATSP. An approximation of the Pareto set to the bi-ATSP is constructed by a new multi-objective genetic algorithm. The experimental evaluation carried out in this paper shows the degree of reduction of the Pareto set approximation for various "quanta of information" and various structures of the bi-ATSP instances generated randomly.Keywords: Reduction of the Pareto set · Multi-objective genetic algorithm · Computational experiment 2 Problem Statement An instance of the traveling salesman problem [2] (TSP) is given by a complete graph G = (V, E), where V = {v 1 , . . . , v n } is the set of vertices and set E

A series of new 1,3‐oxazole derivatives, containing in position 5 both donor and acceptor substituents were synthesized. These substances were considered as potentially active anticancer pharmacophores in the human tumor cell line panel derived from nine cancer types, including lung, colon, melanoma, renal, ovarian, brain, leukemia, breast, and prostate. Primary in vitro one‐dose anticancer screening was shown that compounds with acceptor substituents (such as –C(O)OMe, –CN) in the position 5 inhibit the growth of most cell lines, and compounds with donor substituents (such as –NHR, −SR) in the position 5 do not practically inhibit the growth of cancer cell lines. It can be assumed that the pharmacological activity of 1,3‐oxazole derivatives depends on donor/acceptor nature of the substituents in position 5. It was proposed to evaluate the donor/acceptor ability of 1,3‐oxazole derivatives using the special parameter φ0, which takes into account the relative position of the boundary levels (HOMO end LUMO). The quantum‐chemical modeling was performed; the special parameter φ0 for 1,3‐oxazole derivatives correlates with the experimental results. Quantum‐chemical calculations of the special parameter φ0 allow modeling the pharmacological activity of 1,3‐oxazole derivatives by introducing donor or acceptor substituents at position 2 or 5. This work may be useful for chemists to develop a target synthesis of potential biologically active compounds.

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