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"Teori graf adalah sebuah bidang studi interdisipliner yang memiliki berbagai aplikasi dalam pemodelan matematika dan ilmu komputer. Penelitian dalam teori graf tidak hanya bergantung pada teorema baru, namun juga pada konjektura baru. Algoritma penyanggah konjektura dapat digunakan untuk menyanggah suatu konjektura dengan cara mencari sebuah counterexample, seringnya dengan cara memaksimumkan suatu fungsi skor pada graf. Penelitian ini mengusulkan sebuah algoritma penyanggah konjektura baru, disebut sebagai algoritma adaptive Monte Carlo search (AMCS), yang diperoleh dari hasil modifikasi algoritma Monte Carlo tree search. Setelah dievaluasikan berdasarkan keberhasilannya dalam menemukan counterexample untuk beberapa konjektura teori graf, ditemukan bahwa AMCS mengungguli algoritma-algoritma penyanggah konjektura yang sudah ada. Algoritma tersebut kemudian digunakan untuk menyanggah enam konjektura terbuka, dua di antaranya merupakan konjektura teori graf kimia yang diformulasikan oleh Liu et al. pada 2021 dan empat di antaranya diformulasikan menggunakan sistem komputer AutoGraphiX pada 2006. Akhirnya, empat dari enam konjektura terbuka tersebut disanggah secara kuat dengan cara memperumum konjektura yang telah diperoleh menggunakan AMCS untuk menghasilkan keluarga graf yang mengandung banyak counterexample. Algoritma ini diharapkan dapat membantu para peneliti menguji konjektura-konjektura yang berkaitan dengan teori graf secara lebih efektif.......Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting algorithms attempt to refute conjectures by searching for counterexamples to those conjectures, often by maximizing certain score functions on graphs. This study proposes a novel conjecture-refuting algorithm, referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by modifying the Monte Carlo tree search algorithm. Evaluated based on its success in finding counterexamples to several graph theory conjectures, AMCS outperforms existing conjecture-refuting algorithms. The algorithm is further utilized to refute six open conjectures, two of which were chemical graph theory conjectures formulated by Liu et al. in 2021 and four of which were formulated by the AutoGraphiX computer system in 2006. Finally, four of the open conjectures are strongly refuted by generalizing the counterexamples obtained by AMCS to produce a family of counterexamples. It is expected that the algorithm can help researchers test graph-theoretic conjectures more effectively"

"ABSTRACTZone pricing is one of the most important pricing policies that are prevalently used by very companies. This paper considers integrating zone pricing and location-routing problems for profit maximization. Hence, a node-based model is proposed as mixed integer nonlinear programming to solve the problem. In order to handle the nonlinearity elements and change the model to a mixed integer linear programming, a piecewise linearization method is employed to approximate the problem. Moreover, we introduce a new heuristic variable neighborhood search (VNS) and tabu search algorithm for large-scale problems. The proposed algorithms consist of four intra-tour and seven inter-tour operators in its local search. Finally, some test instances with 20, 200, 400, and 600 nodes are solved and the results of them confirm the efficiency of the proposed algorithms and comparative superiority of the VNS algorithm over the tabu search algorithm."