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Papers by Pouya Baniasadi

Research paper thumbnail of 2 Genetic theory for cubic graphs

Research paper thumbnail of A new benchmark set for Traveling salesman problem and Hamiltonian cycle problem

ArXiv, 2018

We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are dif... more We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are different from the existing benchmark sets. In particular, we focus on small instances which prove to be challenging for one or more state-of-the-art TSP algorithms. These instances are based on difficult instances of Hamiltonian cycle problem (HCP). This includes instances from literature, specially modified randomly generated instances, and instances arising from the conversion of other difficult problems to HCP. We demonstrate that such benchmark instances are helpful in understanding the weaknesses and strengths of algorithms. In particular, we conduct a benchmarking exercise for this new benchmark set totalling over five years of CPU time, comparing the TSP algorithms Concorde, Chained Lin-Kernighan, and LKH. We also include the HCP heuristic SLH in the benchmarking exercise. A discussion about the benefits of specifically considering outlying instances, and in particular instances whi...

Research paper thumbnail of A Transformation Technique for the Clustered Generalized Traveling Salesman Problem with Applications to Logistics

European Journal of Operational Research, 2020

Abstract The clustered generalized traveling salesman problem (CGTSP) is an extension of the clas... more Abstract The clustered generalized traveling salesman problem (CGTSP) is an extension of the classical traveling salesman problem (TSP), where the set of nodes is divided into clusters of nodes, and the clusters are further divided into subclusters of nodes. The objective is to find the minimal route that visits exactly one node from each subcluster in such a way that all subclusters of each cluster are visited consecutively. Due to the additional flexibility of the CGTSP compared to the classical TSP, CGTSP can incorporate a wider range of complexities arising from some practical applications. However, the absence of a good solution method for CGTSP is currently a major impediment in the use of the framework for modeling. Accordingly, the main objective of this paper is to enable the powerful framework of CGTSP for applied problems. To attain this goal, we first develop a solution method by an efficient transformation from CGTSP to TSP. We then demonstrate that not only the solution method provides far superior solution quality compared to existing methods for solving CGTSP, but also it enables practical solutions to far larger CGTSP instances. Finally, to illustrate that the modeling framework and the solution method apply to some practical problems of realistic sizes, we conduct a computational experiment by considering the application of CGTSP to two modern logistics problems; namely, automated storage and retrieval systems (logistics inside the warehouse) and drone-assisted parcel delivery service (logistics outside the warehouse).

Research paper thumbnail of Inherited Properties of Descendants

SpringerBriefs in Operations Research, 2016

Given the results of Chap. 1 that every descendant may be constructed from a complete family of a... more Given the results of Chap. 1 that every descendant may be constructed from a complete family of ancestor genes, we now investigate how the properties of the descendant correspond to the properties of those genes. In particular we consider the properties of Hamiltonicity, bipartiteness and planarity. In all three cases we prove that a descendant may only possess the property if all of its ancestor genes do. In the case of bipartiteness and planarity we also establish sufficient conditions. These results allow us to analyse the properties of a graph by considering its ancestor genes, or alternatively, to construct a graph with desired properties by choosing smaller genes with those properties. We follow each section with a discussion of famous results and conjectures relating to the graph properties, and how the results of this chapter relate to them.

Research paper thumbnail of Uniqueness of Ancestor Genes

Genetic Theory for Cubic Graphs, 2016

In Chap. 1 we stated the result that every graph has a unique complete family of ancestor genes. ... more In Chap. 1 we stated the result that every graph has a unique complete family of ancestor genes. The result is proved in detail in this chapter. The proof is lengthy and is therefore broken up into several intermediate steps. We first show that it is sufficient to prove the result for graphs with no parthenogenic objects. We then consider all possible methods of decomposing a graph into three components via the inverse operations and show that the components so obtained are always the same regardless of the inverse operations used. Next we prove that any complete family of ancestor genes for a graph has cardinality which is a fixed constant for that graph. We then proceed to prove that for any descendant without parthenogenic objects, it is possible to isolate at least two genes with single inverse breeding operations. Finally, we use each of these results to prove the uniqueness theorem.

Research paper thumbnail of Genetic Theory for Cubic Graphs

SpringerBriefs in Operations Research, 2016

We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subs... more We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between the two subsets is the presence of special edge cut sets, called crackers, in the descendants. We show that every descendant can be created by starting from a finite set of genes, and introducing the required crackers by special breeding operations. We prove that it is always possible to identify genes that can be used to generate any given descendant, and provide inverse operations that enable their reconstruction. A number of interesting properties of genes may be inherited by the descendant, and we therefore propose a natural algorithm that decomposes a descendant into its ancestor genes. We conjecture that each descendant can only be generated by starting with a unique set of ancestor genes. The latter is supported by numerical experiments.

Research paper thumbnail of Deterministic “Snakes and Ladders” Heuristic for the Hamiltonian cycle problem

Mathematical Programming Computation, 2013

We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian Cycle Pr... more We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian Cycle Problem (HCP) in an undirected graph of order n. Although finding a Hamiltonian cycle is not theoretically guaranteed, we have observed that the heuristic is successful even in cases where such cycles are extremely rare, and it also performs very well on all HCP instances of large graphs listed on the TSPLIB web page. The heuristic owes its name to a visualisation of its iterations. All vertices of the graph are placed on a given circle in some order. The graph's edges are classified as either snakes or ladders, with snakes forming arcs of the circle and ladders forming its chords. The heuristic strives to place exactly n snakes on the circle, thereby forming a Hamiltonian cycle. The Snakes and Ladders Heuristic (SLH) uses transformations inspired by k−opt algorithms such as the, now classical, Lin-Kernighan heuristic to reorder the vertices on the circle in order to transform some ladders into snakes and vice versa. The use of a suitable stopping criterion ensures the heuristic terminates in polynomial time if no improvement is made in n 3 major iterations.

Research paper thumbnail of 2 Genetic theory for cubic graphs

Research paper thumbnail of A new benchmark set for Traveling salesman problem and Hamiltonian cycle problem

ArXiv, 2018

We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are dif... more We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are different from the existing benchmark sets. In particular, we focus on small instances which prove to be challenging for one or more state-of-the-art TSP algorithms. These instances are based on difficult instances of Hamiltonian cycle problem (HCP). This includes instances from literature, specially modified randomly generated instances, and instances arising from the conversion of other difficult problems to HCP. We demonstrate that such benchmark instances are helpful in understanding the weaknesses and strengths of algorithms. In particular, we conduct a benchmarking exercise for this new benchmark set totalling over five years of CPU time, comparing the TSP algorithms Concorde, Chained Lin-Kernighan, and LKH. We also include the HCP heuristic SLH in the benchmarking exercise. A discussion about the benefits of specifically considering outlying instances, and in particular instances whi...

Research paper thumbnail of A Transformation Technique for the Clustered Generalized Traveling Salesman Problem with Applications to Logistics

European Journal of Operational Research, 2020

Abstract The clustered generalized traveling salesman problem (CGTSP) is an extension of the clas... more Abstract The clustered generalized traveling salesman problem (CGTSP) is an extension of the classical traveling salesman problem (TSP), where the set of nodes is divided into clusters of nodes, and the clusters are further divided into subclusters of nodes. The objective is to find the minimal route that visits exactly one node from each subcluster in such a way that all subclusters of each cluster are visited consecutively. Due to the additional flexibility of the CGTSP compared to the classical TSP, CGTSP can incorporate a wider range of complexities arising from some practical applications. However, the absence of a good solution method for CGTSP is currently a major impediment in the use of the framework for modeling. Accordingly, the main objective of this paper is to enable the powerful framework of CGTSP for applied problems. To attain this goal, we first develop a solution method by an efficient transformation from CGTSP to TSP. We then demonstrate that not only the solution method provides far superior solution quality compared to existing methods for solving CGTSP, but also it enables practical solutions to far larger CGTSP instances. Finally, to illustrate that the modeling framework and the solution method apply to some practical problems of realistic sizes, we conduct a computational experiment by considering the application of CGTSP to two modern logistics problems; namely, automated storage and retrieval systems (logistics inside the warehouse) and drone-assisted parcel delivery service (logistics outside the warehouse).

Research paper thumbnail of Inherited Properties of Descendants

SpringerBriefs in Operations Research, 2016

Given the results of Chap. 1 that every descendant may be constructed from a complete family of a... more Given the results of Chap. 1 that every descendant may be constructed from a complete family of ancestor genes, we now investigate how the properties of the descendant correspond to the properties of those genes. In particular we consider the properties of Hamiltonicity, bipartiteness and planarity. In all three cases we prove that a descendant may only possess the property if all of its ancestor genes do. In the case of bipartiteness and planarity we also establish sufficient conditions. These results allow us to analyse the properties of a graph by considering its ancestor genes, or alternatively, to construct a graph with desired properties by choosing smaller genes with those properties. We follow each section with a discussion of famous results and conjectures relating to the graph properties, and how the results of this chapter relate to them.

Research paper thumbnail of Uniqueness of Ancestor Genes

Genetic Theory for Cubic Graphs, 2016

In Chap. 1 we stated the result that every graph has a unique complete family of ancestor genes. ... more In Chap. 1 we stated the result that every graph has a unique complete family of ancestor genes. The result is proved in detail in this chapter. The proof is lengthy and is therefore broken up into several intermediate steps. We first show that it is sufficient to prove the result for graphs with no parthenogenic objects. We then consider all possible methods of decomposing a graph into three components via the inverse operations and show that the components so obtained are always the same regardless of the inverse operations used. Next we prove that any complete family of ancestor genes for a graph has cardinality which is a fixed constant for that graph. We then proceed to prove that for any descendant without parthenogenic objects, it is possible to isolate at least two genes with single inverse breeding operations. Finally, we use each of these results to prove the uniqueness theorem.

Research paper thumbnail of Genetic Theory for Cubic Graphs

SpringerBriefs in Operations Research, 2016

We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subs... more We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between the two subsets is the presence of special edge cut sets, called crackers, in the descendants. We show that every descendant can be created by starting from a finite set of genes, and introducing the required crackers by special breeding operations. We prove that it is always possible to identify genes that can be used to generate any given descendant, and provide inverse operations that enable their reconstruction. A number of interesting properties of genes may be inherited by the descendant, and we therefore propose a natural algorithm that decomposes a descendant into its ancestor genes. We conjecture that each descendant can only be generated by starting with a unique set of ancestor genes. The latter is supported by numerical experiments.

Research paper thumbnail of Deterministic “Snakes and Ladders” Heuristic for the Hamiltonian cycle problem

Mathematical Programming Computation, 2013

We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian Cycle Pr... more We present a polynomial complexity, deterministic, heuristic for solving the Hamiltonian Cycle Problem (HCP) in an undirected graph of order n. Although finding a Hamiltonian cycle is not theoretically guaranteed, we have observed that the heuristic is successful even in cases where such cycles are extremely rare, and it also performs very well on all HCP instances of large graphs listed on the TSPLIB web page. The heuristic owes its name to a visualisation of its iterations. All vertices of the graph are placed on a given circle in some order. The graph's edges are classified as either snakes or ladders, with snakes forming arcs of the circle and ladders forming its chords. The heuristic strives to place exactly n snakes on the circle, thereby forming a Hamiltonian cycle. The Snakes and Ladders Heuristic (SLH) uses transformations inspired by k−opt algorithms such as the, now classical, Lin-Kernighan heuristic to reorder the vertices on the circle in order to transform some ladders into snakes and vice versa. The use of a suitable stopping criterion ensures the heuristic terminates in polynomial time if no improvement is made in n 3 major iterations.