Homicide and corpse dismemberment: A study of one case

Homicide may be an isolated impulsive act arising from a situation or based on a previous conception, which is premeditation. Despite its nature or motivations, homicide remains a wrongful criminal act at all times and in all places. Several studies conducted in Western countries on this topic have highlighted the overriding concern of the criminal, which includes concealing the criminal offence in most cases.In Africa, apart from cases of infanticide, the discovery of the body of a homicide victim in a public place is a relatively common phenomenon, particularly if it involves mutilation.The body was examined; it was a young adult African female whose corpse was wrapped in a plastic bag. The autopsy established that the section or cutting planes were preferably lodged in the large joints.Death was caused by mechanical asphyxia. The focus of this case lies in the atypical nature of this type of postmortem manipulation in the West African context.The unusual nature of this type of homicide illustrates and underscores some reality in our development context.

Improving Column Generation for Vehicle Routing Problems via Random Coloring and Parallelization

We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation-based linear-programming relaxation for this VRP. Specifically, we focus on algorithms for the “pricing problem,” which corresponds to the resource-constrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2% optimality gaps for most VRP benchmark instances and less than 1% optimality gaps for the medical home care delivery instances, both under a 30-minute computational time limit. The use of cutting planes (e.g., robust cuts) can further reduce optimality gaps on some hard instances, without much increase in the run time. Summary of Contribution: The vehicle routing problem (VRP) is a fundamental combinatorial problem, and its variants have been studied extensively in the literature of operations research and computer science. In this paper, we consider general-purpose algorithms for solving VRPs, including the column-generation approach for the linear programming relaxations of the integer programs of VRPs and the column-enumeration approach for seeking improved integer solutions. We revise the pulse algorithm and also propose a random-coloring algorithm that can be used for solving the elementary shortest path problem that formulates the pricing problem in the column-generation approach. We show that the parallel implementation of both algorithms can significantly improve the performance of column generation and the random coloring algorithm can improve the solution time and quality of the VRP integer solutions produced by the column-enumeration approach. We focus on algorithmic design for VRPs and conduct extensive computational tests to demonstrate the performance of various approaches.

Exact Branch-Price-and-Cut for a Hospital Therapist Scheduling Problem with Flexible Service Locations and Time-Dependent Location Capacity

We study a new variant of the vehicle routing problem, which arises in hospital-wide scheduling of physical therapists. Multiple service locations exist for patients, and resource synchronization for the location capacities is required as only a limited number of patients can be treated at one location at a time. Additionally, operations synchronization between treatments is required as precedence relations exist. We develop an innovative exact branch-price-and-cut algorithm including two approaches targeting the synchronization constraints (1) based on branching on time windows and (2) based on adding combinatorial Benders cuts. We optimally solve realistic hospital instances with up to 120 treatments and find that branching on time windows performs better than adding cutting planes. Summary of Contribution: We present an exact branch-price-and-cut (BPC) algorithm for the therapist scheduling and routing problem (ThSRP), a daily planning problem arising at almost every hospital. The difficulty of this problem stems from its inherent structure that features routing and scheduling while considering multiple possible service locations with time-dependent location capacities. We model the ThSRP as a vehicle routing problem with time windows and flexible delivery locations and synchronization constraints, which are properties relevant to other vehicle routing problem variants as well. In our computational study, we show that the proposed exact BPC algorithm is capable of solving realistic hospital instances and can, thus, be used by hospital planners to derive better schedules with less manual work. Moreover, we show that time window branching can be a valid alternative to cutting planes when addressing synchronization constraints in a BPC algorithm.

SDP-Based Bounds for the Quadratic Cycle Cover Problem via Cutting-Plane Augmented Lagrangian Methods and Reinforcement Learning

We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra’s projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra’s projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations.

Multiobjective Optimization Using Modified Binary PSO for Reduction of Sidelobe Level of the Thinned Array Antenna

To design an efficient communication system, controlling the energy present in the side lobes of the far-field pattern is essential with a considered antenna array. This paper discussed one method for synthesizing a thin antenna array for optimizing three objectives simultaneously. They are several active elements, peak SLL and FNBW. All these objectives are in contrast in nature. This multi-objective technique furnishes appreciable flexibility for any specified application. A planar array antenna of 20X10 and 10X10 is synthesized using modified BPSO and in the position updating equation, a modified sigmoid function is used, including spread distance. Numerical results state that MBPSO performs well, and the array antenna of 20X10 with 54% filled aperture (108 elements) produces maximum PSLL and FNBW of -19.28dB and 280 in the remaining ∅ plane, respectively. The pattern representation in the far-field at three cutting planes with low PSLL’s of -20dB.Whereas 10X10 planar array antenna with 52% thinning percentage produces the best PSLL of -22.04 dB and -23.44 dB in ∅=00 & 900principal planes, respectively. The FNBW has observed in two planes is around 310. And also achieved a compromised solution of PSLL and FNBW of -19.28 dB and 270, respectively.

Chvátal Rank in Binary Polynomial Optimization

Recently, several classes of cutting planes have been introduced for binary polynomial optimization. In this paper, we present the first results connecting the combinatorial structure of these inequalities with their Chvátal rank. We determine the Chvátal rank of all known cutting planes and show that almost all of them have Chvátal rank 1. We observe that these inequalities have an associated hypergraph that is β-acyclic. Our second goal is to derive deeper cutting planes; to do so, we consider hypergraphs that admit β-cycles. We introduce a novel class of valid inequalities arising from odd β-cycles, that generally have Chvátal rank 2. These inequalities allow us to obtain the first characterization of the multilinear polytope for hypergraphs that contain β-cycles. Namely, we show that the multilinear polytope for cycle hypergraphs is given by the standard linearization inequalities, flower inequalities, and odd β-cycle inequalities. We also prove that odd β-cycle inequalities can be separated in linear time when the hypergraph is a cycle hypergraph. This shows that instances represented by cycle hypergraphs can be solved in polynomial time. Last, to test the strength of odd β-cycle inequalities, we perform numerical experiments that imply that they close a significant percentage of the integrality gap.

Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of branch and bound. In this work, we introduce a hierarchy of cutting planes that arise from a reinterpretation of symmetry-exploiting branching methods. There are too many inequalities in the hierarchy to be used efficiently in a direct manner. However, the lowest levels of this cutting-plane hierarchy can be implicitly exploited by enhancing the conflict graph of the integer programming instance and by generating inequalities such as clique cuts valid for the stable set relaxation of the instance. We provide computational evidence that the resulting symmetry-powered clique cuts can improve state-of-the-art symmetry-exploiting methods. The inequalities are then employed in a two-phase approach with high-throughput computations to solve heretofore unsolved symmetric integer programs arising from covering designs, establishing for the first time the covering radii of two binary-ternary codes.