Zbigniew R. Bogdanowicz

A new efficient algorithm for optimal assignment of smart weapons to targets

In the modern battlefields smart weapons inherently rely on the sensors. The benefit of assigning a given weapon to a target often depends on the pre-assigned sensor. In this paper we present an efficient algorithm to optimally assign sensors and weapons to targets. This algorithm is derived from the well-known auction algorithm, and it is named as Swt-opt. We prove that Swt-opt converges to an optimal solution.

Advanced Input Generating Algorithm for Effect-Based Weapon–Target Pairing Optimization

Effect-based weapon-target pairing assigns weapons to targets for the given desired effects on such targets. The most obvious and natural effects on targets are represented by the percentages of damage of these targets. In this paper, we focus on the generation of input for effect-based weapon-target pairing optimization. One way to generate such input is based on the Joint Munition Effectiveness Manual (JMEM). JMEM allows the evaluation of the weapons. It is a database that contains many tables, and each table contains many different data fields. Because of the sheer size of JMEM, the optimization of weapon-target pairing based on JMEM is currently focused mainly on one target at a time. In other words, the optimization of weapon-target pairing for many targets and weapons is not directly supported by JMEM, although all the necessary data is there. In this paper, we derive an input based on the given JMEM and desired effect(s), which should be useful in the follow-on effect-based weapon-target pairing optimization that is not limited to a single weapon or target. In particular, effect-based weapon-target pairing will rely on the scanning of the attack guidance table that we derive from JMEM to determine a preferred set of weapon combinations for engaging a given set of targets.

Quick Collateral Damage Estimation Based on Weapons Assigned to Targets

We present an innovative approach to quickly estimate collateral damage based on the given weapon-target assignment (WTA). That is, having the predetermined WTA, we estimate the collateral damage of friendly or neutral entities based on the lethality of engaging weapons and the geo-locations of all the entities in the theater. Specifically, we calculate the probability of killing/destroying k friendly (or neutral) assets for given k. The main motivation of this paper is twofold. First, quick collateral damage estimation (QCDE) can support commanders in the battlefields with a new quick decision-making capability. Second, our QCDE could support WTA capabilities with collateral damage consideration. Our computational results indicate that the error in estimating collateral damage is significantly less than 1% and that the execution times are of the order of milliseconds for k (k <;9) assets. Hence, the natural research challenge related to this paper would be the extension of our quick collateral damage estimation to k ≥ 9 that would execute in reasonable time and give a reasonable quality solution.

Arc-Disjoint and Edge-Disjoint Hamilton Cycles in Circulants with Two Jumps

In this paper we give new necessary and sufficient conditions for a directed circulant with vertices of outdegree two to have a pair of arc-disjoint Hamilton cycles. These conditions explicitly identify a pair of arc-disjoint Hamilton cycles if such cycles exist. In addition, we give necessary and sufficient conditions for an undirected circulant with vertices of degree four to have a specific pair of edge-disjoint Hamilton cycles.

Decomposition of circulant digraphs with two jumps into cycles of equal lengths

Let G = G n ( a 1 , a 2 ) be a connected circulant digraph of order n with two distinct jumps a 1 , a 2 < n . We give several sufficient conditions for a decomposition of G n ( a 1 , a 2 ) into directed cycles of equal lengths. We then prove that G n ( a 1 , a 2 ) contains a 2-factor consisting of all cycles of equal lengths and comprised of both jumps if and only if g c d ( n , s 1 a 1 + s 2 a 2 ) = k ( s 1 + s 2 ) and a 1 ? a 2 ( mod s 1 + s 2 ) for some positive integers k , s 1 , s 2 . Based on this last result we prove that G n ( a 1 , a 2 ) can be decomposed into two 2-factors with all cycles comprising both jumps if and only if g c d ( n , s 1 a 1 + s 2 a 2 ) = g c d ( n , s 1 a 2 + s 2 a 1 ) = k ( s 1 + s 2 ) and a 1 ? a 2 ( mod s 1 + s 2 ) for some positive integers k , s 1 , s 2 . Furthermore, we prove that if such a decomposition exists then all resulting cycles are of equal lengths.

On isomorphism between circulant and Cartesian product of 2 cycles

In this paper we give the necessary and sufficient conditions for a circulant with two jumps to be isomorphic to a Cartesian product of two cycles.

On arc reversal in balanced digraphs

In this note we consider closed walks, which are cycles that are not necessarily elementary. We prove that any arc reversal in a balanced multidigraph without loops decreases the number of closed walks. This also proves that arc reversal in a simple balanced digraph decreases the number of closed walks.

Isomorphism between circulants and Cartesian products of cycles

Abstract We give the necessary and sufficient conditions for isomorphism between circulants and Cartesian products of cycles. Based on this result, we prove that the problem of determining if a circulant is isomorphic to a Cartesian product of cycles belongs to P problems.

Effect-based weapon-target assignment with minimised collateral damage

We present an advanced algorithm that assigns weapons to targets in such a way that the desired given effects are satisfied with minimal overkill (i.e., minimal excess beyond the desired effects) and minimal collateral damage. The most obvious and natural effects on targets are represented by kill probabilities or percentages of damage these targets. Hence, our algorithm optimises weapon-target assignments with respect to the given desired effects by minimising overkill and minimising collateral damage. Our computation results included in this paper suggest that the benefit gain of decreased collateral damage obtained by our algorithm decisively overcompensates the loss/sacrificed benefit of optimised assignment related to overkill.

On decomposition of the Cartesian product of directed cycles into cycles of equal lengths

Abstract We prove that every Cartesian product of directed cycles whose lengths have a common factor f ≥ 2 , can be decomposed into directed cycles of equal lengths and of the same form. For a Cartesian product of 2 directed cycles we prove that the above condition is also necessary. In addition, based on our results we give a conjecture for the necessary and sufficient condition for decomposition of any Cartesian product of directed cycles into directed cycles of equal lengths.