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Aircraft Cargo Loading Optimization Case Study

A major operational planning problem in the air cargo industry is how to arrange cargo in an aircraft to fly

safely and profitably. MemComputing proposes an innovative solution to

solve this challenge efficiently

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.Aircraft Cargo Loading (ALO)

Air cargo volumes: +3% per year

The air freight sector is particularly wellpositioned today as a result of capacitydiscipline and consolidation in containershipping. According to McKinsey, air-freight volumes will neverthelesscontinue to increase, by an average ofabout 3% per year, at least until 2025and most likely until 2030.

Optimized cargo operationsDespite this very promising prospect,cargo fleets face some challenges. “Afaster growth in belly capacities andmodernized freighter fleets will subjectgeneral cargo to price pressures of up to3% a year” according to McKinsey. Thiswill counterbalance the higher transportvolumes leading to flat revenues.

Optimization of operations and inparticular Aircraft LoadingOptimization (ALO) will play a keyrole in supporting a sustainable growthfor the airlines.

Air Cargo Loading (ALO): a key challenge

A major operational planning problem in the aircargo industry is how to arrange cargo in an aircraftto fly safely and profitably. A challenging planningpuzzle has to be solved for each flight. ALOrequires optimizing the placement of containersof different sizes and weights in an aircraftsubject to limitations on the maximum weightallowed, the maximum tolerable shear and thecenter of gravity.

Different stakeholders have various objectives.Ground handling players want to minimize theireffort and insure an even workload. Aircraftoperations mostly target a minimization of fuelconsumption and of so called Unit Load Device(ULD) operations. On their side, Air cargo salesteams mostly aim at maximizing revenue and cargoloads on planes.

Overall, Airlines make the best use of an aircraft’spayload capability to maximise revenue, optimizefuel burn, lower overall operating costs.

It is the Load Master’s role to accurately plan theload (loadsheet), complying with all operational andsafety requirements. In the past this has beenaccomplished manually but more recent “drag anddrop” applications are used but remain of limiteduse in view of an increased complexity.

Improving Aircraft Loading Optimization A Mathematical &

Computing Challenge

Solutions to today’s computational limits areprovided by more and more sophisticated andhigh-performing CPUs, GPUs as well as bythe insurgence of distributed computing incloud infrastructures. Nevertheless, theunceasing growth in computing demand ispushing towards completely newarchitectures as well as new paradigms.

This can mean not only “handling morecomputation” but also making the computationmore efficient.

Complex optimization problems are oftenclassified as “NP-hard“ or “NP-Complete”.“NP” problems are problems which areunsolvable within a reasonable amount oftime for large input sizes.

NP-Hard problems refer to a class ofproblems that grow exponentially in complexitywith the addition of each new input variable.These problems are often combinatorial, wherethe combination of possible solutions orpermutations grows at an increasing ratefor each additional input.

Consider a simple problem with colors whereyou can have 100% of each color or you canmix them in equal amounts. If you start with asingle color, green, then the only color you canmake is green. If you add red, you can nowhave green, red and yellow (green + red). Ifyou add blue, you can now have green, red,blue, yellow (green + red), cyan (green + blue),magenta (red + blue) and white (green + red +blue). Keep going and you can see that thenumber of possible colors grows exponentiallyeach time you add just one more color.

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Solving Logistics and other Problems with MemComputing

The MemCPUTM Coprocessor technology takes a new approach to computation ofcomplex optimization problems, especially those that are combinatorial in nature. It iscompletely different from any method previously taken. This technology is an extreme turbo-booster for virtually any computer, from the slowest laptop to the fastest supercomputer. Thiscomputing increase isn’t simply ten or one hundred times faster, it is hundreds, thousands,tens of thousands or more times faster depending on the problem. In effect, the harder andmore complex the problem, the greater the boost in performance. MemCPU Coprocessorsare designed to handle massive and complex mathematical computations in a fraction of thetime using a fraction of the resources of today’s best in class solutions.

Today’s classical (non-quantum) computers are confined when it comes to solving aclass of problems categorized as NP-hard and NP-complete. These problems areidentified where the computational time and/or memory resources required explodeexponentially while the inputs and constraints simply grow sequentially.

The outstanding performance of our physics-based approach shows advancements inoptimization computations. In previous benchmarks MemComputing has shown empiricalevidence that a non-combinatorial approach using its MemCPU Coprocessor demonstratedthe availability of efficient solutions to NP-hard problems.

MemCPU Coprocessors are designed to integrate with current workflow. The softwaresupports integer linear programming problems (ILP), quadratic unconstrained binaryoptimization problems (QUBO), polynomial unconstrained binary optimization problems(PUBO), Maximum Satisfiability (Max-SAT) and some Satisfiability problems (SAT), withmore methodologies and capabilities being added. The software supports direct dataexchange as well as file-based data exchange with Mathematical Programming Systems(.mps) and Conjunctive Normal Form (.cnf).

Sketch of the Airbus Aircraft Loading Optimization problem.

The aircraft is to be loaded by selecting aportion of the available payload. Thecontainers can have different shapes.

For this ALO, 3 different shapes areconsidered numbered from 1 to 3 as inthe figure. The maximum weight allowedis limited.

The center of gravity xcg of the systemaircraft + containers must remain withinthe limit [xmin,xmax] and the shear curveS(x) must also be limited to remain undera give shear limit curve Smax(x).

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The Airbus Computing Challenge

In January 2019, Airbus launched a computingchallenge to solve a set of problems relevant forthe aircraft life cycle, expecting to investigatenontraditional solutions for logistics optimizationproblems.

The Airbus Quantum Computing Challenge (AQCC) addresses aerospace flight physicsproblems developed by company experts. It puts forward five distinct flight physics problemswith varying degrees of complexity, ranging from a simple mathematical question to a globalflight physics problem and it aims to investigate how newly-available computing capabilitiescan solve the 5 following real-life industrial challenges met by the aerospace industry today• Aircraft Climb Optimization,• Computational Fluid Dynamics,• Quantum Neural Networks for Solving Partial Differential Equations,• Wingbox Design Optimization,• Aircraft Loading Optimization.

Airlines try to make the best use of an aircraft’s payload capability to maximise revenue,optimize fuel burn and lower overall operating costs. Their scope for optimization is limited bythe aircraft’s operational envelope, which is determined by each mission’s maximum payloadcapacity, the aircraft’s center of gravity and its fuselage shear limits.

The objective of this challenge is to calculate the optimal aircraft configuration under coupledoperational constraints, thus demonstrating how quantum computing can be used for practicalproblem solving and how it can scale towards more complex issues.

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MemComputing’s approach to Aircraft Loading Optimization

A successful solution

• The MemComputing technology candramatically reduce the computingtime needed for processing today’smost complex logistics problems.

• MemCPU Coprocessors are a viablesolution to at least some NP-Hardproblems.

MemComputing employed the software-basedMemCPU Coprocessor to tackle the 5th Airbusproblem efficiently without a quantum computer.

In order to use the MemCPU Coprocessor for the5th Airbus problem, a standard Integer Programming(IP) problem has been formulated that includes allconstraints required by Airbus with no exceptionand no approximation.

The scaling properties assessed during the projectshowed sub-quadratic scaling as a function of thesize of the problem measured by the number ofnonzero elements of the constraint matrix of theassociated IP problem. The scaling properties of theMemCPU Coprocessor allow efficient solutions oflarge ALO problems and…

IT REPRESENTS A SOLUTION READY TO BE DEPLOYED IN THE FIELD TODAY!

Bottom line

MemComputing can solve problemsthat are currently consideredunsolvable because the time requiredcould be years, decades or even eonsfor current best in class solutions usingclassical methods!

MemCPU CoprocessorAn entirely new paradigm

• Computation & Memory Combined in the same circuit with a brand new/patented computer architecture

• Uses classical low power, low heat transistor technology

• Emulated in software, it runs on classical architecture

Transportation, Logistics

MemComputing is working withcompanies on transportationlogistics problems in airline,rail, trucking, busing andshipping.

MemComputing helps solvetraffic problems by optimizingthe routing for taxis in ourlargest cities and by managingtraffic signal assets for smartcities.

One example within theautonomous vehicle market isthat MemComputing cananalyze a larger set of inputsfrom radar data in order tosignificantly improve theresolution and accuracy.

Offloading more and more ofthe computations forautonomous vehicle, such asmotion control and collisionavoidance, to MemComputingalso reduces the amount ofcomputer hardware requiredthus freeing up cargo space

Logistics Beyond Air FreightLogistics casts a net over far more than air cargofreight. The importance of modernizing logistics with digitalautomation will impact all facets of management and controlof the transportation, mobility and warehousing/storage ofgoods for satisfying consumer demands. It’s fundamental tothe supply chain.

As e-commerce continues to explode, and the volume ofgoods being transported worldwide is booming, businessand consumer expectations for faster order delivery willcontinue to place pressure on the entire transportationlogistics and supply chain network. In turn this is puttingstrains on capacity, infrastructure and the workforce. It’smaking logistics problems seem impossible to solve inreasonable amounts of time. The digitalization of multi-modes of transportation as well as extended services totrack the real-time movement of goods into and out ofbusiness is an integral factor in the success of any industrialcompany.

The MemComputing technologysolutions will not replace DataScientists. Companies will stillrequire their scientists to develop themodels for the problems that theywish to solve. We believe that earlyadopter data scientists that takeadvantage of the MemComputingtechnology and integrate aMemCPU Coprocessor into theirsolutions will bring tremendousvalue to their organizations.

ABOUT MEMCOMPUTING, INC.

MemComputing, Inc.’s disruptive coprocessor technology isaccelerating the time to find feasible solutions to the mostchallenging operations research problems in all industries. Usingphysics principles, this novel software architecture is based onthe logic and reasoning functions of the human brain.

MemComputing enables companies to analyze huge amounts ofdata and make informed decisions quickly, bringing efficienciesto areas of operations research such as Big Data analytics,scheduling of resources, routing of vehicles, network and cellulartraffic, genetic assembly and sequencing, portfolio optimization,drug discovery and oil and gas exploration.

MemComputing Inc. has developed disruptive technologies thatare changing the face of computing through a SaaS solution thatimproves the performance of today’s most complex and timeconsuming optimization calculations by 4 orders of magnitude orgreater.

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The company was formed byMemComputing’s inventors,PhD Physicists MassimilianoDi Ventra & Fabio Traversaalong with serialentrepreneur, John Beane.

4250 Executive Square, Suite 200La Jolla, CA 92037

http://memcpu.cominfo@memcomputing.com