--- title: bnb_certified: Exact 0/1 Knapsack Optimization | SpinForge url: https://spin-forge.com/forge15/bnb-certified description: Exact 0/1 knapsack optimization with a checked optimality conclusion when the supported proof completes. --- FORGE15 / 07 / LOGIC & OPTIMIZATION [The full offering](https://spin-forge.com/platform) # bnb_certified. Exact 0/1 knapsack optimization with a checked optimality conclusion when the supported proof completes. [Discuss bnb_certified](https://spin-forge.com/contact?product=forge15%2Fbnb-certified) Customer outcome [Build better plans and decisions](https://spin-forge.com/platform/checked-decisions) Available now CLI MCP Headless Choose your access mode THE PRODUCT, IN PRACTICE ## Choose the items that fit. Know when no better selection remains. A 0/1 knapsack task chooses which items to include under a capacity limit while maximizing their stated value. A feasible selection answers what fits; a completed optimum answers whether a better allowed selection exists. bnb_certified provides that exact problem scope, including the evidence supporting a closed gap when the computation completes. BUILT FOR Optimization developers embedding exact 0/1 knapsack decisions into a larger workflow. CHALLENGES PRODUCT RESPONSE ## The problem you face. What bnb_certified changes. 01 ### A feasible selection may leave value unused Meeting the capacity limit does not establish that the chosen items provide the best modeled value. bnb_certified searches the supported knapsack model for a high-value feasible selection and an applicable optimum conclusion. 02 ### The team needs a stopping criterion with meaning “The search stopped improving” and “the optimum is proved” are not equivalent. For completed supported cases, the tool supplies the checked bound/result evidence establishing that the gap is closed. 03 ### A small exact task is part of a larger system The customer may need one reliable decision component rather than a whole enterprise solver suite. The product can be scoped around the specific weights, values and capacity model being embedded. WHAT YOU GET ## A defined capability. A useful output. The product scope below describes the capability and outputs to confirm for your release. Custom integration, operated delivery and additional engineering are separately agreed. 01 ### A selected item set The binary inclusion decision for the supported knapsack instance. 02 ### A checked capacity result Feasibility of the selection under the original capacity restriction. 03 ### An objective value The modeled value achieved by the returned selection. 04 ### Completion evidence The applicable bound and optimality record when the exact proof completes. AVAILABLE NOW ## One product. Three ways to work. bnb_certified is fully available with CLI, MCP and headless access. Use the interface that fits your terminal, your agents or your automated workflow. 01 / CLI ### For your terminal. Run the product from a terminal or script, alongside the tools your team already uses. [Get CLI access](https://spin-forge.com/contact?product=forge15%2Fbnb-certified&interface=cli&brief=I+would+like+bnb_certified+access+through+CLI.+Please+share+the+setup+documentation+and+configuration+for+the+selected+product.+We+will+confirm+the+environment%2C+license+scope+and+workflow+during+onboarding.) 02 / MCP ### For your agents. Connect MCP-compatible clients and agents to the product’s exposed capabilities. [Get MCP access](https://spin-forge.com/contact?product=forge15%2Fbnb-certified&interface=mcp&brief=I+would+like+bnb_certified+access+through+MCP.+Please+share+the+setup+documentation+and+configuration+for+the+selected+product.+We+will+confirm+the+environment%2C+license+scope+and+workflow+during+onboarding.) 03 / HEADLESS ### For your workflows. Operate without a graphical interface in unattended, scheduled or pipeline-driven work. [Set up headless access](https://spin-forge.com/contact?product=forge15%2Fbnb-certified&interface=headless&brief=I+would+like+bnb_certified+access+through+headless.+Please+share+the+setup+documentation+and+configuration+for+the+selected+product.+We+will+confirm+the+environment%2C+license+scope+and+workflow+during+onboarding.) Product-specific inputs, hardware requirements and result guarantees still apply. An access mode does not change your license or deployment scope. [Explore all product interfaces](https://spin-forge.com/developers?section=access-directory) EXAMPLE CUSTOMER WORKFLOW ## Choose a valuable subset under one capacity limit A software team embeds a supported item-selection subproblem into its planning workflow. Illustrative use of the supported scope, not a customer case study or a measured result. 1. 01 Provide the item weights, values and capacity. 2. 02 Run the exact knapsack task within the chosen limits. 3. 03 Review the selection and completion evidence before applying it. IN YOUR WORKFLOW ## Start with your task. Agree the useful outcome. Optimization developers embedding exact 0/1 knapsack decisions into a larger workflow. What you bring Item weights and values, the capacity limit, execution budget and exact-completion requirement. What a useful evaluation measures - Capacity feasibility and objective agreement - A checked zero gap when completion is claimed - Runtime and memory at the required instance sizes Where it fits Use the selected product in a qualified customer environment, or agree a defined implementation with SpinForge. A hosted or managed service is quoted for its actual operating responsibilities; it is not automatically included with software access. QUESTIONS BEFORE YOU BUY ## A clear scope. No hidden assumptions. **How can we use bnb_certified?**CLI, MCP and headless access are all available. Run from a terminal or script, connect an MCP-compatible client, or use the product without a graphical interface. Choose the mode during onboarding and receive its setup instructions. Runtime requirements and supported operations remain product-specific. **What is the important product boundary? **This is the documented 0/1 knapsack scope, not a universal MIP solver. An interrupted or incomplete run must not be described as a proved optimum. The reported brute-force agreement covers six tested sizes. **What comes with the selected license? **The agreed bnb_certified release, its supported interfaces and outputs, the applicable checks and the support stated in your order. The plan defines users, workflow, environment and capacity. Source-code transfer, unrestricted redistribution and bespoke engineering are not automatically included. **Can SpinForge implement or operate it for us? **Request a scoped engineering or operated-service proposal. It identifies what our team delivers, where the workload runs, infrastructure costs, acceptance requirements and ongoing support. Your software subscription alone does not activate a hosted runtime. [Explore engineering](https://spin-forge.com/engineering) **What evidence is available for review? **P49 / Company-reported. The supplied results matched brute force at all six tested sizes and reported a closed zero gap for those supported knapsack cases. They do not establish general MIP performance. These descriptions come from the supplied product and campaign material. Website checks are not an independent rerun of the engine. Qualification identifies the actual release, workload and available artifacts. [Read the evidence summary](https://spin-forge.com/results) SOFTWARE / OPERATED DELIVERY By proposal Customer-hosted access and a service operated by SpinForge are different scopes. Confirm the release, deployment and included support before activation. [Plans & delivery](https://spin-forge.com/pricing) PUT BNB_CERTIFIED TO WORK ## Tell us what needs to improve. Bring a representative workload and the result your team needs. We’ll define the product, deployment and engineering scope around that task. [Discuss this workflow](https://spin-forge.com/contact?product=forge15%2Fbnb-certified&brief=Product%3A+bnb_certified%0AOur+challenge%3A+A+feasible+selection+may+leave+value+unused%0AWorkload+%2F+baseline%3A+%0AEnvironment%3A+%0ARequired+output%3A+%0AAcceptance+measures%3A+Capacity+feasibility+and+objective+agreement%3B+A+checked+zero+gap+when+completion+is+claimed%3B+Runtime+and+memory+at+the+required+instance+sizes%0ADelivery+preference+%28software+%2F+engineering+%2F+managed%29%3A+) **Related products, workflows and system connections + **RELATED CAPABILITIES ## Connect the right products. Distinct responsibilities. Explore each scope before choosing a combined deployment. [### MIP Mixed-integer optimization for supported decision models with explicit variables, constraints and objectives.](https://spin-forge.com/solvers/mip) [### GARMO UCS A native constraint-search engine for supported logical, integer and engineering decision models.](https://spin-forge.com/ucs) [### UNISOLVE A native solver library, headless command-line program and MCP server that accepts supported models, selects compatible engines and independently checks accepted answers.](https://spin-forge.com/unisolve) ONE PLATFORM / OR A DIRECT PURCHASE ## Checked Decisions with bnb_certified. Activate this capability inside a qualified checked decisions workflow. Compatible methods and required shared checking are included once within that workflow; the product remains independently purchasable. Capacity, release, environment, result contract and operating responsibilities are specified before activation. Choosing an additional method is not permission to add an unrelated workload or unqualified deployment. [Explore Checked Decisions](https://spin-forge.com/platform/checked-decisions) [Choose workflow capacity](https://spin-forge.com/plans?configuration=checked-decisions&product=forge15/bnb-certified) CONNECTED WORKFLOWS ## Use bnb_certified in your workflow. The product remains independently available. These customer-specific solution paths use the relevant supported capabilities, with integration and delivery rights agreed separately. [06 ### Embedded decision services Add a bounded optimization, configuration-checking or re-planning capability to the product your customers already use. Keep your user experience; integrate the computational capability behind it.](https://spin-forge.com/solutions/embedded-decisions) [Explore all 17 solution workflows](https://spin-forge.com/workflows) FROM PRODUCT TO CUSTOMER WORKFLOW ## A useful outcome. A defined delivery. Commission the model, integration and acceptance work needed for your task. Existing products stay independently available. [01 / Scoped customer program ### Explain & repair a constrained plan Commission one supported decision model, a scoped conflict analysis and a comparison of permitted repairs.](https://spin-forge.com/programs/plan-diagnosis) [02 / Scoped customer program ### Maintain a recurring decision Commission a revision-aware workflow that keeps models, assumptions, results and evidence connected as inputs change.](https://spin-forge.com/programs/living-decisions) [Explore decision programs](https://spin-forge.com/decision-systems) THE WHOLE-SYSTEM ROLE ## bnb_certified in a wider workflow. Choose a bounded subset of independent optional compute/profiling tasks under a budget. POTENTIAL SYSTEM CONTRIBUTION Dependency-rich scheduling requires a more appropriate model; not a general MIP replacement. [S1 · Joint workload & machine optimization](https://spin-forge.com/system-synergies/joint-configuration) [S2 · Decision-sensitive computation](https://spin-forge.com/system-synergies/decision-sensitive-compute) [See this product in the map](https://spin-forge.com/system-synergies/product-map?q=bnb_certified) [Define an integration evaluation](https://spin-forge.com/system-synergies/evaluation) The product is independently available through CLI, MCP and headless access. The joins above are integration candidates; compatibility, authority, data rights and end-to-end benefit must be established for the selected workflow. START WITH THIS PRODUCT Use the software directly or ask us to scope the implementation. [Software access](https://spin-forge.com/plans?product=forge15/bnb-certified) [Have us do the work](https://spin-forge.com/contact?product=forge15/bnb-certified&delivery=engineering)